Mathematical Model Of COVID-19 Research Articles

Mathematical Modeling of COVID-19 with Chronic Patients and Sensitivity Analysis

Human health is constantly threatened by the appearance and resurgence of several diseases, as shown by recent epidemics. COVID-19 was one of the epidemics that left its mark on the world in terms of economic and human damages. In the search for solution to this pandemic, the scientific community is involved in all its diversity. Mathematicians are taking part in the fight through mathematical modeling in various approaches. Ordinary derivative compartmental modeling approache is one of the techniques widely used in epidemiological modeling. This paper presents a mathematical contribution to fight against COVID-19 using a compartmental SQEICRS model. This model takes into account five stages. In particular, the role of chronic diseases on the dynamique of COVID-19, is focused. A mathematical analysis of the model has been carried out, and shows that the model is well-posed in the biological and mathematical sense. Aspects such as existence, equilibrium points and their stability, the basic reproduction number R0and sensitivity anlysis have been discussed. Sensitivity analysis allowed us to identify the parameters which contribute to the spread of the disease, including the chronicity rate due to chronic diseases. The direction of disease propagation was also determined according to <I>R</I><sub>0</sub>. Finally, the numerical results with Matlab are in conformity with theoretical results.

Mathematical modeling of COVID-19 with the effects of quarantine and detection

In this paper, we focus on exploring a mathematical model that captures the dynamics of Corona Virus Disease (COVID-19), particularly emphasizing the influence of quarantine measures and the efficiency of detection and diagnosis protocols. Our study aims to comprehensively analyze the model, offering valuable insights and suggestions for effectively addressing the ongoing pandemic situation in various countries. The mathematical model under scrutiny is deterministic, and our approach involves a detailed examination of its equilibria. We rigorously employ methods to identify these points of equilibrium and subsequently undertake a thorough analysis of their stability. This analytical process is crucial in gaining a deeper understanding of the system’s behavior under various conditions, laying the foundation for informed recommendations to manage and mitigate the effects of the pandemic. To enhance the robustness of our findings, we complement our analytic results with numerical simulations. This multi-faceted approach allows us not only to understand the theoretical implications of the model but also to observe and validate its behavior in a simulated environment. The combination of mathematical analysis and numerical simulations strengthens the reliability and applicability of our results, contributing to a more comprehensive understanding of the dynamics at play in the context of COVID-19. Finally, we also discuss the optimal control approach in this paper to bound the epidemic.

Long-Term Side Effects: A Mathematical Modeling of COVID-19 and Stroke with Real Data

The post-effects of COVID-19 have begun to emerge in the long term in society. Stroke has become one of the most common side effects in the post-COVID community. In this study, to examine the relationship between COVID-19 and stroke, a fractional-order mathematical model has been constructed by considering the fear effect of being infected. The model’s positivity and boundedness have been proved, and stability has been examined for disease-free and co-existing equilibrium points to demonstrate the biological meaningfulness of the model. Subsequently, the basic reproduction number (the virus transmission potential (R0)) has been calculated. Next, the sensitivity analysis of the parameters according to R0 has been considered. Moreover, the values of the model parameters have been calculated using the parameter estimation method with real data originating from the United Kingdom. Furthermore, to underscore the benefits of fractional-order differential equations (FODEs), analyses demonstrating their relevance in memory trace and hereditary characteristics have been provided. Finally, numerical simulations have been highlighted to validate our theoretical findings and explore the system’s dynamic behavior. From the findings, we have seen that if the screening rate in the population is increased, more cases can be detected, and stroke development can be prevented. We also have concluded that if the fear in the population is removed, the infection will spread further, and the number of people suffering from a stroke may increase.

Mathematical Model and Simulation of the Spread of COVID-19 with Vaccination, Implementation of Health Protocols, and Treatment

This research develops the SVEIHQR model to simulate the spread of COVID-19 with vaccination, implementation of health protocols, and treatment. The population is divided into twelve subpopulations, resulting in a mathematical model of COVID-19 in the form of a system of twelve differential equations with twelve variables. From the model, we obtain the disease-free equilibrium point, the endemic equilibrium point, and the basic reproduction number (R0). The disease-free equilibrium point is locally asymptotically stable when R0 1 and ∆5 0, where ∆5 is the fifth-order Routh-Hurwitz matrix of the characteristic polynomial of the Jacobian matrix. Additionally, an endemic equilibrium point exists when R0 1. The results of numerical simulations are consistent with the conducted analysis, and the sensitivity analysis reveals that the significant parameters influencing the spread of COVID-19 are the proportion of symptomatic infected individuals and the contact rate with asymptomatic infected individuals.

Backward Bifurcation and Hysteresis in a Mathematical Model of COVID19 with Imperfect Vaccine

Vaccination has been used as strategy to eradicate the spread of COVID-19. But imperfect vaccine has been reported to induce backward bifurcation and hysteresis in mathematical models of disease transmission. Backward bifurcation is a phenomenon whereby a stable endemic equilibrium exists contemporaneously with a stable disease-free equilibrium when the basic reproduction number is less than 1. This situation can cause difficulty in controlling an epidemic because the basic reproduction is no longer the only means of eradicating the disease. In this paper, we propose a mathematical model for the transmission of disease which includes imperfect vaccination. We show that our model is capable of capturing backward bifurcation under certain conditions. By using parameters that are relevant to COVID-19 transmission in Malaysia, our numerical analysis shows that low vaccine efficacy can trigger backward bifurcation.

A mathematical model for transmission dynamics of COVID-19 infection.

In this paper, a mathematical model of COVID-19 has been proposed to study the transmission dynamics of infection by taking into account the role of symptomatic and asymptomatic infected individuals. The model has also considered the effect of non-pharmaceutical interventions (NPIs) in controlling the spread of virus. The basic reproduction number ( ) has been computed and the analysis shows that for , the disease-free state becomes globally stable. The conditions of existence and stability for two other equilibrium states have been obtained. Transcritical bifurcation occurs when basic reproduction number is one (i.e. ). It is found that when asymptomatic cases get increased, infection will persist in the population. However, when symptomatic cases get increased as compared to asymptomatic ones, the endemic state will become unstable and infection may eradicate from the population. Increasing NPIs decrease the basic reproduction number and hence, the epidemic can be controlled. As the COVID-19 transmission is subject to environmental fluctuations, the effect of white noise has been considered in the deterministic model. The stochastic differential equation model has been solved numerically by using the Euler-Maruyama method. The stochastic model gives large fluctuations around the respective deterministic solutions. The model has been fitted by using the COVID-19 data of three waves of India. A good match is obtained between the actual data and the predicted trajectories of the model in all three waves of COVID-19. The findings of this model may assist policymakers and healthcare professionals in implementing the most effective measures to prevent the transmission of COVID-19 in different settings.

Mathematical Modeling of COVID-19 with Vaccination Using Fractional Derivative: A Case Study

Vaccination against any infectious disease is considered to be an effective way of controlling it. This paper studies a fractional order model with vaccine efficacy and waning immunity. We present the model’s dynamics under vaccine efficacy, the impact of immunization, and the waning of the vaccine on coronavirus infection disease. We analyze the model under their equilibrium points. The model under the equilibrium points is discussed and proven that it is locally asymptotically stable if Rv is lesser than unity. We present the backward bifurcation hypothesis of the model and show that there is a parameter β2 that causes the backward bifurcation in the imperfect vaccine model. We show certain assumptions when ψ=1 for the imperfect vaccine case; the model is both stable globally asymptotically at the disease-free (R0≤1) and endemic cases (R0>1). By using infected cases from the recent wave throughout Pakistan, we shall estimate the model parameters and calculate the numerical value of the basic reproductive number R0≈1.2591. We present the comprehensive graphical results for the realistic parameter values and show many useful suggestions regarding the elimination of the infection from society. The vaccination efficacy that provides an important role in disease elimination is discussed in detail.

A mathematical model for COVID-19 considering waning immunity, vaccination and control measures

In this work we define a modified SEIR model that accounts for the spread of infection during the latent period, infections from asymptomatic or pauci-symptomatic infected individuals, potential loss of acquired immunity, people’s increasing awareness of social distancing and the use of vaccination as well as non-pharmaceutical interventions like social confinement. We estimate model parameters in three different scenarios—in Italy, where there is a growing number of cases and re-emergence of the epidemic, in India, where there are significant number of cases post confinement period and in Victoria, Australia where a re-emergence has been controlled with severe social confinement program. Our result shows the benefit of long term confinement of 50% or above population and extensive testing. With respect to loss of acquired immunity, our model suggests higher impact for Italy. We also show that a reasonably effective vaccine with mass vaccination program are successful measures in significantly controlling the size of infected population. We show that for a country like India, a reduction in contact rate by 50% compared to a reduction of 10% reduces death from 0.0268 to 0.0141% of population. Similarly, for a country like Italy we show that reducing contact rate by half can reduce a potential peak infection of 15% population to less than 1.5% of population, and potential deaths from 0.48 to 0.04%. With respect to vaccination, we show that even a 75% efficient vaccine administered to 50% population can reduce the peak number of infected population by nearly 50% in Italy. Similarly, for India, a 0.056% of population would die without vaccination, while 93.75% efficient vaccine given to 30% population would bring this down to 0.036% of population, and 93.75% efficient vaccine given to 70% population would bring this down to 0.034%.

Mathematical Modeling of COVID-19 with Periodic Transmission: The Case of South Africa

The data on SARS-CoV-2 (COVID-19) in South Africa show seasonal transmission patterns to date, with the peaks having occurred in winter and summer since the outbreaks began. The transmission dynamics have mainly been driven by variations in environmental factors and virus evolution, and the two are at the center of driving the different waves of the disease. It is thus important to understand the role of seasonality in the transmission dynamics of COVID-19. In this paper, a compartmental model with a time-dependent transmission rate is formulated and the stabilities of the steady states analyzed. We note that if R 0 < 1 , the disease-free equilibrium is globally asymptotically stable, and the disease completely dies out; and when R 0 > 1 , the system admits a positive periodic solution, and the disease is uniformly or periodically persistent. The model is fitted to data on new cases in South Africa for the first four waves. The model results indicate the need to consider seasonality in the transmission dynamics of COVID-19 and its importance in modeling fluctuations in the data for new cases. The potential impact of seasonality in the transmission patterns of COVID-19 and the public health implications is discussed.

Mathematical modeling of covid-19 with emphasis on infected migrant asymptomatic infected and interacting peoples

An S-A-I-Q-R epidemic model is investigated for Covid-19 as a class of infectious diseases that can be transmitted through carriers, not only infected individuals who are contagious but do not show any disease symptoms but through air which contained the virus droplets. Mathematical analysis is carried out that determines the global dynamics of the Modified Compartmental Epidemiological Model describing the transmission of the SARS-CoV-2 virus. The impacts of disease carriers on the transmission dynamics are analyze with emphasis on infected migrant, asymptomatic infected and social interacting people. We presented our discussion through the basic reproduction number as well as numerical simulations. We derived the condition for boundedness was obtained. Results: It was discovered that when Π δ λ and ρ are increased withing the first week of consideration, the reproduction number asymptotically approaches zero while a sudden increase in τ was observed to result into a sudden increase in reproduction number within the first week of the outbreak and thereafter decreases with further increment in τ. The result also showed that, population under quarantine are rarely infected with the virus except if already infected before being quarantined.

Mathematical modeling of covid-19 with emphasis on infected migrant asymptomatic infected and interacting peoples

Mathematical modeling of covid-19 with emphasis on infected migrant asymptomatic infected and interacting peoples

Application of the Modified Adomian Decomposition Method on a Mathematical Model of COVID-19

Application of the Modified Adomian Decomposition Method on a Mathematical Model of COVID-19

Mathematical model to investigate transmission dynamics of COVID-19 with vaccinated class

<abstract><p>The susceptible, exposed, infected, quarantined and vaccinated (SEIQV) population is accounted for in a mathematical model of COVID-19. This model covers the therapy for diseased people as well as therapeutic measures like immunization for susceptible people to enable understanding of the dynamics of the disease's propagation. Each of the equilibrium points, i.e., disease-free and endemic, has been proven to be globally asymptotically stable under the assumption that $ \mathscr{R}_0 $ is smaller or larger than unity, respectively. Although vaccination coverage is high, the basic reproduction number depends on the vaccine's effectiveness in preventing disease when $ \mathscr{R}_0 > 0 $. The Jacobian matrix and the Routh-Hurwitz theorem are used to derive the aforementioned analysis techniques. The results are further examined numerically by using the standard second-order Runge-Kutta (RK2) method. In order to visualize the global dynamics of the aforementioned model, the proposed model is expanded to examine some piecewise fractional order derivatives. We may comprehend the crossover behavior in the suggested model's illness dynamics by using the relevant derivative. To numerical present the results, we use RK2 method.</p></abstract>

A New Mathematical Model of COVID-19 with Quarantine and Vaccination

A mathematical model revealing the transmission mechanism of COVID-19 is produced and theoretically examined, which has helped us address the disease dynamics and treatment measures, such as vaccination for susceptible patients. The mathematical model containing the whole population was partitioned into six different compartments, represented by the SVEIQR model. Important properties of the model, such as the nonnegativity of solutions and their boundedness, are established. Furthermore, we calculated the basic reproduction number, which is an important parameter in infection models. The disease-free equilibrium solution of the model was determined to be locally and globally asymptotically stable. When the basic reproduction number R0 is less than one, the disease-free equilibrium point is locally asymptotically stable. To discover the approximative solution to the model, a general numerical approach based on the Haar collocation technique was developed. Using some real data, the sensitivity analysis of R0 was shown. We simulated the approximate results for various values of the quarantine and vaccination populations using Matlab to show the transmission dynamics of the Coronavirus-19 disease through graphs. The validation of the results by the Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions for COVID-19.

Dynamics and Transmission of COVID-19 Epidemic in Malaysia: Atangana-Baleanu Fractional Model

The purpose of this artical is to specify the passage and mathematical model of COVID-19. This infectious disease COVID-19 originated in China and has affected the whole world. In the present study, we have considered, SEIR model to evaluate the spread of COVID-19 in Malaysia. In this article, we have explored the gesture of COVID-19 accurately by applying the newly advanced fractional operator of Atangana-Baleanu on the classical SEIR model. Based on (WHO) reported data in this study, we discussed the corona virus's behavior in Malaysia. We have taken the available infection cases from 1st May 2020 to 14th May 2020. We have matched our problem to Malaysia's actual data, which shows a firm agreement with the actual data. From the information collected from WHO, we have found the basic reproduction number . Moreover, stability analysis at DFE (Disease Free Equilibrium) and EE (Endemic Equilibrium) is accomplished for the given model to detect the model's gesture and transportation. The given fractional model has been solved numerically using MATLAB software. The influence of many parameters specifically has been shown graphically and discussed in detail. It is to be noted that in the present study, we have approximated the escalation of disease for the up-coming 300 days.

Investigation of Novel Piecewise Fractional Mathematical Model for COVID-19

The outbreak of coronavirus (COVID-19) began in Wuhan, China, and spread all around the globe. For analysis of the said outbreak, mathematical formulations are important techniques that are used for the stability and predictions of infectious diseases. In the given article, a novel mathematical system of differential equations is considered under the piecewise fractional operator of Caputo and Atangana–Baleanu. The system is composed of six ordinary differential equations (ODEs) for different agents. The given model investigated the transferring chain by taking non-constant rates of transmission to satisfy the feasibility assumption of the biological environment. There are many mathematical models proposed by many scientists. The existence of a solution along with the uniqueness of a solution in the format of a piecewise Caputo operator is also developed. The numerical technique of the Newton interpolation method is developed for the piecewise subinterval approximate solution for each quantity in the sense of Caputo and Atangana-Baleanu-Caputo (ABC) fractional derivatives. The numerical simulation is drawn against the available data of Pakistan on three different time intervals, and fractional orders converge to the classical integer orders, which again converge to their equilibrium points. The piecewise fractional format in the form of a mathematical model is investigated for the novel COVID-19 model, showing the crossover dynamics. Stability and convergence are achieved on small fractional orders in less time as compared to classical orders.

An optimal control model for COVID-19, zika, dengue, and chikungunya co-dynamics with reinfection.

The co‐circulation of different emerging viral diseases is a big challenge from an epidemiological point of view. The similarity of symptoms, cases of virus co‐infection, and cross‐reaction can mislead in the diagnosis of the disease. In this article, a new mathematical model for COVID‐19, zika, chikungunya, and dengue co‐dynamics is developed and studied to assess the impact of COVID‐19 on zika, dengue, and chikungunya dynamics and vice‐versa. The local and global stability analyses are carried out. The model is shown to undergo a backward bifurcation under a certain condition. Global sensitivity analysis is also performed on the parameters of the model to determine the most dominant parameters. If the zika‐related reproduction number ℛ0Z is used as the response function, then important parameters are: the effective contact rate for vector‐to‐human transmission of zika (β2h, which is positively correlated), the human natural death rate (ϑh, positively correlated), and the vector recruitment rate (Ψv, also positively correlated). In addition, using the class of individuals co‐infected with COVID‐19 and zika (ℐCZh) as response function, the most dominant parameters are: the effective contact rate for COVID‐19 transmission (β1, positively correlated), the effective contact rate for vector‐to‐human transmission of zika (β2h, positively correlated). To control the co‐circulation of all the diseases adequately under an endemic setting, time dependent controls in the form of COVID‐19, zika, dengue, and chikungunya preventions are incorporated into the model and analyzed using the Pontryagin's principle. The model is fitted to real COVID‐19, zika, dengue, and chikungunya datasets for Espirito Santo (a city with the co‐circulation of all the diseases), in Brazil and projections made for the cumulative cases of each of the diseases. Through simulations, it is shown that COVID‐19 prevention could greatly reduce the burden of co‐infections with zika, dengue, and chikungunya. The negative impact of the COVID‐19 pandemic on the control of the arbovirus diseases is also highlighted. Furthermore, it is observed that prevention controls for zika, dengue, and chikungunya can significantly reduce the burden of co‐infections with COVID‐19.

Variational Iteration Method for Approximate Solution of COVID-19 Model

In this manuscript, we investigate a mathematical model of COVID-19 for approximate solution using variation iteration method (VIM). With the help of said technique we developed an algorithm to compute series type solution to the considered problem. Then using some real values for parameters and initial data we compute few terms approximate solutions. With the help of MMATLAB, we also plot our approximate solutions for different compartments graphically.

Correction to: Mathematical Modeling of Covid-19 and Dengue Co-Infection Dynamics in Bangladesh: Optimal Control and Data-Driven Analysis

Correction to: Mathematical Modeling of Covid-19 and Dengue Co-Infection Dynamics in Bangladesh: Optimal Control and Data-Driven Analysis

Asymptotic behavior and semi-analytic solution of a novel compartmental biological model

This study proposes a novel mathematical model of COVID-19 and its qualitative properties. Asymptotic behavior of the proposed model with local and global stability analysis is investigated by considering the Lyapunov function. The mentioned model is globally stable around the disease-endemic equilibrium point conditionally. For a better understanding of the disease propagation with vaccination in the population, we split the population into five compartments: susceptible, exposed, infected, vaccinated, and recovered based on the fundamental Kermack-McKendrick model. He's homotopy perturbation technique is used for the semi-analytical solution of the suggested model. For the sake of justification, we present the numerical simulation with graphical results.