SEAHIR: A Specialized Compartmental Model for COVID-19

Latent classification model for censored longitudinal binary outcome

Latent classification model is a class of statistical methods for identifying unobserved class membership among the study samples using some observed data. In this study, we proposed a latent classification model that takes a censored longitudinal binary outcome variable and uses its changing pattern over time to predict individuals' latent class membership. Assuming the time-dependent outcome variables follow a continuous-time Markov chain, the proposed method has two primary goals: (1) estimate the distribution of the latent classes and predict individuals' class membership, and (2) estimate the class-specific transition rates and rate ratios. To assess the model's performance, we conducted a simulation study and verified that our algorithm produces accurate model estimates (ie, small bias) with reasonable confidence intervals (ie, achieving approximately 95% coverage probability). Furthermore, we compared our model to four other existing latent class models and demonstrated that our approach yields higher prediction accuracies for latent classes. We applied our proposed method to analyze the COVID-19 data in Houston, Texas, US collected between January first 2021 and December 31st 2021. Early reports on the COVID-19 pandemic showed that the severity of a SARS-CoV-2 infection tends to vary greatly by cases. We found that while demographic characteristics explain some of the differences in individuals' experience with COVID-19, some unaccounted-for latent variables were associated with the disease.

On the impact of mass screening for SARS-CoV-2 through self-testing in Greece

Background

Screening programs that pre-emptively and routinely test population groups for disease at a massive scale were first implemented during the COVID-19 pandemic in a handful of countries. One of these countries was Greece, which implemented a mass self-testing program during 2021. In contrast to most other non-pharmaceutical interventions (NPIs), mass self-testing programs are particularly attractive for their relatively small financial and social burden, and it is therefore important to understand their effectiveness to inform policy makers and public health officials responding to future pandemics. This study aimed to estimate the number of deaths and hospitalizations averted by the program implemented in Greece and evaluate the impact of several operational decisions.

Methods

Granular data from the mass self-testing program deployed by the Greek government between April and December 2021 were obtained. The data were used to fit a novel compartmental model that was developed to describe the dynamics of the COVID-19 pandemic in Greece in the presence of self-testing. The fitted model provided estimates on the effectiveness of the program in averting deaths and hospitalizations. Sensitivity analyses were used to evaluate the impact of operational decisions, including the scale of the program, targeting of sub-populations, and sensitivity (i.e., true positive rate) of tests.

Results

Conservative estimates show that the program reduced the reproduction number by 4%, hospitalizations by 25%, and deaths by 20%, translating into approximately 20,000 averted hospitalizations and 2,000 averted deaths in Greece between April and December 2021.

Conclusion

Mass self-testing programs are efficient NPIs with minimal social and financial burden; therefore, they are invaluable tools to be considered in pandemic preparedness and response.

Reconstruction of incidence reporting rate for SARS-CoV-2 Delta variant of COVID-19 pandemic in the US

In recent years, advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for future projections, prevention, and control. Unlike other system parameters, i.e., incubation and recovery rates, the case reporting rate, Ψ, and the time-dependent effective reproduction number, R e ( t ) , are directly influenced by a large number of factors making it impossible to pre-estimate these parameters in any meaningful way. In this study, we propose a novel iteratively-regularized trust-region optimization algorithm, combined with SuSvIuIvRD compartmental model, for stable reconstruction of Ψ and R e ( t ) from reported epidemic data on vaccination percentages, incidence cases, and daily deaths. The innovative regularization procedure exploits (and takes full advantage of) a unique structure of the Jacobian and Hessian approximation for the nonlinear observation operator. The proposed inversion method is thoroughly tested with synthetic and real SARS-CoV-2 Delta variant data for different regions in the United States of America from July 9, 2021, to November 25, 2021. Our study shows that case reporting rate during the Delta wave of COVID-19 pandemic in the US is between 12% and 37%, with most states being in the range from 15% to 25%. This confirms earlier accounts on considerable under-reporting of COVID-19 cases due to the impact of "silent spreaders" and the limitations of testing.

Susceptible-Infected-Susceptible type COVID-19 spread with collective effects

Many models developed to forecast and attempt to understand the COVID-19 pandemic are highly complex, and few take collective behavior into account. As the pandemic progressed individual recurrent infection was observed and simpler susceptible-infected type models were introduced. However, these do not include mechanisms to model collective behavior. Here, we introduce an extension of the SIS model that accounts for collective behavior and show that it has four equilibria. Two of the equilibria are the standard SIS model equilibria, a third is always unstable, and a fourth where collective behavior and infection prevalence interact to produce either node-like or oscillatory dynamics. We then parameterized the model using estimates of the transmission and recovery rates for COVID-19 and present phase diagrams for fixed recovery rate and free transmission rate, and both rates fixed. We observe that regions of oscillatory dynamics exist in both cases and that the collective behavior parameter regulates their extent. Finally, we show that the system exhibits hysteresis when the collective behavior parameter varies over time. This model provides a minimal framework for explaining oscillatory phenomena such as recurring waves of infection and hysteresis effects observed in COVID-19, and other SIS-type epidemics, in terms of collective behavior.

Dynamically adjustable SVEIR(MH) model of multiwave epidemics: Estimating the effects of public health measures against COVID-19

The COVID-19 pandemic was characterized by multiple subsequent, overlapping outbreaks, as well as extremely rapid changes in viral genomes. The information about local epidemics spread and the epidemic control measures was shared on a daily basis (number of cases and deaths) via centralized repositories. The vaccines were developed within the first year of the pandemic. New modes of monitoring and sharing of epidemic data were implemented using Internet resources. We modified the basic SEIR compartmental model to include public health measures, multiwave scenarios, and the variation of viral infectivity and transmissibility reflected by the basic reproduction number R0 of emerging viral variants. SVEIR(MH) model considers the capacity of the medical system, lockdowns, vaccination, and changes in viral reproduction rate on the epidemic spread. The developed model uses daily infection reports for assessing the epidemic dynamics, and daily changes of mobility data from mobile phone networks to assess the lockdown effectiveness. This model was deployed to six European regions Baden-Württemberg (Germany), Belgium, Czechia, Lombardy (Italy), Sweden, and Switzerland for the first 2 years of the pandemic. The correlation coefficients between observed and reported infection data showed good concordance for both years of the pandemic (ρ = 0.84-0.94 for the raw data and ρ = 0.91-0.98 for smoothed 7-day averages). The results show stability across the regions and the different epidemic waves. Optimal control of epidemic waves can be achieved by dynamically adjusting epidemic control measures in real-time. SVEIR(MH) model can simulate different scenarios and inform adjustments to the public health policies to achieve the target outcomes. Because this model is highly representative of actual epidemic situations, it can be used to assess both the public health and socioeconomic effects of the public health measures within the first 7 days of the outbreak.

Incidence rate drive the multiple wave in the COVID-19 pandemic

The last three years have been the most challenging for humanity due to the COVID-19 pandemic. The novel viral infection has eventually been able to infect most of the human population. It is now considered to be in the endemic stage, meaning it will remain in our world throughout our lifetime. There will be an intermittent outbreak of the COVID infection from time to time. Therefore, it is necessary to formulate a robust Mathematical model to study the dynamics of disease to have a control mechanism in place. In this article, we suggest a modified MSEIR model to explain the dynamics of COVID-19 infection. We assume that a susceptible person contracting the coronavirus develops a transient immunity to the illness. Further, infectives comprise asymptomatic, symptomatic, hospitalized and quarantined individuals. We assume that the incidence rate is of standard type, and susceptible can only become infective if they come in contact with either asymptomatic or symptomatic individuals. This basic and simple model effectively models the various waves every country has seen during the Pandemic. The simple analysis shows that the model could suggest various waves in future if we carefully select the incidence rate for the infection. In summary, we have discussed the following major points in this article. •We have analysed for local behavior infection-free equilibrium solution. Further, a thorough numerical exploration with various parameter settings has been performed to obtain the different cases of infection dynamics of the coronavirus epidemic.•We have found some interesting scenarios which explain the emergence of multiple waves observed in many countries.

Evaluation of phase-adjusted interventions for COVID-19 using an improved SEIR model

A local COVID-19 outbreak with two community clusters occurred in a large industrial city, Shaoxing, China, in December 2021 after serial interventions were imposed. We aimed to understand the reason by analysing the characteristics of the outbreak and evaluating the effects of phase-adjusted interventions. Publicly available data from 7 December 2021 to 25 January 2022 were collected to analyse the epidemiological characteristics of this outbreak. The incubation period was estimated using Hamiltonian Monte Carlo method. A well-fitted extended susceptible-exposed-infectious-recovered model was used to simulate the impact of different interventions under various combination of scenarios. There were 387 SARS-CoV-2-infected cases identified, and 8.3% of them were initially diagnosed as asymptomatic cases. The estimated incubation period was 5.4 (95% CI 5.2-5.7) days for all patients. Strengthened measures of comprehensive quarantine based on tracing led to less infections and a shorter duration of epidemic. With a same period of incubation, comprehensive quarantine was more effective in containing the transmission than other interventions. Our findings reveal an important role of tracing and comprehensive quarantine in blocking community spread when a cluster occurred. Regions with tense resources can adopt home quarantine as a relatively affordable and low-impact intervention measure compared with centralized quarantine.

Mobility data shows effectiveness of control strategies for COVID-19 in remote, sparse and diffuse populations

Data that is collected at the individual-level from mobile phones is typically aggregated to the population-level for privacy reasons. If we are interested in answering questions regarding the mean, or working with groups appropriately modeled by a continuum, then this data is immediately informative. However, coupling such data regarding a population to a model that requires information at the individual-level raises a number of complexities. This is the case if we aim to characterize human mobility and simulate the spatial and geographical spread of a disease by dealing in discrete, absolute numbers. In this work, we highlight the hurdles faced and outline how they can be overcome to effectively leverage the specific dataset: Google COVID-19 Aggregated Mobility Research Dataset (GAMRD). Using a case study of Western Australia, which has many sparsely populated regions with incomplete data, we firstly demonstrate how to overcome these challenges to approximate absolute flow of people around a transport network from the aggregated data. Overlaying this evolving mobility network with a compartmental model for disease that incorporated vaccination status we run simulations and draw meaningful conclusions about the spread of COVID-19 throughout the state without de-anonymizing the data. We can see that towns in the Pilbara region are highly vulnerable to an outbreak originating in Perth. Further, we show that regional restrictions on travel are not enough to stop the spread of the virus from reaching regional Western Australia. The methods explained in this paper can be therefore used to analyze disease outbreaks in similarly sparse populations. We demonstrate that using this data appropriately can be used to inform public health policies and have an impact in pandemic responses.

A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19

The COVID-19 pandemic has ravaged global health and national economies worldwide. Testing and isolation are effective control strategies to mitigate the transmission of COVID-19, especially in the early stage of the disease outbreak. In this paper, we develop a deterministic model to investigate the impact of testing and compliance with isolation on the transmission of COVID-19. We derive the control reproduction number R C , which gives the threshold for disease elimination or prevalence. Using data from New York State in the early stage of the disease outbreak, we estimate R C = 7.989 . Both elasticity and sensitivity analyses show that testing and compliance with isolation are significant in reducing R C and disease prevalence. Simulation reveals that only high testing volume combined with a large proportion of individuals complying with isolation have great impact on mitigating the transmission. The testing starting date is also crucial: the earlier testing is implemented, the more impact it has on reducing the infection. The results obtained here would also be helpful in developing guidelines of early control strategies for pandemics similar to COVID-19.

The impact of traffic control measures on the spread of COVID-19 within urban agglomerations based on a modified epidemic model

With the spatial structure of urban agglomerations, well-developed transportation networks and close economic ties can increase the risk of intercity transmission of infectious diseases. To reveal the epidemic transmission mechanism in urban agglomerations and to explore the effectiveness of traffic control measures, this study proposes an Urban-Agglomeration-based Epidemic and Mobility Model (UAEMM) based on the reality of urban transportation networks and population mobility factors. Since the model considers the urban population inflow, along with the active intracity population, it can be used to estimate the composition of urban cases. The model was applied to the Chang-Zhu-Tan urban agglomeration, and the results show that the model can better simulate the transmission process of the urban agglomeration for a certain scale of epidemic. The number of cases within the urban agglomeration is higher than the number of cases imported into the urban agglomeration from external cities. The composition of cases in the core cities of the urban agglomeration changes with the adjustment of prevention and control measures. In contrast, the number of cases imported into the secondary cities is consistently greater than the number of cases transmitted within the cities. A traffic control measures discount factor is introduced to simulate the development of the epidemic in the urban agglomeration under the traffic control measures of the first-level response to major public health emergency, traffic blockades in infected areas, and public transportation shutdowns. If none of those traffic control measures had been taken after the outbreak of COVID-19, the number of cases in the urban agglomeration would theoretically have increased to 3879, which is 11.61 times the actual number of cases that occurred. If only one traffic control measure had been used alone, each of the three measures would have reduced the number of cases in the urban agglomeration to 30.19 %-57.44 % of the theoretical values of infection cases, with the best blocking effect coming from the first-level response to major public health emergency. Traffic control measures have a significant effect in interrupting the spread of COVID-19 in urban agglomerations. The methodology and main findings presented in this paper are of general interest and can also be used in studies in other countries for similar purposes to help understand the spread of COVID-19 in urban agglomerations.

COVID-19 contact tracing as an indicator for evaluating the pandemic situation: a simulation study

BACKGROUND

Contact tracing is a fundamental intervention in Public Health. When systematically applied, it enables the breaking of chains of transmission, important in controlling COVID-19 transmission. In a theoretically perfect contact tracing, all new cases should occur among quarantined individuals and an epidemic should vanish. However, the availability of resources influences the capacity to perform contact tracing. Therefore, it prompts the need to estimate its effectiveness threshold. We propose that this effectiveness threshold may be indirectly estimated by the ratio of COVID-19 cases arising from quarantined high-risk contacts, where higher ratios indicate better control and under a threshold contact tracing may fail and other restrictions become necessary.

OBJECTIVE

To study the ratio of COVID-19 cases in high-risk contacts quarantined through contact tracing and its potential use as an ancillary pandemic control indicator.

METHODS

We built a 6-compartment epidemiological model to emulate COVID-19 infection flow according to publicly available data from Portuguese authorities. Our model extended the usual SEIR model by adding a compartment Q with individuals in mandated quarantine that could develop infection or return to the susceptible pool; and a compartment P with individuals protected from infection due to vaccination. To model infection dynamics, data on SARS-CoV-2 infection risk, time until infection and vaccine efficacy were collected. Estimation was needed for vaccine data, to reflect the timing of inoculation and booster efficacy. Two simulations were built: the first (A) adjusting for the presence and absence of variants or vaccination, and the second (B) maximizing infection risk in quarantined individuals. Both simulations were based on a set of 100 unique parameterizations. The daily ratio of infected cases arising from high-risk contacts (q estimate) was calculated. A theoretical effectiveness threshold of contact tracing was defined for 14-day average q estimates based on the classification of COVID-19 daily cases according to the Pandemic phases and was compared with the timing of population lockdowns in Portugal. A sensitivity analysis was performed to understand the relation between different parameter values and the threshold obtained.

RESULTS

An inverse relationship was found between the q estimate and the daily cases in both simulations (correlations over -0.70). The theoretical effectiveness thresholds for both simulations attained an Alert phase predictive positive value of over 70% and could have anticipated the need for additional measures in at least 4 days for the second and fourth lockdowns. Sensitivity analysis showed that only the infection risk and the booster dose efficacy at inoculation significantly impacted the q estimates.

CONCLUSIONS

We demonstrate the impact of applying an effectiveness threshold for contact tracing in decision-making. While only theoretical thresholds could be provided, their relationship with the number of confirmed cases and prediction of pandemic phases shows the role as indirect indicator of the efficacy of contact tracing.

CLINICALTRIAL

Multiple Concurrent Causal Relationships and Multiple Governance Pathways for Non-Pharmaceutical Intervention Policies in Pandemics: A Fuzzy Set Qualitative Comparative Analysis Based on 102 Countries and Regions

The global outbreak of COVID-19 has been wreaking havoc on all aspects of human societies. In addition to pharmaceutical interventions, non-pharmaceutical intervention policies have been proven to be crucial in slowing down the spread of the virus and reducing the impact of the outbreak on economic development, daily life, and social stability. However, no studies have focused on which non-pharmaceutical intervention policies are more effective; this is the focus of our study. We used data samples from 102 countries and regions around the world and selected seven categories of related policies, including work and school suspensions, assembly restrictions, movement restrictions, home isolation, international population movement restrictions, income subsidies, and testing and screening as the condition variables. A susceptible-exposed-infected-quarantined-recovered (SEIQR) model considering non-pharmaceutical intervention policies and latency with infectiousness was constructed to calculate the epidemic transmission rate as the outcome variable, and a fuzzy set qualitative comparative analysis (fsQCA) method was applied to explore the multiple concurrent causal relationships and multiple governance paths of non-pharmaceutical intervention policies for epidemics from the configuration perspective. We found a total of four non-pharmaceutical intervention policy pathways. Among them, L1 was highly suppressive, L2 was moderately suppressive, and L3 was externally suppressive. The results also showed that individual non-pharmaceutical intervention policy could not effectively suppress the spread of the pandemic. Moreover, three specific non-pharmaceutical intervention policies, including work stoppage and school closure, testing and screening, and economic subsidies, had a universal effect in the policies grouping for effective control of the pandemic transmission.

Genome Structure, Life Cycle, and Taxonomy of Coronaviruses and the Evolution of SARS-CoV-2

Coronaviruses have a broad host range and exhibit high zoonotic potential. In this chapter, we describe their genomic organization in terms of encoded proteins and provide an introduction to the peculiar discontinuous transcription mechanism. Further, we present evolutionary conserved genomic RNA secondary structure features, which are involved in the complex replication mechanism. With a focus on computational methods, we review the emergence of SARS-CoV-2 starting with the 2019 strains. In that context, we also discuss the debated hypothesis of whether SARS-CoV-2 was created in a laboratory. We focus on the molecular evolution and the epidemiological dynamics of this recently emerged pathogen and we explain how variants of concern are detected and characterised. COVID-19, the disease caused by SARS-CoV-2, can spread through different transmission routes and also depends on a number of risk factors. We describe how current computational models of viral epidemiology, or more specifically, phylodynamics, have facilitated and will continue to enable a better understanding of the epidemic dynamics of SARS-CoV-2.

Assessment Model for Rapid Suppression of SARS-CoV-2 Transmission under Government Control

The rapid suppression of SARS-CoV-2 transmission remains a priority for maintaining public health security throughout the world, and the agile adjustment of government prevention and control strategies according to the spread of the epidemic is crucial for controlling the spread of the epidemic. Thus, in this study, a multi-agent modeling approach was developed for constructing an assessment model for the rapid suppression of SARS-CoV-2 transmission under government control. Different from previous mathematical models, this model combines computer technology and geographic information system to abstract human beings in different states into micro-agents with self-control and independent decision-making ability; defines the rules of agent behavior and interaction; and describes the mobility, heterogeneity, contact behavior patterns, and dynamic interactive feedback mechanism of space environment. The real geospatial and social environment in Taiyuan was considered as a case study. In the implemented model, the government agent could adjust the response level and prevention and control policies for major public health emergencies in real time according to the development of the epidemic, and different intervention strategies were provided to improve disease control methods in the simulation experiment. The simulation results demonstrate that the proposed model is widely applicable, and it can not only judge the effectiveness of intervention measures in time but also analyze the virus transmission status in complex urban systems and its change trend under different intervention measures, thereby providing scientific guidance to support urban public health safety.

A Modified PINN Approach for Identifiable Compartmental Models in Epidemiology with Application to COVID-19

Many approaches using compartmental models have been used to study the COVID-19 pandemic, with machine learning methods applied to these models having particularly notable success. We consider the Susceptible-Infected-Confirmed-Recovered-Deceased (SICRD) compartmental model, with the goal of estimating the unknown infected compartment I, and several unknown parameters. We apply a variation of a "Physics Informed Neural Network" (PINN), which uses knowledge of the system to aid learning. First, we ensure estimation is possible by verifying the model's identifiability. Then, we propose a wavelet transform to process data for the network training. Finally, our central result is a novel modification of the PINN's loss function to reduce the number of simultaneously considered unknowns. We find that our modified network is capable of stable, efficient, and accurate estimation, while the unmodified network consistently yields incorrect values. The modified network is also shown to be efficient enough to be applied to a model with time-varying parameters. We present an application of our model results for ranking states by their estimated relative testing efficiency. Our findings suggest the effectiveness of our modified PINN network, especially in the case of multiple unknown variables.

Ranking the effectiveness of non-pharmaceutical interventions to counter COVID-19 in UK universities with vaccinated population

Several universities around the world have resumed in-person teaching after successful vaccination campaigns have covered 70/80% of the population. In this study, we combine a new compartmental model with an optimal control formulation to discover, among different non-pharmaceutical interventions, the best prevention strategy to maximize on-campus activities while keeping spread under control. Composed of two interconnected Susceptible-Exposed-Infected-Quarantined-Recovered (SEIQR) structures, the model enables staff-to-staff infections, student-to-staff cross infections, student-to-student infections, and environment-to-individual infections. Then, we model input variables representing the implementation of different non-pharmaceutical interventions and formulate and solve optimal control problems for four desired scenarios: minimum number of cases, minimum intervention, minimum non-quarantine intervention, and minimum quarantine intervention. Our results reveal the particular significance of mask wearing and social distancing in universities with vaccinated population (with proportions according to UK data). The study also reveals that quarantining infected students has a higher importance than quarantining staff. In contrast, other measures such as environmental disinfection seems to be less important.

How Effective Is a Traffic Control Policy in Blocking the Spread of COVID-19? A Case Study of Changsha, China

(1) Background: COVID-19 is still affecting people’s daily lives. In the past two years of epidemic control, a traffic control policy has been an important way to block the spread of the epidemic. (2) Objectives: To delve into the blocking effects of different traffic control policies on COVID-19 transmission. (3) Methods: Based on the classical SIR model, this paper designs and improves the coefficient of the infectious rate, and it builds a quantitative SEIR model that considers the infectivity of the exposed for traffic control policies. Taking Changsha, a typical city of epidemic prevention and control, as a study case, this paper simulates the epidemic trends under three traffic control policies adopted in Changsha: home quarantine, road traffic control, and public transport suspension. Meanwhile, to explore the time sensitivity of all traffic control policies, this paper sets four distinct scenarios where the traffic control policies were implemented at the first medical case, delayed by 3, 5, and 7 days, respectively. (4) Results: The implementation of the traffic control policies has decreased the peak value of the population of the infective in Changsha by 66.03%, and it has delayed the peak period by 58 days; with the home-quarantine policy, the road traffic control policy, and the public transport suspension policy decreasing the peak value of the population of the infective by 56.81%, 39.72%, and 45.31% and delaying the peak period by 31, 18, and 21 days, respectively; in the four scenarios where the traffic control policies had been implemented at the first medical case, delayed by 3, 5, and 7 days, respectively, the variations of both the peak value and the peak period timespan of confirmed cases under the home-quarantine policy would have been greater than under the road traffic control and the public transport suspension policies. (5) Conclusions: The implementation of traffic control policies is significantly effective in blocking the epidemic across the city of Changsha. The home-quarantine policy has the highest time sensitivity: the earlier this policy is implemented, the more significant its blocking effect on the spread of the epidemic.

Application of genetic algorithm combined with improved SEIR model in predicting the epidemic trend of COVID-19, China

Since the outbreak of the 2019 Coronavirus disease (COVID-19) at the end of 2019, it has caused great adverse effects on the whole world, and it has been hindering the global economy. It is ergent to establish an infectious disease model for the current COVID-19 epidemic to predict the trend of the epidemic. Based on the SEIR model, the improved SEIR models were established with considering the incubation period, the isolated population, and genetic algorithm (GA) parameter optimization method. The improved SEIR models can predict the trend of the epidemic situation better and obtain the more accurate epidemic-related parameters. Comparing some key parameters, it is capable to evaluate the impact of different epidemic prevention measures and the implementation of different epidemic prevention levels on the COVID-19, which has significant guidance for further epidemic prevention measures.

Optimal Drug Regimen and Combined Drug Therapy and Its Efficacy in the Treatment of COVID-19: A Within-Host Modeling Study

The COVID-19 pandemic has resulted in more than 524 million cases and 6 million deaths worldwide. Various drug interventions targeting multiple stages of COVID-19 pathogenesis can significantly reduce infection-related mortality. The current within-host mathematical modeling study addresses the optimal drug regimen and efficacy of combination therapies in the treatment of COVID-19. The drugs/interventions considered include Arbidol, Remdesivir, Interferon (INF) and Lopinavir/Ritonavir. It is concluded that these drugs, when administered singly or in combination, reduce the number of infected cells and viral load. Four scenarios dealing with the administration of a single drug, two drugs, three drugs and all four are discussed. In all these scenarios, the optimal drug regimen is proposed based on two methods. In the first method, these medical interventions are modeled as control interventions and a corresponding objective function and optimal control problem are formulated. In this framework, the optimal drug regimen is derived. Later, using the comparative effectiveness method, the optimal drug regimen is derived based on the basic reproduction number and viral load. The average number of infected cells and viral load decreased the most when all four drugs were used together. On the other hand, the average number of susceptible cells decreased the most when Arbidol was administered alone. The basic reproduction number and viral load decreased the most when all four interventions were used together, confirming the previously obtained finding of the optimal control problem. The results of this study can help physicians make decisions about the treatment of the life-threatening COVID-19 infection.

Why Controlling the Asymptomatic Infection Is Important: A Modelling Study with Stability and Sensitivity Analysis

The large proportion of asymptomatic patients is the major cause leading to the COVID-19 pandemic which is still a significant threat to the whole world. A six-dimensional ODE system (SEIAQR epidemical model) is established to study the dynamics of COVID-19 spreading considering infection by exposed, infected, and asymptomatic cases. The basic reproduction number derived from the model is more comprehensive including the contribution from the exposed, infected, and asymptomatic patients. For this more complex six-dimensional ODE system, we investigate the global and local stability of disease-free equilibrium, as well as the endemic equilibrium, whereas most studies overlooked asymptomatic infection or some other virus transmission features. In the sensitivity analysis, the parameters related to the asymptomatic play a significant role not only in the basic reproduction number R0. It is also found that the asymptomatic infection greatly affected the endemic equilibrium. Either in completely eradicating the disease or achieving a more realistic goal to reduce the COVID-19 cases in an endemic equilibrium, the importance of controlling the asymptomatic infection should be emphasized. The three-dimensional phase diagrams demonstrate the convergence point of the COVID-19 spreading under different initial conditions. In particular, massive infections will occur as shown in the phase diagram quantitatively in the case R0>1. Moreover, two four-dimensional contour maps of Rt are given varying with different parameters, which can offer better intuitive instructions on the control of the pandemic by adjusting policy-related parameters.

The Hybrid Incidence Susceptible-Transmissible-Removed Model for Pandemics : Scaling Time to Predict an Epidemic's Population Density Dependent Temporal Propagation

The susceptible-transmissible-removed (STR) model is a deterministic compartment model, based on the susceptible-infected-removed (SIR) prototype. The STR replaces 2 SIR assumptions. SIR assumes that the emigration rate (due to death or recovery) is directly proportional to the infected compartment’s size. The STR replaces this assumption with the biologically appropriate assumption that the emigration rate is the same as the immigration rate one infected period ago. This results in a unique delay differential equation epidemic model with the delay equal to the infected period. Hamer’s mass action law for epidemiology is modified to resemble its chemistry precursor—the law of mass action. Constructing the model for an isolated population that exists on a surface bounded by the extent of the population’s movements permits compartment density to replace compartment size. The STR reduces to a SIR model in a timescale that negates the delay—the transmissible timescale. This establishes that the SIR model applies to an isolated population in the disease’s transmissible timescale. Cyclical social interactions will define a rhythmic timescale. It is demonstrated that the geometric mean maps transmissible timescale properties to their rhythmic timescale equivalents. This mapping defines the hybrid incidence (HI). The model validation demonstrates that the HI-STR can be constructed directly from the disease’s transmission dynamics. The basic reproduction number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}R0) is an epidemic impact property. The HI-STR model predicts that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0 \propto \root \mathfrak{B} \of {\rho_n}$$\end{document}R0∝ρnB where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document}ρn is the population density, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{B}}$$\end{document}B is the ratio of time increments in the transmissible- and rhythmic timescales. The model is validated by experimentally verifying the relationship. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}R0’s dependence on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document}ρn is demonstrated for droplet-spread SARS in Asian cities, aerosol-spread measles in Europe and non-airborne Ebola in Africa.

Measuring the impact of nonpharmaceutical interventions on the SARS-CoV-2 pandemic at a city level: An agent-based computational modelling study of the City of Natal

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic hit almost all cities in Brazil in early 2020 and lasted for several months. Despite the effort of local state and municipal governments, an inhomogeneous nationwide response resulted in a death toll amongst the highest recorded globally. To evaluate the impact of the nonpharmaceutical governmental interventions applied by different cities-such as the closure of schools and businesses in general-in the evolution and epidemic spread of SARS-CoV-2, we constructed a full-sized agent-based epidemiological model adjusted to the singularities of particular cities. The model incorporates detailed demographic information, mobility networks segregated by economic segments, and restricting bills enacted during the pandemic period. As a case study, we analyzed the early response of the City of Natal-a midsized state capital-to the pandemic. Although our results indicate that the government response could be improved, the restrictive mobility acts saved many lives. The simulations show that a detailed analysis of alternative scenarios can inform policymakers about the most relevant measures for similar pandemic surges and help develop future response protocols.

Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies

In this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non controlled model and calculate the basic reproduction number and do the stability analysis. We then formulate an optimal control problem with vaccination and treatment as control variables and study the same. Pontryagin’s Minimum Principle is used to obtain the optimal vaccination and treatment rates. Optimal vaccination and treatment policies are analysed for different values of the weight constant associated with the cost of vaccination and different efficacy levels of vaccine. Findings from these suggested that the combined strategies (vaccination and treatment) worked best in minimizing the infection and disease induced mortality. In order to reduce COVID-19 infection and COVID-19 induced deaths to maximum, it was observed that optimal control strategy should be prioritized to the population with age greater than 40 years. Varying the cost of vaccination it was found that sufficient implementation of vaccines (more than 77 %) reduces the size of COVID-19 infections and number of deaths. The infection curves varying the efficacies of the vaccines against infection were also analysed and it was found that higher efficacy of the vaccine resulted in lesser number of infections and COVID induced deaths. The findings would help policymakers to plan effective strategies to contain the size of the COVID-19 pandemic.

Time Optimal Control Studies on COVID-19 Incorporating Adverse Events of the Antiviral Drugs

COVID -19 pandemic has resulted in more than 257 million infections and 5.15 million deaths worldwide. Several drug interventions targeting multiple stages of the pathogenesis of COVID -19 can significantly reduce induced infection and thus mortality. In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number R 0. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin’s Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field.

Occupational Health of Frontline Healthcare Workers in the United Arab Emirates during the COVID-19 Pandemic: A Snapshot of Summer 2020

The study aim was to understand the availability of personal protective equipment (PPE) and the levels of anxiety, depression, and burnout of healthcare workers (HCWs) in the United Arab Emirates (UAE). This study was an online-based, cross-sectional survey during July and August 2020. Participants were eligible from the entire country, and 1290 agreed to participate. The majority of HCWs were females aged 30-39 years old, working as nurses, and 80% considered PPE to be available. Twelve percent of respondents tested positive for SARS-CoV-2. Half of HCWs considered themselves physically tired (52.2%), reported musculoskeletal pain or discomfort (54.2%), and perceived moderate-to-high levels of burnout on at least one of three burnout domains (52.8%). A quarter of HCWs reported anxiety (26.3%) or depression (28.1%). HCWs reporting not having musculoskeletal pain, having performed physical activity, and higher scores of available PPE reported lower scores of anxiety, depression, and burnout. UAE HCWs experienced more access to PPE and less anxiety, depression, and burnout compared with HCWs in other countries. Study findings can be used by healthcare organizations and policymakers to ensure adequate measures are implemented to maximize the health and wellbeing of HCWs during the current COVID-19 and future pandemics.

Modeling of the Long-Term Epidemic Dynamics of COVID-19 in the United States

Coronavirus 2019 (COVID-19) is causing a severe pandemic that has resulted in millions of confirmed cases and deaths around the world. In the absence of effective drugs for treatment, non-pharmaceutical interventions are the most effective approaches to control the disease. Although some countries have the pandemic under control, all countries around the world, including the United States (US), are still in the process of controlling COVID-19, which calls for an effective epidemic model to describe the transmission dynamics of COVID-19. Meeting this need, we have extensively investigated the transmission dynamics of COVID-19 from 22 January 2020 to 14 February 2021 for the 50 states of the United States, which revealed the general principles underlying the spread of the virus in terms of intervention measures and demographic properties. We further proposed a time-dependent epidemic model, named T-SIR, to model the long-term transmission dynamics of COVID-19 in the US. It was shown in this paper that our T-SIR model could effectively model the epidemic dynamics of COVID-19 for all 50 states, which provided insights into the transmission dynamics of COVID-19 in the US. The present study will be valuable to help understand the epidemic dynamics of COVID-19 and thus help governments determine and implement effective intervention measures or vaccine prioritization to control the pandemic.

Assessing the impact of vaccination in a COVID-19 compartmental model

BACKGROUND

The aim of this research is to understand the role played by vaccination in the dynamics of a given COVID-19 compartmental model. Most of all, how vaccination modifies the stability, sensitivity, and the reproduction number of a susceptible population.

METHODS

The proposed COVID-19 compartmental model (SVEIRD) has seven compartments. Namely, susceptible (S), vaccinated (V), exposed (E, infected but not yet infectious), symptomatic infectious (I _s ), asymptomatic infectious (I _a ), recovered (R), and dead by Covid-19 disease (D).We have developed a computational code to mimic the first wave of the coronavirus pandemic in a state like New York (NYS).

FINDINGS

First a stability analysis was carried out. Next, a sensitivity analysis showed that the more relevant parameters are birth rate, transmission coefficient, and vaccine failure. We found an alternative procedure to easily calculate the vaccinated reproductive number of the proposed SVEIRD model. Our graphical results allow to make a comparison between unvaccinated (SEIRD) and vaccinated (SVEIRD) populations. In the peak of the first wave, we estimated 21% (2.5%) and 6% (0.8%) of the unvaccinated (vaccinated) susceptible population was symptomatic and asymptomatic, respectively. At 180 days of the NYS pandemic, the model forecast about 25786 deaths by coronavirus. A vaccine with 95% efficacy could reduce the number of deaths from 25786 to 3784.

CONCLUSION

The proposed compartmental model can be used to mimic different possible scenarios of the pandemic not only in NYS, but in any country or region. Further, for an unvaccinated reproductive number R > 1, we showed that the vaccine's efficacy must be greater than the herd immunity to stop the spread of the COVID-19 disease.