Mathematical modeling of the COVID-19 pandemic with intervention strategies

Mathematical Contact Tracing Models for the COVID-19 Pandemic: A Systematic Review of the Literature

Background: Contact tracing (CT) is a primary means of controlling infectious diseases, such as coronavirus disease 2019 (COVID-19), especially in the early months of the pandemic. Objectives: This work is a systematic review of mathematical models used during the COVID-19 pandemic that explicitly parameterise CT as a potential mitigator of the effects of the pandemic. Methods: This review is registered in PROSPERO. A comprehensive literature search was conducted using the PubMed, EMBASE, Cochrane Library, CINAHL, and Scopus databases. Two reviewers independently selected the title/abstract, full text, data extraction, and risk of bias. Disagreements were resolved through discussion. The characteristics of the studies and mathematical models were collected from each study. Results: A total of 53 articles out of 2101 were included. The modelling of the COVID-19 pandemic was the main objective of 23 studies, while the remaining articles evaluated the forecast transmission of COVID-19. Most studies used compartmental models to simulate COVID-19 transmission (26, 49.1%), while others used agent-based (16, 34%), branching processes (5, 9.4%), or other mathematical models (6). Most studies applying compartmental models consider CT in a separate compartment. Quarantine and basic reproduction numbers were also considered in the models. The quality assessment scores ranged from 13 to 26 of 28. Conclusions: Despite the significant heterogeneity in the models and the assumptions on the relevant model parameters, this systematic review provides a comprehensive overview of the models proposed to evaluate the COVID-19 pandemic, including non-pharmaceutical public health interventions such as CT. Prospero Registration: CRD42022359060.

Detailed-level modelling of influence spreading on complex networks

The progress in high-performance computing makes it increasingly possible to build detailed models to investigate spreading processes on complex networks. However, current studies have been lacking detailed computational methods to describe spreading processes in large complex networks. To fill this gap we present a new modelling approach for analysing influence spreading via individual nodes and links on various network structures. The proposed influence-spreading model uses a probability matrix to capture the spreading probability from one node to another in the network. This approach enables analysing network characteristics in a number of applications and spreading processes using metrics that are consistent with the quantities used to model the network structures. In addition, this study combines sub-models and offers a comprehensive look at different applications and metrics previously discussed in cases of social networks, community detection, and epidemic spreading. Here, we also note that the centrality measures based on the probability matrix are used to identify the most significant nodes in the network. Furthermore, the model can be expanded to include additional properties, such as introducing individual breakthrough probabilities for the nodes and specific temporal distributions for the links.

Epidemiological modeling of COVID-19 data with Advanced statistical inference based on Type-II progressive censoring

This research proposes the Kavya-Manoharan Unit Exponentiated Half Logistic (KM-UEHL) distribution as a novel tool for epidemiological modeling of COVID-19 data. Specifically designed to analyze data constrained to the unit interval, the KM-UEHL distribution builds upon the unit exponentiated half logistic model, making it suitable for various data from COVID-19. The paper emphasizes the KM-UEHL distribution's adaptability by examining its density and hazard rate functions. Its effectiveness is demonstrated in handling the diverse nature of COVID-19 data through these functions. Key characteristics like moments, quantile functions, stress-strength reliability, and entropy measures are also comprehensively investigated. Furthermore, the KM-UEHL distribution is employed for forecasting future COVID-19 data under a progressive Type-II censoring scheme, which acknowledges the time-dependent nature of data collection during outbreaks. The paper presents various methods for constructing prediction intervals for future-order statistics, including maximum likelihood estimation, Bayesian inference (both point and interval estimates), and upper-order statistics approaches. The Metropolis-Hastings and Gibbs sampling procedures are combined to create the Markov chain Monte Carlo simulations because it is mathematically difficult to acquire closed-form solutions for the posterior density function in the Bayesian framework. The theoretical developments are validated with numerical simulations, and the practical applicability of the KM-UEHL distribution is showcased using real-world COVID-19 datasets.

A six-compartment model for COVID-19 with transmission dynamics and public health strategies

The global crisis of the COVID-19 pandemic has highlighted the need for mathematical models to inform public health strategies. The present study introduces a novel six-compartment epidemiological model that uniquely incorporates a higher isolation rate for unreported symptomatic cases of COVID-19 compared to reported cases, aiming to enhance prediction accuracy and address the challenge of initial underreporting. Additionally, we employ optimal control theory to assess the cost-effectiveness of interventions and adapt these strategies to specific epidemiological scenarios, such as varying transmission rates and the presence of asymptomatic carriers. By applying this model to COVID-19 data from India (30 January 2020 to 24 November 2020), chosen to capture the initial outbreak and subsequent waves, we calculate a basic reproduction number of 2.147, indicating the high transmissibility of the virus during this period in India. A sensitivity analysis reveals the critical impact of detection rates and isolation measures on disease progression, showing the robustness of our model in estimating the basic reproduction number. Through optimal control simulations, we demonstrate that increasing isolation rates for unreported cases and enhancing detection reduces the spread of COVID-19. Furthermore, our cost-effectiveness analysis establishes that a combined strategy of isolation and treatment is both more effective and economically viable. This research offers novel insights into the efficacy of non-pharmaceutical interventions, providing a tool for strategizing public health interventions and advancing our understanding of infectious disease dynamics.

Construction of effective reproduction number of infectious disease individuals based on spatiotemporal discriminant search model: take hand-foot-mouth disease as an example

OBJECTIVE

In order to facilitate the tracing of infectious diseases in a small area and to effectively carry out disease control and epidemiological investigations, this research proposes a novel spatiotemporal model to estimate effective reproduction number(Re)for infectious diseases, based on the fundamental concept of contact tracing.

METHODS

This study utilizes the incidence of hand, foot, and mouth disease (HFMD) among children in Bishan District, Chongqing, China from 2015 to 2019. The study incorporates the epidemiological characteristics of HFMD and aims to construct a Spatiotemporal Correlation Discrimination of HFMD. Utilizing ARC ENGINE and C# programming for the creation of a spatio-temporal database dedicated to HFMD to facilitate data collection and analysis. The scientific validity of the proposed method was verified by comparing the effective reproduction number obtained by the traditional SEIR model.

RESULTS

We have ascertained the optimal search radius for the spatiotemporal search model to be 1.5 km. Upon analyzing the resulting Re values, which range from 1.14 to 4.75, we observe a skewed distribution pattern from 2015 to 2019. The median and quartile Re value recorded is 2.42 (1.98, 2.72). Except for 2018, the similarity coefficient r of the years 2015, 2016, 2017, and 2019 were all close to 1, and p <0.05 in the comparison of the two models, indicating that the Re values obtained by using the search model and the traditional SEIR model are correlated and closely related. The results exhibited similarity between the Re curves of both models and the epidemiological characteristics of HFMD. Finally, we illustrated the regional distribution of Re values obtained by the search model at various time intervals on Geographic Information System (GIS) maps which highlighted variations in the incidence of diseases across different communities, neighborhoods, and even smaller areas.

CONCLUSION

The model comprehensively considers both temporal variation and spatial heterogeneity in disease transmission and accounts for each individual's distinct time of onset and spatial location. This proposed method differs significantly from existing mathematical models used for estimating Re in that it is founded on reasonable scientific assumptions and computer algorithms programming that take into account real-world spatiotemporal factors. It is particularly well-suited for estimating the Re of infectious diseases in relatively stable mobile populations within small geographical areas.

Studying the impacts of variant evolution for a generalized age-group transmission model

The differences of SARS-CoV-2 variants brought the changes of transmission characteristics and clinical manifestations during the prevalence of COVID-19. In order to explore the evolution mechanisms of SARS-CoV-2 variants and the impacts of variant evolution, the classic SIR (Susceptible-Infected-Recovered) compartment model was modified to a generalized SVEIR (Susceptible-Vaccinated-Exposed-Infected-Recovered) compartment model with age-group and varying variants in this study. By using of the SVEIR model and least squares method, the optimal fittings against the surveillance data from Fujian Provincial Center for Disease Control and Prevention were performed for the five epidemics of Fujian Province. The main epidemiological characteristics such as basic reproduction number, effective reproduction number, sensitivity analysis, and cross-variant scenario investigations were extensively investigated during dynamic zero-COVID policy. The study results showed that the infectivities of the variants became fast from wild strain to the Delta variant, further to the Omicron variant. Meanwhile, the cross-variant investigations showed that the average incubation periods were shortened, and that the infection scales quickly enhanced. Further, the risk estimations with the new variants were performed without implements of the non-pharmaceutical interventions, based on the dominant variants XBB.1.9.1 and EG.5. The results of the risk estimations suggested that non-pharmaceutical interventions were necessary on the Chinese mainland for controlling severe infections and deaths, and also that the regular variant monitors were still workable against the aggressive variant evolution and the emergency of new transmission risks in the future.

A mathematical model of COVID-19 with multiple variants of the virus under optimal control in Ghana

In this paper, we suggest a mathematical model of COVID-19 with multiple variants of the virus under optimal control. Mathematical modeling has been used to gain deeper insights into the transmission of COVID-19, and various prevention and control strategies have been implemented to mitigate its spread. Our model is a SEIR-based model for multi-strains of COVID-19 with 7 compartments. We also consider the circulatory structure to account for the termination of immunity for COVID-19. The model is established in terms of the positivity and boundedness of the solution and the existence of equilibrium points, and the local stability of the solution. As a result of fitting data of COVID-19 in Ghana to the model, the basic reproduction number of the original virus and Delta variant was estimated to be 1.9396, and the basic reproduction number of the Omicron variant was estimated to be 3.4905, which is 1.8 times larger than that. We observe that even small differences in the incubation and recovery periods of two strains with the same initial transmission rate resulted in large differences in the number of infected individuals. In the case of COVID-19, infections caused by the Omicron variant occur 1.5 to 10 times more than those caused by the original virus. In terms of the optimal control strategy, we formulate three control strategies focusing on social distancing, vaccination, and testing-treatment. We have developed an optimal control model for the three strategies outlined above for the multi-strain model using the Pontryagin's Maximum Principle. Through numerical simulations, we analyze three optimal control strategies for each strain and also consider combinations of the two control strategies. As a result of the simulation, all control strategies are effective in reducing disease spread, in particular, vaccination strategies are more effective than the other two control strategies. In addition the combination of the two strategies also reduces the number of infected individuals by 1/10 compared to implementing one strategy, even when mild levels are implemented. Finally, we show that if the testing-treatment strategy is not properly implemented, the number of asymptomatic and unidentified infections may surge. These results could help guide the level of government intervention and prevention strategy formulation.

Evaluating the impact of double dose vaccination on SARS-CoV-2 spread through optimal control analysis

This paper presents a new nonlinear epidemic model for the spread of SARS-CoV-2 that incorporates the effect of double dose vaccination. The model is analyzed using qualitative, stability, and sensitivity analysis techniques to investigate the impact of vaccination on the spread of the virus. We derive the basic reproduction number and perform stability analysis of the disease-free and endemic equilibrium points. The model is also subjected to sensitivity analysis to identify the most influential model parameters affecting the disease dynamics. The values of the parameters are estimated with the help of the least square curve fitting tools. Finally, the model is simulated numerically to assess the effectiveness of various control strategies, including vaccination and quarantine, in reducing the spread of the virus. Optimal control techniques are employed to determine the optimal allocation of resources for implementing control measures. Our results suggest that increasing the vaccination coverage, adherence to quarantine measures, and resource allocation are effective strategies for controlling the epidemic. The study provides valuable insights into the dynamics of the pandemic and offers guidance for policymakers in formulating effective control measures.

A stochastic scale conjugate neural network procedure for the SIRC epidemic delay differential system

In this study, a stochastic computing structure is provided for the numerical solutions of the SIRC epidemic delay differential model, i.e. SIRC-EDDM using the dynamics of the COVID-19. The design of the scale conjugate gradient (CG) neural networks (SCGNNs) is presented for the numerical treatment of SIRC-EDDM. The mathematical model is divided into susceptible S ( ρ ) , recovered R ( ρ ) , infected I ( ρ ) , and cross-immune C ( ρ ) , while the numerical performances have been provided into three different cases. The exactitude of the SCGNNs is perceived through the comparison of the accomplished and reference outcomes (Runge-Kutta scheme) and the negligible absolute error (AE) that are performed around 10-06 to 10-08 for each case of the SIRC-EDDM. The obtained results have been presented to reduce the mean square error (MSE) using the performances of train, validation, and test data. The neuron analysis is also performed that shows the AE by taking 14 neurons provide more accurateness as compared to 4 numbers of neurons. To check the proficiency of SCGNNs, the comprehensive studies are accessible using the error histograms (EHs) investigations, state transitions (STs) values, MSE performances, regression measures, and correlation.

Assessing the impact of different contact patterns on disease transmission: Taking COVID-19 as a case

Human-to-human contact plays a leading role in the transmission of infectious diseases, and the contact pattern between individuals has an important influence on the intensity and trend of disease transmission. In this paper, we define regular contacts and random contacts. Then, taking the COVID-19 outbreak in Yangzhou City, China as an example, we consider age heterogeneity, household structure and two contact patterns to establish discrete dynamic models with switching between daytime and nighttime to depict the transmission mechanism of COVID-19 in population. We studied the changes in the reproduction number with different age groups and household sizes at different stages. The effects of the proportion of two contacts patterns on reproduction number were also studied. Furthermore, taking the final size, the peak value of infected individuals in community and the peak value of quarantine infected individuals and nucleic acid test positive individuals as indicators, we evaluate the impact of the number of random contacts, the duration of the free transmission stage and summer vacation on the spread of the disease. The results show that a series of prevention and control measures taken by the Chinese government in response to the epidemic situation are reasonable and effective, and the young and middle-aged adults (aged 18-59) with household size of 6 have the strongest transmission ability. In addition, the results also indicate that increasing the proportion of random contact is beneficial to the control of the infectious disease in the phase with interventions. This work enriches the content of infectious disease modeling and provides theoretical guidance for the prevention and control of follow-up major infectious diseases.

Analysis of a COVID-19 model with media coverage and limited resources

The novel coronavirus disease (COVID-19) pandemic has profoundly impacted the global economy and human health. The paper mainly proposed an improved susceptible-exposed-infected-recovered (SEIR) epidemic model with media coverage and limited medical resources to investigate the spread of COVID-19. We proved the positivity and boundedness of the solution. The existence and local asymptotically stability of equilibria were studied and a sufficient criterion was established for backward bifurcation. Further, we applied the proposed model to study the trend of COVID-19 in Shanghai, China, from March to April 2022. The results showed sensitivity analysis, bifurcation, and the effects of critical parameters in the COVID-19 model.

The relationship between compartment models and their stochastic counterparts: A comparative study with examples of the COVID-19 epidemic modeling

Deterministic compartment models (CMs) and stochastic models, including stochastic CMs and agent-based models, are widely utilized in epidemic modeling. However, the relationship between CMs and their corresponding stochastic models is not well understood. The present study aimed to address this gap by conducting a comparative study using the susceptible, exposed, infectious, and recovered (SEIR) model and its extended CMs from the coronavirus disease 2019 modeling literature. We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations. Based on this equivalence, we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment. The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics. However, it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs. Additionally, we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents. This model offered a balance between computational efficiency and accuracy. The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling. Furthermore, the results had implications for the development of hybrid models that integrated the strengths of both frameworks. Overall, the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.

A data-driven Markov process for infectious disease transmission

The 2019 coronavirus pandemic exudes public health and socio-economic burden globally, raising an unprecedented concern for infectious diseases. Thus, describing the infectious disease transmission process to design effective intervention measures and restrict its spread is a critical scientific issue. We propose a level-dependent Markov model with infinite state space to characterize viral disorders like COVID-19. The levels and states in this model represent the stages of outbreak development and the possible number of infectious disease patients. The transfer of states between levels reflects the explosive transmission process of infectious disease. A simulation method with heterogeneous infection is proposed to solve the model rapidly. After that, simulation experiments were conducted using MATLAB according to the reported data on COVID-19 published by Johns Hopkins. Comparing the simulation results with the actual situation shows that our proposed model can well capture the transmission dynamics of infectious diseases with and without imposed interventions and evaluate the effectiveness of intervention strategies. Further, the influence of model parameters on transmission dynamics is analyzed, which helps to develop reasonable intervention strategies. The proposed approach extends the theoretical study of mathematical modeling of infectious diseases and contributes to developing models that can describe an infinite number of infected persons.

Investigation on the possibility of dynamic COVID-Zero strategy in China: a population-based transmission model analysis and economic evaluation

OBJECTIVE

To explore the feasible and cost-effective intervention strategies to achieve the goal of dynamic COVID-Zero in China.

DESIGN

A Susceptible-Exposed-Infectious-Recovered model combined economic evaluation was used to generate the number of infections, the time for dynamic COVID-Zero and calculate cost-effectiveness under different intervention strategies. The model simulated the 1 year spread of COVID-19 in mainland China after 100 initial infections were imported.

INTERVENTIONS

According to close contact tracing degree from 80% to 100%, close contact tracing time from 2 days to 1 day, isolation time from 14 days to 7 days, scope of nucleic acid testing (NAT) from 10% to 100% and NAT frequency from weekly to every day, 720 scenarios were simulated.

OUTCOME MEASURE

Cumulative number of infections (CI), social COVID-Zero duration (SCD), total cost (TC) and incremental cost-effectiveness ratio.

RESULTS

205 of 720 scenarios could achieve the total COVID-Zero since the first case was reported. The fastest and most cost-effective strategy was Scenario 680, in which all close contacts were traced within 1 day, the isolation time was 14 days and 10% of the national population was randomly checked for NAT every day. In Scenario 680, the CI was 280 (100 initial infections) and the SCD was 13 days. The TC was ¥4126 hundred million and the cost of reducing one infection was ¥47 470. However, when the close contact tracing time was 2 days and the degree of close contact tracing was 80%-90%, the SCD would double to 24-101 days and the TCs increased by ¥16 505 to 37 134 hundred million compared with Scenario 680.

CONCLUSIONS

If all close contact was controlled within 1 day, the rapid social COVID-Zero can be achieved effectively and cost-effectively. Therefore, the future prevention and control of emerging respiratory infectious diseases can focus on enhancing the ability of close contact tracing.

Stability and numerical analysis via non-standard finite difference scheme of a nonlinear classical and fractional order model

In this paper, we develop a new mathematical model for an in-depth understanding of COVID-19 (Omicron variant). The mathematical study of an omicron variant of the corona virus is discussed. In this new Omicron model, we used idea of dividing infected compartment further into more classes i.e asymptomatic, symptomatic and Omicron infected compartment. Model is asymptotically locally stable whenever R0<1 and when R0≤1 at disease free equilibrium the system is globally asymptotically stable. Local stability is investigated with Jacobian matrix and with Lyapunov function global stability is analyzed. Moreover basic reduction number is calculated through next generation matrix and numerical analysis will be used to verify the model with real data. We consider also the this model under fractional order derivative. We use Grunwald-Letnikov concept to establish a numerical scheme. We use nonstandard finite difference (NSFD) scheme to simulate the results. Graphical presentations are given corresponding to classical and fractional order derivative. According to our graphical results for the model with numerical parameters, the population's risk of infection can be reduced by adhering to the WHO's suggestions, which include keeping social distances, wearing facemasks, washing one's hands, avoiding crowds, etc.

Impact of COVID-19 outbreak on the mental health in sports: a review

Global pandemic, lockdown restrictions, and COVID-19 compulsory social isolation guidelines have raised unprecedented mental health in the sports community. The COVID-19 pandemic is found to affect the mental health of the population. In critical situations, health authorities and sports communities must identify their priorities and make plans to maintain athletes' health and athletic activities. Several aspects play an important role in prioritization and strategic planning, e.g., physical and mental health, distribution of resources, and short to long-term environmental considerations. To identify the psychological health of sportspeople and athletes due to the outbreak of COVID-19 has been reviewed in this research. This review article also analyzes the impact of COVID-19 on health mental in databases. The COVID-19 outbreak and quarantine would have a serious negative impact on the mental health of athletes. From the accessible sources, 80 research articles were selected and examined for this purpose such as Research Gate, PubMed, Google Scholar, Springer, Scopus, and Web of Science and based on the involvement for this study 14 research articles were accessed. This research has an intention on mental health issues in athletes due to the Pandemic. This report outlines the mental, emotional and behavioural consequences of COVID-19 home confinement. Further, research literature reported that due to the lack of required training, physical activity, practice sessions, and collaboration with teammates and coaching staff are the prime causes of mental health issues in athletes. The discussions also reviewed several pieces of literature which examined the impacts on sports and athletes, impacts on various countries, fundamental issues of mental health and the diagnosis for the sports person and athletes, and the afterlife of the COVID-19 pandemic for them. Because of the compulsory restrictions and guidelines of this COVID-19 eruption, the athletes of different sports and geographical regions are suffering from fewer psychological issues which were identified in this paper. Accordingly, the COVID-19 pandemic appears to negatively affect the mental health of the athletes with the prevalence and levels of anxiety and stress increasing, and depression symptoms remaining unaltered. Addressing and mitigating the negative effect of COVID-19 on the mental health of this population identified from this review.

Optimal interventional policy based on discrete-time fuzzy rules equivalent model utilizing with COVID-19 pandemic data

In this paper, a mathematical model of the COVID-19 pandemic is formulated by fitting it to actual data collected during the fifth wave of the COVID-19 pandemic in Coahuila, Mexico, from June 2022 to October 2022. The data sets used are recorded on a daily basis and presented in a discrete-time sequence. To obtain the equivalent data model, fuzzy rules emulated networks are utilized to derive a class of discrete-time systems based on the daily hospitalized individuals' data. The aim of this study is to investigate the optimal control problem to determine the most effective interventional policy including precautionary and awareness measures, the detection of asymptomatic and symptomatic individuals, and vaccination. A main theorem is developed to guarantee the closed-loop system performance by utilizing approximate functions of the equivalent model. The numerical results indicate that the proposed interventional policy can eradicate the pandemic within 1-8 weeks. Additionally, the results show that if the policy is implemented within the first 3 weeks, the number of hospitalized individuals remains below the hospital's capacity.

Predicting COVID-19 positivity and hospitalization with multi-scale graph neural networks

The pandemic of COVID-19 is undoubtedly one of the biggest challenges for modern healthcare. In order to analyze the spatio-temporal aspects of the spread of COVID-19, technology has helped us to track, identify and store information regarding positivity and hospitalization, across different levels of municipal entities. In this work, we present a method for predicting the number of positive and hospitalized cases via a novel multi-scale graph neural network, integrating information from fine-scale geographical zones of a few thousand inhabitants. By leveraging population mobility data and other features, the model utilizes message passing to model interaction between areas. Our proposed model manages to outperform baselines and deep learning models, presenting low errors in both prediction tasks. We specifically point out the importance of our contribution in predicting hospitalization since hospitals became critical infrastructure during the pandemic. To the best of our knowledge, this is the first work to exploit high-resolution spatio-temporal data in a multi-scale manner, incorporating additional knowledge, such as vaccination rates and population mobility data. We believe that our method may improve future estimations of positivity and hospitalization, which is crucial for healthcare planning.

A Novel Mathematical Model That Predicts the Protection Time of SARS-CoV-2 Antibodies

Infectious diseases such as SARS-CoV-2 pose a considerable threat to public health. Constructing a reliable mathematical model helps us quantitatively explain the kinetic characteristics of antibody-virus interactions. A novel and robust model is developed to integrate antibody dynamics with virus dynamics based on a comprehensive understanding of immunology principles. This model explicitly formulizes the pernicious effect of the antibody, together with a positive feedback stimulation of the virus-antibody complex on the antibody regeneration. Besides providing quantitative insights into antibody and virus dynamics, it demonstrates good adaptivity in recapturing the virus-antibody interaction. It is proposed that the environmental antigenic substances help maintain the memory cell level and the corresponding neutralizing antibodies secreted by those memory cells. A broader application is also visualized in predicting the antibody protection time caused by a natural infection. Suitable binding antibodies and the presence of massive environmental antigenic substances would prolong the protection time against breakthrough infection. The model also displays excellent fitness and provides good explanations for antibody selection, antibody interference, and self-reinfection. It helps elucidate how our immune system efficiently develops neutralizing antibodies with good binding kinetics. It provides a reasonable explanation for the lower SARS-CoV-2 mortality in the population that was vaccinated with other vaccines. It is inferred that the best strategy for prolonging the vaccine protection time is not repeated inoculation but a directed induction of fast-binding antibodies. Eventually, this model will inform the future construction of an optimal mathematical model and help us fight against those infectious diseases.

An algorithm to estimate the real time secondary infections in sub-urban bus travel: COVID-19 epidemic experience at Chennai Metropolitan city India

Globalization, global climatic changes, and human behavior pose threats to highly pathogenic avian influenza (HPAI) virus spillover from animals to human. Current SARS-CoV2 transmission continues in several countries despite drastic reduction in COVID-19 cases following world-wide containment measures including RNA vaccines. China reimposed lockdown in November 2022 following the surge in commercial hubs. Urban population density and intracity travel in over-crowded public transport play crucial roles in early transition to an exponential phase of the epidemic in metro-cities. Based on the SARS-CoV2 transmission during the lockdown period in Chennai metro-city, we developed an algorithm that mimics a real-time scenario of passengers boarding and deboarding at each bus-stop on a trip of 36.1 km in 21G bus service in Chennai city to understand the pattern of secondary infections on a daily basis. The algorithm was simulated to estimate R0, and the COVID-19 secondary infections was estimated for each bus trip. Results showed that the R0 depended on the boarding and deboarding of the infected individuals at various bus stops. R0 varied from 0 to 1.04, each trip generated 5-9 secondary infections and four bus stops as potential locations for a higher transmission level. More than 80% of the working population in metro-cities depends on unorganized sectors, and separate mitigation strategies must be in place for successful epidemic containment. The developed algorithm has significant public health relevance and can be utilized to draw necessary containment plans in near future in the event of new COVID-19 wave or any other similar epidemic.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13337-022-00804-9.

Application of big data and artificial intelligence in epidemic surveillance and containment

Faced with the current time-sensitive COVID-19 pandemic, the overburdened healthcare systems have resulted in a strong demand to develop newer methods to control the spread of the pandemic. Big data and artificial intelligence (AI) have been leveraged amid the COVID-19 pandemic; however, little is known about their use for supporting public health efforts. In epidemic surveillance and containment, efforts are needed to treat critical patients, track and manage the health status of residents, isolate suspected cases, and develop vaccines and antiviral drugs. The applications of emerging practices of artificial intelligence and big data have become powerful "weapons" to fight against the pandemic and provide strong support in pandemic prevention and control, such as early warning, analysis and judgment, interruption and intervention of epidemic, to achieve goals of early detection, early report, early diagnosis, early isolation and early treatment. These are the decisive factors to control the spread of the epidemic and reduce the mortality. This paper systematically summarized the application of big data and AI in epidemic, and describes practical cases and challenges with emphasis on epidemic prevention and control. The included studies showed that big data and AI have the potential strength to fight against COVID-19. However, many of the proposed methods are not yet widely accepted. Thus, the most rewarding research would be on methods that promise value beyond COVID-19. More efforts are needed for developing standardized reporting protocols or guidelines for practice.

Effect of vaccination on the case fatality rate for COVID-19 infections 2020-2021: multivariate modelling of data from the US Department of Veterans Affairs

OBJECTIVES

To evaluate the benefits of vaccination on the case fatality rate (CFR) for COVID-19 infections.

DESIGN, SETTING AND PARTICIPANTS

The US Department of Veterans Affairs has 130 medical centres. We created multivariate models from these data-339 772 patients with COVID-19-as of 30 September 2021.

OUTCOME MEASURES

The primary outcome for all models was death within 60 days of the diagnosis. Logistic regression was used to derive adjusted ORs for vaccination and infection with Delta versus earlier variants. Models were adjusted for confounding factors, including demographics, comorbidity indices and novel parameters representing prior diagnoses, vital signs/baseline laboratory tests and outpatient treatments. Patients with a Delta infection were divided into eight cohorts based on the time from vaccination to diagnosis. A common model was used to estimate the odds of death associated with vaccination for each cohort relative to that of unvaccinated patients.

RESULTS

9.1% of subjects were vaccinated. 21.5% had the Delta variant. 18 120 patients (5.33%) died within 60 days of their diagnoses. The adjusted OR for a Delta infection was 1.87±0.05, which corresponds to a relative risk (RR) of 1.78. The overall adjusted OR for prior vaccination was 0.280±0.011 corresponding to an RR of 0.291. Raw CFR rose steadily after 10-14 weeks. The OR for vaccination remained stable for 10-34 weeks.

CONCLUSIONS

Our CFR model controls for the severity of confounding factors and priority of vaccination, rather than solely using the presence of comorbidities. Our results confirm that Delta was more lethal than earlier variants and that vaccination is an effective means of preventing death. After adjusting for major selection biases, we found no evidence that the benefits of vaccination on CFR declined over 34 weeks. We suggest that this model can be used to evaluate vaccines designed for emerging variants.

Optimal control strategies to combat COVID-19 transmission: A mathematical model with incubation time delay

The coronavirus disease 2019, started spreading around December 2019, still persists in the population all across the globe. Though different countries have been able to cope with the disease to some extent and vaccination for the same has been developed, it cannot be ignored that the disease is still not on the verge of completely eradicating, which in turn creates a need for having deeper insights of the disease in order to understand it well and hence be able to work towards its eradication. Meanwhile, using mitigation strategies like non-pharmaceutical interventions can help in controlling the disease. In this work, our aim is to study the dynamics of COVID-19 using compartmental approach by applying various analytical methods. We obtain formula for important tools like R0 and establish the stability of disease-free equilibrium point for R0<1. Further, based on R0, we discuss the stability and existence of the endemic equilibrium point. We incorporate various control strategies possible and using optimal control theory, study their expected positive impacts on the spread of the disease. Later, using a biologically feasible set of parameters, we numerically analyse the model. We even study the trend of the outbreak in China, for over 120 days, where the active cases rise up to a peak and then the curve flattens.

Clinical effects of 2-DG drug restraining SARS-CoV-2 infection: A fractional order optimal control study

Fractional calculus is very convenient tool in modeling of an emergent infectious disease system comprising previous disease states, memory of disease patterns, profile of genetic variation etc. Significant complex behaviors of a disease system could be calibrated in a proficient manner through fractional order derivatives making the disease system more realistic than integer order model. In this study, a fractional order differential equation model is developed in micro level to gain perceptions regarding the effects of host immunological memory in dynamics of SARS-CoV-2 infection. Additionally, the possible optimal control of the infection with the help of an antiviral drug, viz. 2-DG, has been exemplified here. The fractional order optimal control would enable to employ the proper administration of the drug minimizing its systematic cost which will assist the health policy makers in generating better therapeutic measures against SARS-CoV-2 infection. Numerical simulations have advantages to visualize the dynamical effects of the immunological memory and optimal control inputs in the epidemic system.

Place of distancing measures in containing epidemics: a scoping review

Distancing is one of the barrier measures in mitigating epidemics. We aimed to investigate the typology, effectiveness, and side effects of distancing rules during epidemics. Electronic searches were conducted on MEDLINE, PubMed in April 2020, using Mesh-Terms representing various forms of distancing ('social isolation', 'social distancing', 'quarantine') combining with 'epidemics'. PRISMA-ScR statement was consulted to report this review. A total of 314 titles were identified and 93 were finally included. 2009 influenza A and SARS-CoV-2 epidemics were the most studied. Distancing measures were mostly classified as case-based and community-based interventions. The combination of distancing rules, like school closure, home working, isolation and quarantine, has proven to be effective in reducing R0 and flattening the epidemic curve, also when initiated early at a high rate and combined with other non-pharmaceutical interventions. Epidemiological and modeling studies showed that Isolation and quarantine in the 2009 Influenza pandemic were effective measures to decrease attack rate also with high level of compliance but there was an increased risk of household transmission. lockdown was also effective to reduce R0 from 2.6 to 0.6 and to increase doubling time from 2 to 4 days in the covid-19 pandemic. The evidence for school closure and workplace distancing was moderate as single intervention. Psychological disorder, unhealthy behaviors, disruption of economic activities, social discrimination, and stigmatization were the main side effects of distancing measures. Earlier implementation of combined distancing measures leads to greater effectiveness in containing outbreaks. Their indication must be relevant and based on evidence to avoid adverse effects on the community. These results would help decision-makers to develop response plans based on the required experience and strengthen the capacity of countries to fight against future epidemics. Mesh words: Physical Distancing, Quarantine, Epidemics, Public Health, Scoping Review.

Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate

COVID-19 pandemic represents an unprecedented global health crisis which has an enormous impact on the world population and economy. Many scientists and researchers have combined efforts to develop an approach to tackle this crisis and as a result, researchers have developed several approaches for understanding the COVID-19 transmission dynamics and the way of mitigating its effect. The implementation of a mathematical model has proven helpful in further understanding the behaviour which has helped the policymaker in adopting the best policy necessary for reducing the spread. Most models are based on a system of equations which assume an instantaneous change in the transmission dynamics. However, it is believed that SARS-COV-2 have an incubation period before the tendency of transmission. Therefore, to capture the dynamics adequately, there would be a need for the inclusion of delay parameters which will account for the delay before an exposed individual could become infected. Hence, in this paper, we investigate the SEIR epidemic model with a convex incidence rate incorporated with a time delay. We first discussed the epidemic model as a form of a classical ordinary differential equation and then the inclusion of a delay to represent the period in which the susceptible and exposed individuals became infectious. Secondly, we identify the disease-free together with the endemic equilibrium state and examine their stability by adopting the delay differential equation stability theory. Thereafter, we carried out numerical simulations with suitable parameters choice to illustrate the theoretical result of the system and for a better understanding of the model dynamics. We also vary the length of the delay to illustrate the changes in the model as the delay parameters change which enables us to further gain an insight into the effect of the included delay in a dynamical system. The result confirms that the inclusion of delay destabilises the system and it forces the system to exhibit an oscillatory behaviour which leads to a periodic solution and it further helps us to gain more insight into the transmission dynamics of the disease and strategy to reduce the risk of infection.

Quantifying the dynamic transmission of COVID-19 asymptomatic and symptomatic infections: Evidence from four Chinese regions

The dynamic transmission of asymptomatic and symptomatic COVID-19 infections is difficult to quantify because asymptomatic infections are not readily recognized or self-identified. To address this issue, we collected data on asymptomatic and symptomatic infections from four Chinese regions (Beijing, Dalian, Xinjiang, and Guangzhou). These data were considered reliable because the government had implemented large-scale multiple testing during the outbreak in the four regions. We modified the classical susceptible-exposure-infection-recovery model and combined it with mathematical tools to quantitatively analyze the number of infections caused by asymptomatic and symptomatic infections during dynamic transmission, respectively. The results indicated that the ratios of the total number of asymptomatic to symptomatic infections were 0.13:1, 0.48:1, 0.29:1, and 0.15:1, respectively, in the four regions. However, the ratio of the total number of infections caused by asymptomatic and symptomatic infections were 4.64:1, 6.21:1, 1.49:1, and 1.76:1, respectively. Furthermore, the present study describes the daily number of healthy people infected by symptomatic and asymptomatic transmission and the dynamic transmission process. Although there were fewer asymptomatic infections in the four aforementioned regions, their infectivity was found to be significantly higher, implying a greater need for timely screening and control of infections, particularly asymptomatic ones, to contain the spread of COVID-19.

The economic impact of COVID-19 interventions: A mathematical modeling approach

Prior to vaccination or drug treatment, non-pharmaceutical interventions were almost the only way to control the coronavirus disease 2019 (COVID-19) epidemic. After vaccines were developed, effective vaccination strategies became important. The prolonged COVID-19 pandemic has caused enormous economic losses worldwide. As such, it is necessary to estimate the economic effects of control policies, including non-pharmaceutical interventions and vaccination strategies. We estimated the costs associated with COVID-19 according to different vaccination rollout speeds and social distancing levels and investigated effective control strategies for cost minimization. Age-structured mathematical models were developed and used to study disease transmission epidemiology. Using these models, we estimated the actual costs due to COVID-19, considering costs associated with medical care, lost wages, death, vaccination, and gross domestic product (GDP) losses due to social distancing. The lower the social distancing (SD) level, the more important the vaccination rollout speed. SD level 1 was cost-effective under fast rollout speeds, but SD level 2 was more effective for slow rollout speeds. If the vaccine rollout rate is fast enough, even implementing SD level 1 will be cost effective and can control the number of critically ill patients and deaths. If social distancing is maintained at level 2 at the beginning and then relaxed when sufficient vaccinations have been administered, economic costs can be reduced while maintaining the number of patients with severe symptoms below the intensive care unit (ICU) capacity. Korea has wellequipped medical facilities and infrastructure for rapid vaccination, and the public's desire for vaccination is high. In this case, the speed of vaccine supply is an important factor in controlling the COVID-19 epidemic. If the speed of vaccination is fast, it is possible to maintain a low level of social distancing without a significant increase in the number of deaths and hospitalized patients with severe symptoms, and the corresponding costs can be reduced.

Modified SIR model for COVID-19 transmission dynamics: Simulation with case study of UK, US and India

Corona virus disease 2019 (COVID-19) is an infectious disease and has spread over more than 200 countries since its outbreak in December 2019. This pandemic has posed the greatest threat to global public health and seems to have changing characteristics with altering variants, hence various epidemiological and statistical models are getting developed to predict the infection spread, mortality rate and calibrating various impacting factors. But the aysmptomatic patient counts and demographical factors needs to be considered in model evaluation. Here we have proposed a new seven compartmental model, Susceptible- Exposed- Infected-Asymptomatic-Quarantined-Fatal-Recovered (SEIAQFR) which is based on classical Susceptible-Infected-Recovered (SIR) model dynamic of infectious disease, and considered factors like asymptomatic transmission and quarantine of patients. We have taken UK, US and India as a case study for model evaluation purpose. In our analysis, it is found that the Reproductive Rate ( R 0 ) of the disease is dynamic over a long period and provides better results in model performance ( > 0 . 98 R-square score) when model is fitted across smaller time period. On an average 40 % - 50 % cases are asymptomatic and have contributed to model accuracy. The model is employed to show accuracy in correspondence with different geographic data in both wave of disease spread. Different disease spreading factors like infection rate, recovery rate and mortality rate are well analyzed with best fit of real world data. Performance evaluation of this model has achieved good R-Square score which is 0 . 95 - 0 . 99 for infection prediction and 0 . 90 - 0 . 99 for death prediction and an average 1 % - 5 % MAPE in different wave of the disease in UK, US and India.

How do the contaminated environment influence the transmission dynamics of COVID-19 pandemic?

COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that first appeared in Wuhan city and then globally. The COVID-19 pandemic exudes public health and socio-economic burden globally. Mathematical modeling plays a significant role to comprehend the transmission dynamics and controlling factors of rapid spread of the disease. Researchers focus on the human-to-human transmission of the virus but the SARS-CoV-2 virus also contaminates the environment. In this study we proposed a nonlinear mathematical model for the COVID-19 pandemic to analyze the transmission dynamics of the disease in India. We have also incorporated the environment contamination by the infected individuals as the population density is very high in India. The model is fitted and parameterized using daily new infection data from India. Analytical study of the proposed COVID-19 model, including feasibility of critical points and their stability reveals that the infection-free steady state is stable if the basic reproduction number is less than unity otherwise the system shows significant outbreak. Numerical illustrations demonstrates that if the rate of environment contamination increased then the number of infected persons also increased. But if the environment is disinfected by sanitization then the number of infected persons cannot drastically increase.

Anti-Spike and Neutralizing Antibodies after Two Doses of COVID-19 Sinopharm/BIBP Vaccine

Host response to COVID-19 vaccines is partially evaluated through the estimation of antibody response, specifically the binding anti-spike (anti-S) and the neutralizing antibodies (nAbs) against SARS-CoV-2. Vaccine-induced humoral response affects decisions on the choice of vaccine type, vaccine acceptance, and the need for boosting. Identification of risk factors for poor antibody response helps to stratify individuals who might potentially require booster doses. The primary objective of this cross-sectional study was to investigate the antibody response after receiving two Sinopharm vaccine doses. Factors affecting antibody response were additionally studied. Moreover, a predictive cutoff for anti-S was generated to predict positivity of nAbs. Blood samples were collected from 92 adults and relevant data were recorded. Antibody levels (anti-S and nAbs) against SARS-CoV-2 were tested one month following the second dose of Sinopharm vaccine using two commercial ELISA tests. Among the 92 participants, 88 tested positive for anti-S (95.7%), with a median level of 52.15 RU/mL (equivalent to 166.88 BAU/mL). Fewer participants (67.4%) were positive for nAbs, with a median percentage of inhibition (%IH) of 50.62% (24.05−84.36). A significant positive correlation existed between the titers of both antibodies (correlation coefficient = 0.875, p < 0.001). When the anti-S titer was greater than 40 RU/mL (128 BAU/mL), nAbs were also positive with a sensitivity of 80.6% and a specificity of 90%. Positive nAbs results were associated with a higher anti-S titers (62.1 RU/mL) compared to negative nAbs (mean anti-S titer of 18.6 RU/mL). History of COVID-19 infection was significantly associated with higher titers of anti-S (p = 0.043) and higher IH% of nAbs (p = 0.048). Hypertensive participants were found to have significantly higher median titers of anti-S (101.18 RU/mL) compared with non-hypertensive ones (42.15 RU/mL), p = 0.034. Post-vaccination headache was significantly higher among those with higher anti-S than those with relatively lower titers (98.82 versus 43.69 RU/mL, p = 0.048). It can be concluded that the Sinopharm vaccine produced high levels of binding antibodies but with low neutralizing abilities. Also, levels of anti-S titer greater than 40 RU/mL could adequately predict positivity of nAbs without need for their testing.

The COVID-19 pandemic as inspiration to reconsider epidemic models: A novel approach to spatially homogeneous epidemic spread modeling

Epidemic spread models are useful tools to study the spread and the effectiveness of the interventions at a population level, to an epidemic. The workhorse of spatially homogeneous class models is the SIR-type ones comprising ordinary differential equations for the unknown state variables. The transition between different states is expressed through rate functions. Inspired by -but not restricted to- features of the COVID-19 pandemic, a new framework for modeling a disease spread is proposed. The main concept refers to the assignment of properties to each individual person as regards his response to the disease. A multidimensional distribution of these properties represents the whole population. The temporal evolution of this distribution is the only dependent variable of the problem. All other variables can be extracted by post-processing of this distribution. It is noteworthy that the new concept allows an improved consideration of vaccination modeling because it recognizes vaccination as a modifier of individuals response to the disease and not as a means for individuals to totally defeat the disease. At the heart of the new approach is an infection age model engaging a sharp cut-off. This model is analyzed in detail, and it is shown to admit self-similar solutions. A hierarchy of models based on the new approach, from a generalized one to a specific one with three dominant properties, is derived. The latter is implemented as an example and indicative results are presented and discussed. It appears that the new framework is general and versatile enough to simulate disease spread processes and to predict the evolution of several variables of the population during this spread.

Understanding Dynamics of Pandemic Models to Support Predictions of COVID-19 Transmission: Parameter Sensitivity Analysis of SIR-Type Models

Despite efforts made to model and predict COVID-19 transmission, large predictive uncertainty remains. Failure to understand the dynamics of the nonlinear pandemic prediction model is an important reason. To this end, local and multiple global sensitivity analysis approaches are synthetically applied to analyze the sensitivities of parameters and initial state variables and community size (N) in susceptible-infected-recovered (SIR) and its variant susceptible-exposed-infected-recovered (SEIR) models and basic reproduction number (R0), aiming to provide prior information for parameter estimation and suggestions for COVID-19 prevention and control measures. We found that N influences both the maximum number of actively infected cases and the date on which the maximum number of actively infected cases is reached. The high effect of N on maximum actively infected cases and peak date suggests the necessity of isolating the infected cases in a small community. The protection rate and average quarantined time are most sensitive to the infected populations, with a summation of their first-order sensitivity indices greater than 0.585, and their interactions are also substantial, being 0.389 and 0.334, respectively. The high sensitivities and interaction between the protection rate and average quarantined time suggest that protection and isolation measures should always be implemented in conjunction and started as early as possible. These findings provide insights into the predictability of the pandemic models by estimating influential parameters and suggest how to effectively prevent and control epidemic transmission.

A global report on the dynamics of COVID-19 with quarantine and hospitalization: A fractional order model with non-local kernel

In this paper, a compartmental mathematical model has been utilized to gain a better insight about the future dynamics of COVID-19. The total human population is divided into eight various compartments including susceptible, exposed, pre-asymptomatic, asymptomatic, symptomatic, quarantined, hospitalized and recovered or removed individuals. The problem was modeled in terms of highly nonlinear coupled system of classical order ordinary differential equations (ODEs) which was further generalized with the Atangana-Balaeanu (ABC) fractional derivative in Caputo sense with nonlocal kernel. Furthermore, some theoretical analyses have been done such as boundedness, positivity, existence and uniqueness of the considered. Disease-free and endemic equilibrium points were also assessed. The basic reproduction was calculated through next generation technique. Due to high risk of infection, in the present study, we have considered the reported cases from three continents namely Americas, Europe, and south-east Asia. The reported cases were considered between 1st May 2021 and 31st July 2021 and on the basis of this data, the spread of infection is predicted for the next 200 days. The graphical solution of the considered nonlinear fractional model was obtained via numerical scheme by implementing the MATLAB software. Based on the fitted values of parameters, the basic reproduction number ℜ0 for the case of America, Asia and Europe were calculated as ℜ0≈2.92819, ℜ0≈2.87970 and ℜ0≈2.23507 respectively. It is also observed that the spread of infection in America is comparatively high followed by Asia and Europe. Moreover, the effect of fractional parameter is shown on the dynamics of spread of infection among different classes. Additionally, the effect of quarantined and treatment of infected individuals is also shown graphically. From the present analysis it is observed that awareness of being quarantine and proper treatment can reduce the infection rate dramatically and a minimal variation in quarantine and treatment rates of infected individuals can lead us to decrease the rate of infection.

Mathematical COVID-19 model with vaccination: a case study in Saudi Arabia

The discovery of a new form of corona-viruses in December 2019, SARS-CoV-2, commonly named COVID-19, has reshaped the world. With health and economic issues at stake, scientists have been focusing on understanding the dynamics of the disease, in order to provide the governments with the best policies and strategies allowing them to reduce the span of the virus. The world has been waiting for the vaccine for more than one year. The World Health Organization (WHO) is advertising the vaccine as a safe and effective measure to fight off the virus. Saudi Arabia was the fourth country in the world to start to vaccinate its population. Even with the new simplified COVID-19 rules, the third dose is still mandatory. COVID-19 vaccines have raised many questions regarding in its efficiency and its role to reduce the number of infections. In this work, we try to answer these question and propose a new mathematical model with five compartments, including susceptible, vaccinated, infectious, asymptotic and recovered individuals. We provide theoretical results regarding the effective reproduction number, the stability of endemic equilibrium and disease free equilibrium. We provide numerical analysis of the model based on the Saudi case. Our developed model shows that the vaccine reduces the transmission rate and provides an explanation to the rise in the number of new infections immediately after the start of the vaccination campaign in Saudi Arabia.

Loss of Livelihood, Wages, and Employment During the COVID-19 Pandemic in Selected Districts of Chhattisgarh in India, and Its Impact on Food Insecurity and Hunger

The COVID-19 pandemic has exacerbated the existing food insecurity in developing nations. The cumulative effect of restricted mobility to curtail the spread of the infection, loss of livelihood and income, worst affected the economically weaker sections. Our work examined the availability, accessibility, and affordability of food during the first wave of the pandemic using the FAO, HFIAS questionnaire, in a random sample (N = 401) from Kanker and Narayanpur districts in Chattisgarh, an Empowered Action Group state, in India. Total food security scores were derived by summing the individual scores. Percentages above and below the median scores were used to assess food insecurity. Proportion Z test was used to compare settings and a generalized linear model was used to determine the association between dependent and independent variables. Of the 63% non-tribal population, a greater percent experienced income loss (13.4%) and worried about not having sufficient food (40%). A significantly higher proportion from the non-tribal regions reported food scarcity in the household (34%) and experienced hunger (15%). Non-tribal participants (77%) scored ≤ median (score 8) demonstrating high food insecurity. The odds of poor food access increased in the non-tribal settings (B: 0.024, 95% CI: 0.011–0.051, P < 0.001), income between Rs. 10,000–29,000/- per month (B: 0.385, 95% CI: 0.146–1.014, P < 0.05) and among those experiencing total or partial income loss (B: 0.505, 95% CI: 0.252–1.011, P < 0.05). Urban residence increased the odds of poor food availability (B: 15.933, 95% CI: 3.473–73.096, P < 0.001). Being male (B: 0.450, 95% CI: 0.208–0.972, P < 0.05), and not experiencing income loss (B: 0.367, 95% CI: 0.139–0.969, P < 0.05) decreased the odds of poor availability and affordability (B: 0.153, 95% CI: 0.067–0.349, P < 0.001). Non-tribal setting increased the odds of poor affordability (B: 11.512, 95% CI: 5.577–23.765, P < 0.001) and hunger (B: 19.532, 95% CI: 7.705–49.515, P < 0.001). Being male (B: 0.445, 95% CI: 0.277–0.715, P < 0.05) and higher age (B: 0.936, 95% CI: 0.936–0.906, P < 0.001) decreased the odds of food insecurity as per the total food security score. While India is likely to experience multiple waves, actions urgent and targeted toward the needs of the vulnerable sections be prioritized to endure and overcome the impact of the pandemic.

Effects of greenhouse gases and hypoxia on the population of aquatic species: a fractional mathematical model

Study of ecosystems has always been an interesting topic in the view of real-world dynamics. In this paper, we propose a fractional-order nonlinear mathematical model to describe the prelude of deteriorating quality of water cause of greenhouse gases on the population of aquatic animals. In the proposed system, we recall that greenhouse gases raise the temperature of water, and because of this reason, the dissolved oxygen level goes down, and also the rate of circulation of disintegrated oxygen by the aquatic animals rises, which causes a decrement in the density of aquatic species. We use a generalized form of the Caputo fractional derivative to describe the dynamics of the proposed problem. We also investigate equilibrium points of the given fractional-order model and discuss the asymptotic stability of the equilibria of the proposed autonomous model. We recall some important results to prove the existence of a unique solution of the model. For finding the numerical solution of the established fractional-order system, we apply a generalized predictor-corrector technique in the sense of proposed derivative and also justify the stability of the method. To express the novelty of the simulated results, we perform a number of graphs at various fractional-order cases. The given study is fully novel and useful for understanding the proposed real-world phenomena.

Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak

34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible (S), asymptomatic infected (A), clinically ill or symptomatic infected (I), quarantine (Q), isolation (J) and recovered (R), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin's maximum principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore, the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.

Supplementary Information

The online version supplementary material available at 10.1007/s11071-022-07235-7.

A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics

Simple Summary

Predicting the spreading trend of the COVID-19 epidemic is one of the hot topics in the modeling field. In this study, we applied a continuous Markov-chain model to simulate the spread of the COVID-19 epidemic. The results of this study indicate that the herd immunity threshold should be significantly higher than 1 − 1/R₀. Taking the immunity waning effect into consideration, the model could predict an epidemic resurgence after the herd immunity threshold. Meanwhile, this Markov-chain approach could also forecast the epidemic distribution and predict the epidemic hotspots at different times. It is implied from our model that it is significantly challenging to eradicate SARS-CoV-2 in the short term. The actual epidemic development is consistent with our prediction. In the end, this method displayed great potential as an alternative approach to traditional compartment models.

Abstract

To address the urgent need to accurately predict the spreading trend of the COVID-19 epidemic, a continuous Markov-chain model was, for the first time, developed in this work to predict the spread of COVID-19 infection. A probability matrix of infection was first developed in this model based upon the contact frequency of individuals within the population, the individual’s characteristics, and other factors that can effectively reflect the epidemic’s temporal and spatial variation characteristics. The Markov-chain model was then extended to incorporate both the mutation effect of COVID-19 and the decaying effect of antibodies. The developed comprehensive Markov-chain model that integrates the aforementioned factors was finally tested by real data to predict the trend of the COVID-19 epidemic. The result shows that our model can effectively avoid the prediction dilemma that may exist with traditional ordinary differential equations model, such as the susceptible–infectious–recovered (SIR) model. Meanwhile, it can forecast the epidemic distribution and predict the epidemic hotspots geographically at different times. It is also demonstrated in our result that the influence of the population’s spatial and geographic distribution in a herd infection event is needed in the model for a better prediction of the epidemic trend. At the same time, our result indicates that no simple derivative relationship exists between the threshold of herd immunity and the virus basic reproduction number R₀. The threshold of herd immunity achieved through natural immunity is significantly higher than 1 − 1/R₀. These not only explain the theoretical misconceptions of herd immunity thresholds in herd immunity theory but also provide a guidance for predicting the optimal vaccination coverage. In addition, our model can predict the temporal and spatial distribution of infections in different epidemic waves. It is implied from our model that it is challenging to eradicate COVID-19 in the short term for a large population size and a wide spatial distribution. It is predicted that COVID-19 is likely to coexist with humans for a long time and that it will exhibit multipoint epidemic effects at a later stage. The statistical evidence is consistent with our prediction and strongly supports our modeling results.

Optimal control analysis of COVID-19 vaccine epidemic model: a case study

The purpose of this research is to explore the complex dynamics and impact of vaccination in controlling COVID-19 outbreak. We formulate the classical epidemic compartmental model by introducing vaccination class. Initially, the proposed mathematical model is analyzed qualitatively. The basic reproductive number is computed and its numerical value is estimated using actual reported data of COVID-19 for Pakistan. The sensitivity analysis is performed to analyze the contribution of model embedded parameters in transmission of the disease. Further, we compute the equilibrium points and discussed its local and global stability. In order to investigate the influence of model key parameters on the transmission and controlling of the disease, we perform numerical simulations describing the impact of various scenarios of vaccine efficacy rate and other controlling measures. Further, on the basis of sensitivity analysis, the proposed model is restructured to obtained optimal control model by introducing time-dependent control variablesu 1 ( t ) for isolation,u 2 ( t ) for vaccine efficacy andu 3 ( t ) for treatment enhancement. Using optimal control theory and Pontryagin's maximum principle, the model is optimized and important optimality conditions are derived. In order to explore the impact of various control measures on the disease dynamics, we considered three different scenarios, i.e., single and couple and threefold controlling interventions. Finally, the graphical interpretation of each case is depicted and discussed in detail. The simulation results revealed that although single and couple scenarios can be implemented for the disease minimization but, the effective case to curtail the disease incidence is the threefold scenario which implements all controlling measures at the same time.

A new mathematical model of multi-faced COVID-19 formulated by fractional derivative chains

It has been reported that there are seven different types of coronaviruses realized by individuals, containing those responsible for the SARS, MERS, and COVID-19 epidemics. Nowadays, numerous designs of COVID-19 are investigated using different operators of fractional calculus. Most of these mathematical models describe only one type of COVID-19 (infected and asymptomatic). In this study, we aim to present an altered growth of two or more types of COVID-19. Our technique is based on the ABC-fractional derivative operator. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion between infected and asymptomatic people. The consequence is accordingly connected with a macroscopic rule for the individuals. In this analysis, we utilize the concept of a fractional chain. This type of chain is a fractional differential-difference equation combining continuous and discrete variables. The existence of solutions is recognized by formulating a matrix theory. The solution of the approximated system is shown to have a minimax point at the origin.

Modeling the dynamics of COVID-19 pandemic with implementation of intervention strategies

The ongoing COVID-19 epidemic spread rapidly throughout India, with 34,587,822 confirmed cases and 468,980 deaths as of November 30, 2021. Major behavioral, clinical, and state interventions have implemented to mitigate the outbreak and prevent the persistence of the COVID-19 in human-to-human transmission in India and worldwide. Hence, the mathematical study of the disease transmission becomes essential to illuminate the real nature of the transmission behavior and control of the diseases. We proposed a compartmental model that stratify into nine stages of infection. The incidence data of the SRAS-CoV-2 outbreak in India was analyzed for the best fit to the epidemic curve and we estimated the parameters from the best fitted curve. Based on the estimated model parameters, we performed a short-term prediction of our model. We performed sensitivity analysis with respect to R 0 and obtained that the disease transmission rate has an impact in reducing the spread of diseases. Furthermore, considering the non-pharmaceutical and pharmaceutical intervention policies as control functions, an optimal control problem is implemented to reduce the disease fatality. To mitigate the infected individuals and to minimize the cost of the controls, an objective functional has been formulated and solved with the aid of Pontryagin's maximum principle. This study suggest that the implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Our numerical simulations exhibit that the combination of two controls is more effective when compared with the combination of single control as well as no control.

Evaluating the Impact of SARS-CoV-2 Variants on the COVID-19 Epidemic and Social Restoration in the United States: A Mathematical Modelling Study

Background: Multiple SARS-CoV-2 variants are still rampant across the United States (US). We aimed to evaluate the impact of vaccination scale-up and potential reduction in the vaccination effectiveness on the COVID-19 epidemic and social restoration in the US. Methods: We extended a published compartmental model and calibrated the model to the latest US COVID-19 data. We estimated the vaccine effectiveness against the variant and evaluated the impact of a potential reduction in vaccine effectiveness on the epidemics. We explored the epidemic trends under different levels of social restoration. Results: We estimated the overall existing vaccine effectiveness against the variant as 88.5% (95% CI: 87.4-89.5%) with the vaccination coverage of 70% by the end of August, 2021. With this vaccine effectiveness and coverage, there would be 498,972 (109,998-885,947) cumulative infections and 15,443 (3,828-27,057) deaths nationwide over the next 12 months, of which 95.0% infections and 93.3% deaths were caused by the variant. Complete social restoration at 60, 65, 70% vaccination coverage would increase cumulative infections to 1.6 (0.2-2.9) million 0.7 (0.1-1.2) million, and 511,159 (110,578-911,740), respectively. At same time it would increase cumulative deaths to 39,040 (5,509-72,570), 19,562 (3,873-35,250), 15,739 (3,841-27,638), respectively. However, if the vaccine effectiveness were reduced to 75%, 50% or 25% due to new SARS-CoV-2 variants, there would be 667,075 (130,682-1,203,468), 1.7 (0.2-3.2) million, 19.0 (5.3-32.7) million new infections and 19,249 (4,281-34,217), 42,265 (5,081-79,448), 426,860 (117,229-736,490) cumulative deaths to occur over the next 12 months. Further, social restoration at a lower vaccination coverage would lead to even greater secondary outbreaks. Conclusion: Current COVID-19 vaccines remain effective against the SARS-CoV-2 variant, and 70% vaccination coverage would be sufficient to restore social activities to a pre-pandemic level. Further reduction in vaccine effectiveness against SARS-CoV-2 variants would result in a potential surge of the epidemic. Multiple measures, including public health interventions, vaccination scale-up and development of a new vaccine booster, should be integrated to counter the new challenges of new SARS-CoV-2 variants.

Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory

The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The COVID-19 is one of the deadliest pandemics in history due to its high mortality rate in a short period. Many approaches have been adopted for disease minimization and eradication. In this paper, we studied the impact of various constant and time-dependent variable control measures coupled with vaccination on the dynamics of COVID-19. The optimal control theory is used to optimize the model and set an effective control intervention for the infection. Initially, we formulate the mathematical epidemic model for the COVID-19 without variable controls. The model basic mathematical assessment is presented. The nonlinear least-square procedure is utilized to parameterize the model from actual cases reported in Pakistan. A well-known technique based on statistical tools known as the Latin-hypercube sampling approach (LHS) coupled with the partial rank correlation coefficient (PRCC) is applied to present the model global sensitivity analysis. Based on global sensitivity analysis, the COVID-19 vaccine model is reformulated to obtain a control problem by introducing three time dependent control variables for isolation, vaccine efficacy and treatment enhancement represented byu 1 ( t ) ,u 2 ( t ) andu 3 ( t ) , respectively. The necessary optimality conditions of the control problem are derived via the optimal control theory. Finally, the simulation results are depicted with and without variable controls using the well-known Runge-Kutta numerical scheme. The simulation results revealed that time-dependent control measures play a vital role in disease eradication.

COVID-19 severity determinants inferred through ecological and epidemiological modeling

Understanding variations in the severity of infectious diseases is essential for planning proper mitigation strategies. Determinants of COVID-19 clinical severity are commonly assessed by transverse or longitudinal studies of the fatality counts. However, the fatality counts depend both on disease clinical severity and transmissibility, as more infected also lead to more deaths. Instead, we use epidemiological modeling to propose a disease severity measure that accounts for the underlying disease dynamics. The measure corresponds to the ratio of population-averaged mortality and recovery rates (m/r), is independent of the disease transmission dynamics (i.e., the basic reproduction number), and has a direct mechanistic interpretation. We use this measure to assess demographic, medical, meteorological, and environmental factors associated with the disease severity. For this, we employ an ecological regression study design and analyze different US states during the first disease outbreak. Principal Component Analysis, followed by univariate, and multivariate analyses based on machine learning techniques, is used for selecting important predictors. The usefulness of the introduced severity measure and the validity of the approach are confirmed by the fact that, without using prior knowledge from clinical studies, we recover the main significant predictors known to influence disease severity, in particular age, chronic diseases, and racial factors. Additionally, we identify long-term pollution exposure and population density as not widely recognized (though for the pollution previously hypothesized) significant predictors. The proposed measure is applicable for inferring severity determinants not only of COVID-19 but also of other infectious diseases, and the obtained results may aid a better understanding of the present and future epidemics. Our holistic, systematic investigation of disease severity at the human-environment intersection by epidemiological dynamical modeling and machine learning ecological regressions is aligned with the One Health approach. The obtained results emphasize a syndemic nature of COVID-19 risks.

A dynamical map to describe COVID-19 epidemics

Nonlinear dynamics perspective is an interesting approach to describe COVID-19 epidemics, providing information to support strategic decisions. This paper proposes a dynamical map to describe COVID-19 epidemics based on the classical susceptible-exposed-infected-recovered (SEIR) differential model, incorporating vaccinated population. On this basis, the novel map represents COVID-19 discrete-time dynamics by adopting three populations: infected, cumulative infected and vaccinated. The map promotes a dynamical description based on algebraic equations with a reduced number of variables and, due to its simplicity, it is easier to perform parameter adjustments. In addition, the map description allows analytical calculations of useful information to evaluate the epidemic scenario, being important to support strategic decisions. In this regard, it should be pointed out the estimation of the number deaths, infection rate and the herd immunization point. Numerical simulations show the model capability to describe COVID-19 dynamics, capturing the main features of the epidemic evolution. Reported data from Germany, Italy and Brazil are of concern showing the map ability to describe different scenario patterns that include multi-wave pattern with bell shape and plateaus characteristics. The effect of vaccination is analyzed considering different campaign strategies, showing its importance to control the epidemics.

The Impact of Disease Control Measures on the Spread of COVID-19 in the Province of Sindh, Pakistan

The province of Sindh reported the first COVID-19 case in Pakistan on 26th February 2020. The Government of Sindh has employed numerous control measures to limit its spread. However, for low-and middle-income countries such as Pakistan, the management protocols for controlling a pandemic are not always as definitive as they would be in other developed nations. Given the dire socio-economic conditions of Sindh, continuation of province-wise lockdowns may inadvertently cause a potential economic breakdown. By using a data driven SEIR modelling framework, this paper describes the evolution of the epidemic projections because of government control measures. The data from reported COVID-19 prevalence and google mobility is used to parameterize the model at different time points. These time points correspond to the government's call for advice on the prerequisite actions required to curtail the spread of COVID-19 in Sindh. Our model predicted the epidemic peak to occur by 18th June 2020 with approximately 3500 reported cases at that peak, this projection correlated with the actual recorded peak during the first wave of the disease in Sindh. The impact of the governmental control actions and religious ceremonies on the epidemic profile during this first wave of COVID-19 are clearly reflected in the model outcomes through variations in the epidemic peaks. We also report these variations by displaying the trajectory of the epidemics had the control measures been guided differently; the epidemic peak may have occurred as early as the end of May 2020 with approximately 5000 reported cases per day had there been no control measures and as late as August 2020 with only around 2000 cases at the peak had the lockdown continued, nearly flattening the epidemic curve.

A mathematical model for human-to-human transmission of COVID-19: a case study for Turkey's data

In this study, a mathematical model for simulating the human-to-human transmission of the novel coronavirus disease (COVID-19) is presented for Turkey's data. For this purpose, the total population is classified into eight epidemiological compartments, including the super-spreaders. The local stability and sensitivity analysis in terms of the model parameters are discussed, and the basic reproduction number, R₀, is derived. The system of nonlinear ordinary differential equations is solved by using the Galerkin finite element method in the FEniCS environment. Furthermore, to guide the interested reader in reproducing the results and/or performing their own simulations, a sample solver is provided. Numerical simulations show that the proposed model is quite convenient for Turkey's data when used with appropriate parameters.

Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon

This work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). A multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism is proposed first. Indeed, there are human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self-infection by susceptible individuals. The global stability of the disease-free equilibrium is shown when a given threshold T 0 is less or equal to 1 and the basic reproduction number R 0 is calculated. A convergence index T 1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of infectious extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. Using Partial Rank Correlation Coefficient with a three levels fractional experimental design, the sensitivity of  R 0 , T 0 and T 1 to control parameters is evaluated. Following this study, the most significant parameter is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into account economic impacts of SARS-CoV-2, optimal fighting strategies are determined and discussed. The study is applied to real and available data from Cameroon with a model fitting. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy against SARS-CoV-2.

COVID-19 Critical Care Simulations: An International Cross-Sectional Survey

Objective: To describe the utility and patterns of COVID-19 simulation scenarios across different international healthcare centers. Methods: This is a cross-sectional, international survey for multiple simulation centers team members, including team-leaders and healthcare workers (HCWs), based on each center's debriefing reports from 30 countries in all WHO regions. The main outcome measures were the COVID-19 simulations characteristics, facilitators, obstacles, and challenges encountered during the simulation sessions. Results: Invitation was sent to 343 simulation team leaders and multidisciplinary HCWs who responded; 121 completed the survey. The frequency of simulation sessions was monthly (27.1%), weekly (24.8%), twice weekly (19.8%), or daily (21.5%). Regarding the themes of the simulation sessions, they were COVID-19 patient arrival to ER (69.4%), COVID-19 patient intubation due to respiratory failure (66.1%), COVID-19 patient requiring CPR (53.7%), COVID-19 transport inside the hospital (53.7%), COVID-19 elective intubation in OR (37.2%), or Delivery of COVID-19 mother and neonatal care (19%). Among participants, 55.6% reported the team's full engagement in the simulation sessions. The average session length was 30-60 min. The debriefing process was conducted by the ICU facilitator in (51%) of the sessions followed by simulation staff in 41% of the sessions. A total of 80% reported significant improvement in clinical preparedness after simulation sessions, and 70% were satisfied with the COVID-19 sessions. Most perceived issues reported were related to infection control measures, followed by team dynamics, logistics, and patient transport issues. Conclusion: Simulation centers team leaders and HCWs reported positive feedback on COVID-19 simulation sessions with multidisciplinary personnel involvement. These drills are a valuable tool for rehearsing safe dynamics on the frontline of COVID-19. More research on COVID-19 simulation outcomes is warranted; to explore variable factors for each country and healthcare system.