Mathematical modeling and analysis of COVID-19: A study of new variant Omicron

Stability analysis and numerical evaluations of a COVID-19 model with vaccination

A novel (nonlinear) mathematical model for the transmission of Coronavirus 19 (COVID-19) with eight compartments and considering the impact of vaccination is examined in this manuscript. The qualitative behavior of the system such as the boundedness of solutions, the basic reproduction number, and the stability of the equilibrium points is investigated in detail. Some domestic real data collected from the Kerman University of Medical Science (KUMC) is used to estimate the parameters of the proposed model. We predict the dynamical behavior of the system through numerical simulations based on a combined spectral matrix collocation methodology. In this respect, we first linearize the nonlinear system of equations by the method of quasilinearization (QLM). Hence, the shifted version of Chebyshev polynomials of the second kind (SCPSK) is utilized along with the domain-splitting strategy to acquire the solutions of the system over a long time interval. The uniform convergence and upper bound estimation of the SCPSK bases are proved in a rigorous manner. Moreover, the technique of residual error functions is used to testify the accuracy of the QLM-SCPSK method. The presented numerical results justify the robustness and good accuracy of the QLM-SCPSK technique. The achieved numerical orders of convergence indicate that the QLM-SCSK algorithm has exponential rate of convergence. Using the linearization technique in one hand and the domain-splitting strategy on the other hand, enable us to predict the behaviour of similar disease problems with high accuracy and maximum efficiency on an arbitrary domain of interest.

Long-term monitoring of SARS-CoV-2 seroprevalence and variants in Ethiopia provides prediction for immunity and cross-immunity

Under-reporting of COVID-19 and the limited information about circulating SARS-CoV-2 variants remain major challenges for many African countries. We analyzed SARS-CoV-2 infection dynamics in Addis Ababa and Jimma, Ethiopia, focusing on reinfection, immunity, and vaccination effects. We conducted an antibody serology study spanning August 2020 to July 2022 with five rounds of data collection across a population of 4723, sequenced PCR-test positive samples, used available test positivity rates, and constructed two mathematical models integrating this data. A multivariant model explores variant dynamics identifying wildtype, alpha, delta, and omicron BA.4/5 as key variants in the study population, and cross-immunity between variants, revealing risk reductions between 24% and 69%. An antibody-level model predicts slow decay leading to sustained high antibody levels. Retrospectively, increased early vaccination might have substantially reduced infections during the delta and omicron waves in the considered group of individuals, though further vaccination now seems less impactful.

Behavioral game of quarantine during the monkeypox epidemic: Analysis of deterministic and fractional order approach

This work concerns the epidemiology of infectious diseases like monkeypox (mpox) in humans and animals. Our models examine transmission scenarios, including transmission dynamics between humans, animals, and both. We approach this using evolutionary game theory, specifically the intervention game-theoretical (IGT) framework, to study how human behavior can mitigate disease transmission without perfect vaccines and treatments. To do this, we use non-pharmaceutical intervention, namely the quarantine policy, which demonstrates the delayed effect of the epidemic. Additionally, we contemplate quarantine-based behavioral intervention policies in deterministic and fractional-order models to show behavioral impact in the context of the memory effect. Firstly, we extensively analyzed the model's positivity and boundness of the solution, reproduction number, disease-free and endemic equilibrium, possible stability, existence, concavity, and Ulam-Hyers stability for the fractional order. Subsequently, we proceeded to present a numerical analysis that effectively illustrates the repercussions of varying quarantine-related factors, information probability, and protection probability. We aimed to comprehensively examine the effects of non-pharmaceutical interventions on disease control, which we conveyed through line graphs and 2D heat maps. Our findings underscored the significant influence of strict quarantine measures and the protection of both humans and animals in mitigating disease outbreaks. These measures not only significantly curtailed the spread of the disease but also delayed the occurrence of the epidemic's peak. Conversely, when quarantine maintenance policies were implemented at lower rates and protection levels diminished, we observed contrasting outcomes that exacerbated the situation. Eventually, our analysis revealed the emergence of animal reservoirs in cases involving disease transmission between humans and animals.

Mathematical analysis and optimal control of an epidemic model with vaccination and different infectivity

This paper aims to explore the complex dynamics and impact of vaccinations on controlling epidemic outbreaks. An epidemic transmission model which considers vaccinations and two different infection statuses with different infectivity is developed. In terms of a dynamic analysis, we calculate the basic reproduction number and control reproduction number and discuss the stability of the disease-free equilibrium. Additionally, a numerical simulation is performed to explore the effects of vaccination rate, immune waning rate and vaccine ineffective rate on the epidemic transmission. Finally, a sensitivity analysis revealed three factors that can influence the threshold: transmission rate, vaccination rate, and the hospitalized rate. In terms of optimal control, the following three time-related control variables are introduced to reconstruct the corresponding control problem: reducing social distance, enhancing vaccination rates, and enhancing the hospitalized rates. Moreover, the characteristic expression of optimal control problem. Four different control combinations are designed, and comparative studies on control effectiveness and cost effectiveness are conducted by numerical simulations. The results showed that Strategy C (including all the three controls) is the most effective strategy to reduce the number of symptomatic infections and Strategy A (including reducing social distance and enhancing vaccination rate) is the most cost-effective among the three strategies.

On a two-strain epidemic model involving delay equations

We propose an epidemiological model for the interaction of either two viruses or viral strains with cross-immunity, where the individuals infected by the first virus cannot be infected by the second one, and without cross-immunity, where a secondary infection can occur. The model incorporates distributed recovery and death rates and consists of integro-differential equations governing the dynamics of susceptible, infectious, recovered, and dead compartments. Assuming that the recovery and death rates are uniformly distributed in time throughout the duration of the diseases, we can simplify the model to a conventional ordinary differential equation (ODE) model. Another limiting case arises if the recovery and death rates are approximated by the delta-function, thereby resulting in a new point-wise delay model that incorporates two time delays corresponding to the durations of the diseases. We establish the positiveness of solutions for the distributed delay models and determine the basic reproduction number and an estimate for the final size of the epidemic for the delay model. According to the results of the numerical simulations, both strains can coexist in the population if the disease transmission rates for them are close to each other. If the difference between them is sufficiently large, then one of the strains dominates and eliminates the other one.

Impact of vaccine measures on the transmission dynamics of COVID-19

In many nations, efforts to prevent and control COVID-19 have been significantly impeded by the SARS-CoV-2 virus ongoing mutation. The Omicron strain, a more recent and prevalent strain, has had more significant detrimental effects in countries worldwide. To investigate the impact of the Omicron BA.2 strain on vaccine efficacy, we proposed a model with vaccination and immunological decline in this research. Then, we fitted our model based on the number of daily new instances reported by the government in Jilin and Shanghai, China. We estimated the effective reproduction number Re = 4.71 for the Jilin and Re = 3.32 for Shanghai. Additionally, we do sensitivity analysis to identify the critical factors affecting the effective reproduction number Re. It was found that vaccination rate, effectiveness rate, and declining rate had a significant effect on Re. Further, we investigate the relevant parameter thresholds that make Re lower than unity. Finally, rich numerical experiments were then carried out. We observed that even when vaccine efficiency was not high, increasing vaccination rates had a significant effect on early disease transmission, that limiting social distance was the most economical and rational measure to control the spread of disease, and that for a short period, reducing immune decline was not significant in curbing disease transmission.

SIRC epidemic model with cross-immunity and multiple time delays

Multi-strain diseases lead to the development of some degree of cross-immunity among people. In the present paper, we propose a multi-delayed SIRC epidemic model with incubation and immunity time delays. Here we aim to examine and investigate the effects of incubation delay [Formula: see text] and the impact of vaccine which provides partial/cross-immunity with immunity delay parameter ([Formula: see text]) on the disease dynamics. Also, we study the impact of the strength of cross-immunity [Formula: see text] on the disease prevalence. The positivity and boundedness of the solutions of the epidemic model have been established. Two different types of equilibrium points (disease-free and endemic) have been deduced. Expression for basic reproduction number has been derived. The stability conditions and Hopf-bifurcation about both the equilibrium points in the absence and presence of both delays have been discussed. The Lyapunov stability conditions about the endemic equilibrium point have been established. Numerical simulations have been performed to support our analytical results. We quantitatively demonstrate how oscillations and Hopf-bifurcation allow time delays to alter the dynamics of the system. The combined impacts of both the delays on disease prevalence has been studied. Through parameter sensitivity analysis, we observe that the infected population decreases with an increase in vaccination rate and the system starts to stabilize early with the increase in cross-immunity rate. Global sensitivity analysis for the basic reproduction number has been performed using Latin hypercube sampling and partial rank correlation coefficients techniques. The combined effect of vaccination rate with transmission rate and vaccination rate with re-infection probability (i.e. strength of cross-immunity) on [Formula: see text] have been discussed. Our research underlines the need to take cross-immunity and time delays into account in the epidemic model in order to better understand disease dynamics.

Modeling the dynamics of COVID-19 with real data from Thailand

In recent years, COVID-19 has evolved into many variants, posing new challenges for disease control and prevention. The Omicron variant, in particular, has been found to be highly contagious. In this study, we constructed and analyzed a mathematical model of COVID-19 transmission that incorporates vaccination and three different compartments of the infected population: asymptomatic [Formula: see text], symptomatic [Formula: see text], and Omicron [Formula: see text]. The model is formulated in the Caputo sense, which allows for fractional derivatives that capture the memory effects of the disease dynamics. We proved the existence and uniqueness of the solution of the model, obtained the effective reproduction number, showed that the model exhibits both endemic and disease-free equilibrium points, and showed that backward bifurcation can occur. Furthermore, we documented the effects of asymptomatic infected individuals on the disease transmission. We validated the model using real data from Thailand and found that vaccination alone is insufficient to completely eradicate the disease. We also found that Thailand must monitor asymptomatic individuals through stringent testing to halt and subsequently eradicate the disease. Our study provides novel insights into the behavior and impact of the Omicron variant and suggests possible strategies to mitigate its spread.

Wastewater surveillance beyond COVID-19: a ranking system for communicable disease testing in the tri-county Detroit area, Michigan, USA

Introduction

Throughout the coronavirus disease 2019 (COVID-19) pandemic, wastewater surveillance has been utilized to monitor the disease in the United States through routine national, statewide, and regional monitoring projects. A significant canon of evidence was produced showing that wastewater surveillance is a credible and effective tool for disease monitoring. Hence, the application of wastewater surveillance can extend beyond monitoring SARS-CoV-2 to encompass a diverse range of emerging diseases. This article proposed a ranking system for prioritizing reportable communicable diseases (CDs) in the Tri-County Detroit Area (TCDA), Michigan, for future wastewater surveillance applications at the Great Lakes Water Authority's Water Reclamation Plant (GLWA's WRP).

Methods

The comprehensive CD wastewater surveillance ranking system (CDWSRank) was developed based on 6 binary and 6 quantitative parameters. The final ranking scores of CDs were computed by summing the multiplication products of weighting factors for each parameter, and then were sorted based on decreasing priority. Disease incidence data from 2014 to 2021 were collected for the TCDA. Disease incidence trends in the TCDA were endowed with higher weights, prioritizing the TCDA over the state of Michigan.

Results

Disparities in incidences of CDs were identified between the TCDA and state of Michigan, indicating epidemiological differences. Among 96 ranked CDs, some top ranked CDs did not present relatively high incidences but were prioritized, suggesting that such CDs require significant attention by wastewater surveillance practitioners, despite their relatively low incidences in the geographic area of interest. Appropriate wastewater sample concentration methods are summarized for the application of wastewater surveillance as per viral, bacterial, parasitic, and fungal pathogens.

Discussion

The CDWSRank system is one of the first of its kind to provide an empirical approach to prioritize CDs for wastewater surveillance, specifically in geographies served by centralized wastewater collection in the area of interest. The CDWSRank system provides a methodological tool and critical information that can help public health officials and policymakers allocate resources. It can be used to prioritize disease surveillance efforts and ensure that public health interventions are targeted at the most potentially urgent threats. The CDWSRank system can be easily adopted to geographical locations beyond the TCDA.

Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R₀ < 1 and the exogenous reinfection rate greater than a threshold (η > η∗). The analytical results show that reducing R₀ < 1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.

Modeling the SARS-CoV-2 Omicron variant dynamics in the United States with booster dose vaccination and waning immunity

We carried out a theoretical and numerical analysis for an epidemic model to analyze the dynamics of the SARS-CoV-2 Omicron variant and the impact of vaccination campaigns in the United States. The model proposed here includes asymptomatic and hospitalized compartments, vaccination with booster doses, and the waning of natural and vaccine-acquired immunity. We also consider the influence of face mask usage and efficiency. We found that enhancing booster doses and using N95 face masks are associated with a reduction in the number of new infections, hospitalizations and deaths. We highly recommend the use of surgical face masks as well, if usage of N95 is not a possibility due to the price range. Our simulations show that there might be two upcoming Omicron waves (in mid-2022 and late 2022), caused by natural and acquired immunity waning with respect to time. The magnitude of these waves will be 53% and 25% lower than the peak in January 2022, respectively. Hence, we recommend continuing to use face masks to decrease the peak of the upcoming COVID-19 waves.

A multi-strain model with asymptomatic transmission: Application to COVID-19 in the US

COVID-19, induced by the SARS-CoV-2 infection, has caused an unprecedented pandemic in the world. New variants of the virus have emerged and dominated the virus population. In this paper, we develop a multi-strain model with asymptomatic transmission to study how the asymptomatic or pre-symptomatic infection influences the transmission between different strains and control strategies that aim to mitigate the pandemic. Both analytical and numerical results reveal that the competitive exclusion principle still holds for the model with the asymptomatic transmission. By fitting the model to the COVID-19 case and viral variant data in the US, we show that the omicron variants are more transmissible but less fatal than the previously circulating variants. The basic reproduction number for the omicron variants is estimated to be 11.15, larger than that for the previous variants. Using mask mandate as an example of non-pharmaceutical interventions, we show that implementing it before the prevalence peak can significantly lower and postpone the peak. The time of lifting the mask mandate can affect the emergence and frequency of subsequent waves. Lifting before the peak will result in an earlier and much higher subsequent wave. Caution should also be taken to lift the restriction when a large portion of the population remains susceptible. The methods and results obtained her e may be applied to the study of the dynamics of other infectious diseases with asymptomatic transmission using other control measures.

The reproduction rate of severe acute respiratory syndrome coronavirus 2 different variants recently circulated in human: a narrative review

SARS-COV-2 is responsible for the current worldwide pandemic, which started on December 2019 in Wuhan, China. On March 2020 World Health Organization announced COVID-19 as the new pandemic. Some SARS-COV-2 variants have increased transmissibility, cause more severe disease (e.g., increased hospitalizations or deaths), are resistant to antibodies produced by the previous infection or vaccination, and there is more difficulty in treatment and diagnosis of them. World Health Organization considered them as SARS-CoV-2 variants of concern. The introductory reproduction rate (R₀) is an epidemiologic index of the transmissibility of the virus, defined as the average number of persons infected by the virus after known contact with an infectious person in a susceptible population. An R₀ > 1 means that the virus is spreading exponentially, and R₀ < 1, means that the outbreak is subsiding. In various studies, the estimated R and VOC growth rates were reported to be greater than the ancestral strains. However, it was also a low level of concordance between the estimated Rt of the same variant in different studies. It is because the R of a variant not only dependent on the biological and intrinsic factors of the virus but also several parameters can affect the R0, including the duration of contagiousness and the likelihood of infection per contact. Evaluation of changes in SARS-CoV-2 has shown that the rate of human-to-human transmission of this virus has increased. Like other viruses with non-human sources which succeeded in surviving in the human population, SARS-CoV-2 has gradually adapted to the human population, and its ability to transmit from human to human has increased. Of course, due to the continuous changes in this virus, it is crucial to survey the rate of transmission of the virus over time.

Spatio-Temporal SIR Model with Robin Boundary Condition and Automatic Lockdown Policy

This paper presents the SIR space-time model, which is a coupled reaction-diffusion system with nonlinear Robin boundary conditions. These boundary conditions are supposed to lock the border (no outflow neither immigration nor migration) when the number of infected individuals explode, and this may be considered as an automatic containment or lock-down. In practice, we can precise some threshold for the number of infected individuals and when it is reached the model locks the region automatically. This work provides a thorough study of the presented model, including the existence and uniqueness of the solution, its boundedness and its asymptotic behaviour. We end with some numerical experiments performed on the basis of the finite difference approach and Newton's method to highlight and validate the theoretical results.

Quantitative evaluation of the role of Fangcang shelter hospitals in the control of Omicron transmission: A case study of the outbreak in Shanghai, China in 2022

Since Omicron began to spread in China, Shanghai has become one of the cities with more severe outbreaks. Under the comprehensive consideration of the vaccine coverage rate, the number of Fangcang shelter hospital beds and the number of designated hospital beds in Shanghai, this paper established a deterministic compartmental model and used the Nelder-Mead Simplex Direct Search Algorithm and chi-square values to estimate the model parameters. we calculate ℛ₀ = 3.6429 when the number of beds in the Fangcang shelter hospital is relatively tight in the second stage and ℛ₀ = 0.4974 in the fifth stage when there are enough beds in both Fangcang shelter hospital and designated hospital. Then we perform a sensitivity analysis on ℛ₀ by using perturbation of fixed point estimation of model parameters in the fifth stage, and obtain three parameters that are more sensitive to ℛ₀, which are transmission rate (β _1d ), proportion of the infectious (η) and the hospitalization rate of asymptomatic infected cases (δ ₁). Through simulation, we obtain that if the hospitalization rate of asymptomatic infections δ ₂ > 0.9373 or the transmission rate β _1b  < 0.0467, the second stage of Omicron transmission in Shanghai can be well controlled. Finally, we find the measure that converting the National Convention and Exhibition Center (NECC) into a Fangcang shelter hospital has played an important role in curbing the epidemic. Whether this temporary Fangcang shelter hospital is not built or delayed, the cumulative number of confirmed cases will both exceed 100,000, and the cumulative asymptomatic infections will both exceed 1 million. In addition, for a city of 10 million people, we obtain that if a permanent Fangcang shelter hospital with 17,784 beds is built ahead of epidemic, there will be no shortage of beds during the outbreak of Omicron. Our findings enrich the content of the impact of Fangcang shelter hospital beds on the spread of Omicron and confirm the correct policy adopted by the Chinese government.

Bayesian SIR model with change points with application to the Omicron wave in Singapore

The Omicron variant has led to a new wave of the COVID-19 pandemic worldwide, with unprecedented numbers of daily confirmed new cases in many countries and areas. To analyze the impact of society or policy changes on the development of the Omicron wave, the stochastic susceptible-infected-removed (SIR) model with change points is proposed to accommodate the situations where the transmission rate and the removal rate may vary significantly at change points. Bayesian inference based on a Markov chain Monte Carlo algorithm is developed to estimate both the locations of change points as well as the transmission rate and removal rate within each stage. Experiments on simulated data reveal the effectiveness of the proposed method, and several stages are detected in analyzing the Omicron wave data in Singapore.

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.

A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data

Natural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We consider the real infection data of COVID-19 in Saudi Arabia and present its detailed mathematical results. We first present the existence and uniqueness of the deterministic model and later study the dynamical properties of the deterministic model and determine the global asymptotic stability of the system for R0≤1. We then study the dynamic properties of the stochastic model and present its global unique solution for the model. We further study the extinction of the stochastic model. Further, we use the nonlinear least-square fitting technique to fit the data to the model for the deterministic and stochastic case and the estimated basic reproduction number is R0≈1.1367. We show that the stochastic model provides a good fitting to the real data. We use the numerical approach to solve the stochastic system by presenting the results graphically. The sensitive parameters that significantly impact the model dynamics and reduce the number of infected cases in the future are shown graphically.

Systematic description of COVID-19 pandemic using exact SIR solutions and Gumbel distributions

An epidemiological study is carried out in several countries analyzing the first wave of the COVID-19 pandemic using the SIR model and Gumbel distribution. The equations of the SIR model are solved exactly using the proper time as a parameter. The physical time is obtained by integration of the inverse of the infected function over proper time. Some properties of the solutions of the SIR model are studied such as time scaling and the asymmetry, which allows to obtain the basic reproduction number from the data. Approximations to the solutions of the SIR model are studied using Gumbel distributions by least squares fit or by adjusting the maximum of the infected function. Finally, the parameters of the SIR model and the Gumbel function are extracted from the death data and compared for the different countries. It is found that ten of the selected countries are very well described by the solutions of the SIR model, with a basic reproduction number between 3 and 8.

A case study of 2019-nCoV in Russia using integer and fractional order derivatives

In this article, we define a mathematical model to analyze the outbreaks of the most deadly disease of the decade named 2019-nCoV by using integer and fractional order derivatives. For the case study, the real data of Russia is taken to perform novel parameter estimation by using the Trust Region Reflective (TRR) algorithm. First, we define an integer order model and then generalize it by using fractional derivatives. A novel optimal control problem is derived to see the impact of possible preventive measures against the spread of 2019-nCoV. We implement the forward-backward sweep method to numerically solve our proposed model and control problem. A number of graphs have been plotted to see the impact of the proposed control practically. The Russian data-based parameter estimation along with the proposal of a mathematical model in the sense of Caputo fractional derivative that contains the memory term in the system are the main novel features of this study.

Application of piecewise fractional differential equation to COVID-19 infection dynamics

We proposed a new mathematical model to study the COVID-19 infection in piecewise fractional differential equations. The model was initially designed using the classical differential equations and later we extend it to the fractional case. We consider the infected cases generated at health care and formulate the model first in integer order. We extend the model into Caputo fractional differential equation and study its background mathematical results. We show that the fractional model is locally asymptotically stable when R 0 < 1 at the disease-free case. For R 0 ≤ 1 , we show the global asymptotical stability of the model. We consider the infected cases in Saudi Arabia and determine the parameters of the model. We show that for the real cases, the basic reproduction is R 0 ≈ 1 . 7372 . We further extend the Caputo model into piecewise stochastic fractional differential equations and discuss the procedure for its numerical simulation. Numerical simulations for the Caputo case and piecewise models are shown in detail.

An Epidemic Model with Time Delay Determined by the Disease Duration

Immuno-epidemiological models with distributed recovery and death rates can describe the epidemic progression more precisely than conventional compartmental models. However, the required immunological data to estimate the distributed recovery and death rates are not easily available. An epidemic model with time delay is derived from the previously developed model with distributed recovery and death rates, which does not require precise immunological data. The resulting generic model describes epidemic progression using two parameters, disease transmission rate and disease duration. The disease duration is incorporated as a delay parameter. Various epidemic characteristics of the delay model, namely the basic reproduction number, the maximal number of infected, and the final size of the epidemic are derived. The estimation of disease duration is studied with the help of real data for COVID-19. The delay model gives a good approximation of the COVID-19 data and of the more detailed model with distributed parameters.

Assessing the potential impact of COVID-19 Omicron variant: Insight through a fractional piecewise model

We consider a new mathematical model for the COVID-19 disease with Omicron variant mutation. We formulate in details the modeling of the problem with omicron variant in classical differential equations. We use the definition of the Atangana-Baleanu derivative and obtain the extended fractional version of the omicron model. We study mathematical results for the fractional model and show the local asymptotical stability of the model for infection-free case if R 0 < 1 . We show the global asymptotically stable of the model for the disease free case when R 0 ≤ 1 . We show the existence and uniqueness of solution of the fractional model. We further extend the fractional order model into piecewise differential equation system and give a numerical algorithm for their numerical simulation. We consider the real cases of COVID-19 in South Africa of the third wave March 2021-Sep 2021 and estimate the model parameters and get R 0 ≈ 1 . 4004 . The real parameters values are used to show the graphical results for the fractional and piecewise model.

Transmission dynamics of COVID-19 pandemic with combined effects of relapse, reinfection and environmental contribution: A modeling analysis

Reinfection and reactivation of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have recently raised public health pressing concerns in the fight against the current pandemic globally. In this study, we propose a new dynamic model to study the transmission of the coronavirus disease 2019 (COVID-19) pandemic. The model incorporates possible relapse, reinfection and environmental contribution to assess the combined effects on the overall transmission dynamics of SARS-CoV-2. The model's local asymptotic stability is analyzed qualitatively. We derive the formula for the basic reproduction number ( R 0 ) and final size epidemic relation, which are vital epidemiological quantities that are used to reveal disease transmission status and guide control strategies. Furthermore, the model is validated using the COVID-19 reported situations in Saudi Arabia. Moreover, sensitivity analysis is examined by implementing a partial rank correlation coefficient technique to obtain the ultimate rank model parameters to control or mitigate the pandemic effectively. Finally, we employ a standard Euler technique for numerical simulations of the model to elucidate the influence of some crucial parameters on the overall transmission dynamics. Our results highlight that contact rate, hospitalization rate, and reactivation rate are the fundamental parameters that need particular emphasis for the prevention, mitigation and control.