ABSTRACT
Based on the SEIR model, two compartments for self-protection and isolation are introduced, and a more general infectious disease transmission model is proposed.Through qualitative analysis of the model, the basic reproduction number of the model is calculated, and the local asymptotic stability of the disease-free equilibrium point and the endemic equilibrium point of the model is analyzed through eigenvalue theory and Routh-Hurwitz criterion.The numerical simulation and fitting results of COVID-19 virus show that the proposed SEIQRP model can effectively describe the dynamic transmission process of the infectious disease.In the model, the three parameters, i.e.protection rate, incubation period isolation rate, and infected person isolation rate play a very critical role in the spread of the disease.Raising people's awareness of self-protection, focusing on screening for patients in the incubation period, and isolating and treating infected people can effectively reduce the spread of infectious diseases. © 2023 Northeastern University.All rights reserved.
ABSTRACT
Globally, the COVID-19 pandemic's development has presented significant societal and economic challenges. The carriers of COVID-19 transmission have also been identified as asymptomatic infected people. Yet, most epidemic models do not consider their impact when accounting for the disease's indirect transmission. This study suggested and investigated a mathematical model replicating the spread of coronavirus disease among asymptomatic infected people. A study was conducted on every aspect of the system's solution. The equilibrium points and the basic reproduction number were computed. The endemic equilibrium point and the disease-free equilibrium point had both undergone local stability analyses. A geometric technique was used to look into the global dynamics of the endemic point, whereas the Castillo-Chavez theorem was used to look into the global stability of the disease-free point. The system's transcritical bifurcation at the disease-free point was discovered to exist. The system parameters were changed using the basic reproduction number's sensitivity technique. Ultimately, a numerical simulation was used to apply the model to the population of Iraq in order to validate the findings and define the factors that regulate illness breakout.
ABSTRACT
Bulgaria has the lowest COVID-19 vaccination rate in the European Union and the second-highest COVID-19 mortality rate in the world. That is why we think it is important better to understand the reason for this situation and to analyse the development of the disease over time. In this paper, an extended time-dependent SEIRS model SEIRS-VB is used to investigate the long-term behaviour of the COVID-19 epidemic. This model includes vaccination and vital dynamics. To apply the SEIRS-VB model some numerical simulation tools have been developed and for this reason a family of time-discrete variants are introduced. Suitable inverse problems for the identification of parameters in discrete models are solved. A methodology is proposed for selecting a discrete model from the constructed family, which has the closest parameter values to these in the differential SEIRS-VB model. To validate the studied models, Bulgarian COVID-19 data are used. To obtain all these results for the discrete models a mathematical analysis is carried out to illustrate some biological properties of the differential model SEIRS-VB, such as the non-negativity, boundedness, existence, and uniqueness. Using the next-generation method, the basic reproduction number associated with the model in the autonomous case is defined. The local stability of the disease-free equilibrium point is studied. Finally, a sensitivity analysis of the basic reproduction number is performed.
ABSTRACT
Humanity is currently living a true nightmare never seen before due to the pandemic caused by COVID-19 disease, scientific researchers are working day and night to find an ideal vaccine that eradicates this pandemic. The purpose of this paper is to investigate a SIHV pandemic model taking into account a vaccination strategy. For this aim, we consider a model with four compartments that describes the interaction between the susceptible cases S, the real infected cases I, the hospitalized, confirmed infected cases H and the vaccinated-treated individuals V. We establish the local stability of our model, depending on the basic reproduction number, by using the Routh-Hurwitz theorem. We perform some numerical simulations in order to confirm our theoretical results and discuss the effect of the rate of vaccination on controlling the spread of COVID-19. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.
ABSTRACT
COVID-19 is the short name of the coronavirus disease discovered in Wuhan, China, in 2019. In the context of Tanzania, we develop a mathematical model in this work that compares lockdown and quarantine. Again, we provide evidence in favor of local and global stability, with the basic reproduction number, R 0 , determined to be 0.31 at the diagnostic test rates k 1 = k 2 = 0.05. In comparison to the lockdown, it has been discovered that isolating (or quarantining) affected individuals is the most effective way to stop the spread of COVID-19. Additionally, it is advised that governments in Tanzania and other African countries permit their citizens to go about their daily lives as long as they take the necessary precautions, such as donning face masks, washing their hands, and avoiding crowded gatherings in case of a recurrence of any form of COVID-19. [ FROM AUTHOR] Copyright of Computational & Mathematical Methods in Medicine is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)
ABSTRACT
In this paper, we introduce a SIVR model using the Laplace Adomian decomposition. This model focuses on a new trend in mathematical epidemiology dedicated to studying the characteristics of vaccination of infected communities. We analyze the epidemiological parameters using equilibrium stability and numerical analysis techniques. New mathematical strategies are also applied to establish our epidemic model, which is a pandemic model as well. In addition, we mathematically establish the chance for the next wave of any pandemic disease and show that a consistent vaccination strategy could control it. Our proposal is the first model introducing a vaccination strategy to actively infected cases. We are sure this work will serve as the basis for future research on COVID-19 and pandemic diseases since our study also considers the vaccinated population. © 2023 by the authors.
ABSTRACT
Beside the unexpected toll of mortality and morbidity caused by COVID-19 worldwide, low- and middle-income countries are more suffering from the devastating issues on economic and social life. This disease has fostered mathematical modelling. In this paper, a SEIAR mathematical model is presented to illustrate how policymakers may apply efficient strategies to end or at least to control the devastating wide spread of COVID-19. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
ABSTRACT
Purpose: The ongoing COVID-19 pandemic imposes serious short-term and long-term health costs on populations. Restrictive government policy measures decrease the risks of infection, but produce similarly serious social, mental health, and economic problems. Citizens have varying preferences about the desirability of restrictive policies, and governments are thus forced to navigate this tension in making pandemic policy. This paper analyses the situation facing government using a game-theoretic epidemiological model. Methodology: We classify individuals into health-centered individuals and freedom-centered individuals to capture the heterogeneous preferences of citizens. We first use the extended Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) model (adding individual preferences) and the signaling game model (adding government) to analyze the strategic situation against the backdrop of a realistic model of COVID-19 infection. Findings: We find the following: 1. There exists two pooling equilibria. When health-centered and freedom-centered individuals send anti-epidemic signals, the government will adopt strict restrictive policies under budget surplus or balance. When health-centered and freedom-centered individuals send freedom signals, the government chooses not to implement restrictive policies. 2. When governments choose not to impose restrictions, the extinction of an epidemic depends on whether it has a high infection transmission rate; when the government chooses to implement non-pharmacological interventions (NPIs), whether an epidemic will disappear depends on how strict the government's restrictions are. Originality/value: Based on the existing literature, we add individual preferences and put the government into the game as a player. Our research extends the current form of combining epidemiology and game theory. By using both we get a more realistic understanding of the spread of the virus and combine that with a richer understanding of the strategic social dynamics enabled by game theoretic analysis. Our findings have important implications for public management and government decision-making in the context of COVID-19 and for potential future public health emergencies.
ABSTRACT
To investigate the influence of human behavior on the spread of COVID-19, we propose a reaction-diffusion model that incorporates contact rate functions related to human behavior. The basic reproduction number R0 is derived and a threshold-type result on its global dynamics in terms of R0 is established. More precisely, we show that the disease-free equilibrium is globally asymptotically stable if R0≤1; while there exists a positive stationary solution and the disease is uniformly persistent if R0>1. By the numerical simulations of the analytic results, we find that human behavior changes may lower infection levels and reduce the number of exposed and infected humans.
ABSTRACT
Inapparent infection plays an important role in the disease spread, which is an infection by a pathogen that causes few or no signs or symptoms of infection in the host. Many pathogens, including HIV, typhoid fever, and coronaviruses such as COVID-19 spread in their host populations through inapparent infection. In this paper, we formulated a degenerated reaction-diffusion host-pathogen model with multiple infection period. We split the infectious individuals into two distinct classes: apparent infectious individuals and inapparent infectious individuals, coming from exposed individuals with a ratio of (1-p) and p, respectively. Some preliminary results and threshold-type results are achieved by detailed mathematical analysis. We also investigate the asymptotic profiles of the positive steady state (PSS) when the diffusion rate of susceptible individuals approaches zero or infinity. When all parameters are all constants, the global attractivity of the constant endemic equilibrium is established. It is verified by numerical simulations that spatial heterogeneity of the transmission rates can enhance the intensity of an epidemic. Especially, the transmission rate of inapparent infectious individuals significantly increases the risk of disease transmission, compared to that of apparent infectious individuals and pathogens in the environment, and we should pay special attentions to how to regulate the inapparent infectious individuals for disease control and prevention, which is consistent with the result on the sensitive analysis to the transmission rates through the normalized forward sensitivity index. We also find that disinfection of the infected environment is an important way to prevent and eliminate the risk of environmental transmission.
ABSTRACT
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.
ABSTRACT
Covid-19 is a serious disease for human. It can be easily spread between human. In order to model the spread of Covid-19 and determinate the appropriate policy by government, I use the SEIRD model, which is extended from SIR model. In this paper, the SEIRD model studies the transmissibility of Covid-19 in China. This work first gives out the flowchart of the SEIRD model and then I derive the differential equation and find out the disease-free equilibrium based on the flowchart. Then I calculate the generation matrix and basic reproduction number which is directly related to the transmissibility of the virus. At last, the sensitivity analysis analyzes the different impact from different parameter. From that, we can find out the best way to control the transmission. The result is that the parameter that refer to strictness has a great impact on the spread of Covid-19. However, it doesn't have to be as large as possible since the covid can be well controlled with an appropriate value of strictness and smallest negative effect for people. This paper tries to find out the best extent of strictness of policy that is able to control the transmission. © 2023 SPIE.
ABSTRACT
In this paper, the effect of contaminated objects on a SIRS Model with vaccination and hospitalization compartments is modeled. Positivity and boundedness properties of the solutions of model are proved, basic reproduction number of the model is founded through criteria which make the eigenvalues of the Jacobean matrix at the disease-free equilibrium point, negative. Globally stability analysis of the disease-free equilibrium point is proved when the basic reproduction number is less than unity. The existence, uniqueness of the endemic equilibrium point is investigated when the basic reproduction number is greater than unity. Parameter values regarding to spreading covid-19 in Kurdistan region are estimated. Finally, sensitivity analysis of the reproduction number is carried out. © 2022 Production by the University of Garmian. This is an open access article under the LICENSE.
ABSTRACT
Before reopening society in December 2022, China had not achieved sufficiently high vaccination coverage among people aged 80 years and older, who are vulnerable to severe infection and death owing to COVID-19. Suddenly ending the zero-COVID policy was anticipated to lead to substantial mortality. To investigate the mortality impact of COVID-19, we devised an age-dependent transmission model to derive a final size equation, permitting calculation of the expected cumulative incidence. Using an age-specific contact matrix and published estimates of vaccine effectiveness, final size was computed as a function of the basic reproduction number, R0. We also examined hypothetical scenarios in which third-dose vaccination coverage was increased in advance of the epidemic, and also in which mRNA vaccine was used instead of inactivated vaccines. Without additional vaccination, the final size model indicated that a total of 1.4 million deaths (half of which were among people aged 80 years and older) were anticipated with an assumed R0 of 3.4. A 10% increase in third-dose coverage would prevent 30,948, 24,106, and 16,367 deaths, with an assumed second-dose effectiveness of 0%, 10%, and 20%, respectively. With mRNA vaccine, the mortality impact would have been reduced to 1.1 million deaths. The experience of reopening in China indicates the critical importance of balancing pharmaceutical and non-pharmaceutical interventions. Ensuring sufficiently high vaccination coverage is vital in advance of policy changes.
Subject(s)
COVID-19 , Epidemics , Humans , China/epidemiology , Basic Reproduction Number , Vaccination , mRNA VaccinesABSTRACT
The COVID-19 epidemic is an unprecedented and major social and economic challenge worldwide due to the various restrictions. Inflow of infective immigrants have not been given prominence in several mathematical and epidemiological models. To investigate the impact of imported infection on the number of deaths, cumulative infected and cumulative asymptomatic, we formulate a mathematical model with infective immigrants and considering vaccination. The basic reproduction number of the special case of the model without immigration of infective people is derived. We varied two key factors that affect the transmission of COVID-19, namely the immigration and vaccination rates. In addition, we considered two different SARS-CoV-2 transmissibilities in order to account for new more contagious variants such as Omicron. Numerical simulations using initial conditions approximating the situation in the US when the vaccination program was starting show that increasing the vaccination rate significantly improves the outcomes regarding the number of deaths, cumulative infected and cumulative asymptomatic. Other factors are the natural recovery rates of infected and asymptomatic individuals, the waning rate of the vaccine and the vaccination rate. When the immigration rate is increased significantly, the number of deaths, cumulative infected and cumulative asymptomatic increase. Consequently, accounting for the level of inflow of infective immigrants may help health policy/decision-makers to formulate policies for public health prevention programs, especially with respect to the implementation of the stringent preventive lock down measure.
ABSTRACT
BACKGROUND: At the beginning of the coronavirus disease (COVID-19) pandemic, hydroxychloroquine (HCQ) was widely used as a possible antiviral agent. Current knowledge indicates that HCQ has little or no effect on individual clinical outcomes of COVID-19, but populational effects on disease transmissibility are still unknown. OBJECTIVE: This study investigates the hypothesis that massive HCQ consumption by a population may contribute to reducing the transmissibility of SARS-CoV-2 and COVID-19 spread by reducing the viral load of infected individuals. METHODS: Public database of seven states from Brazil in 2020 were assessed, before the start of COVID-19 vaccination. The daily values of the COVID-19 effective reproduction number (Rt) were obtained. Associations between Rt values and the proposed predictor variables (prevalence of COVID-19 as a marker of collective immunity; social isolation indices; consumption of HCQ) were tested using multiple linear regression analysis. RESULTS: In all seven states, consumption of HCQ was a significant negative predictor of Rt (ß ranged from -0.295 to -0.502, p = 0.001). Furthermore, the mean derivative of Rt during the declining period of the COVID-19 incidence (the mean rate of variation) was also significantly negatively related to the mean HCQ consumption in that period (R2 = 0.895; ß = -0.783; p = 0.011), meaning that the higher the HCQ consumption, the faster the decline of COVID-19 Rt. It suggests a dose-response phenomenon and a causal relationship in this association. CONCLUSION: The results of this study are compatible with the hypothesis that HCQ has small but significant in vivo antiviral effects that are able to reduce SARS-CoV-2 transmissibility at the populational level.
ABSTRACT
The COVID-19 pandemic has affected the whole world quite seriously. The number of new infectious cases and death cases are rapidly increasing over time. In this study, a theoretical linguistic fuzzy rule-based susceptible-exposed-infectious-isolated-recovered (SEIIsR) compartmental model has been proposed to predict the dynamics of the transmission of COVID-19 over time considering population immunity and infectiousness heterogeneity based on viral load in the model. The model's equilibrium points have been calculated, and stability analysis of the model's equilibrium points has been conducted. Consequently, the fuzzy basic reproduction number, R0f, of the fuzzy model has been formulated. Finally, the temporal dynamics of different compartmental populations with immunity and infectiousness heterogeneity using the fuzzy Mamdani model are delineated, and some disease control policies have been suggested to get over the infection in no time. Copyright © 2022, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
ABSTRACT
To dynamically measure COVID-19 transmissibility consistently normalized by population size in each country.A reduced-form model enhanced from the classical SIR is proposed to stochastically represent the Reproduction Number and Mortality Rate, directly measuring the combined effects of viral evolution and population behavioral response functions.Evidences are shown that this e(hanced)-SIR model has the power to fit country-specific empirical data, produce interpretable model parameters to be used for generating probabilistic scenarios adapted to the still unfolding pandemic.Stochastic processes embedded within compartmental epidemiological models can produce measurables and actionable information for surveillance and planning purposes.
ABSTRACT
We introduced the S-HI model, a generalized SEIR model to describe the dynamics of the SARS-CoV-2 virus in a community without herd immunity and performed simulations for six months. The S- HI model consists of eight equations corresponding to susceptible individuals, exposed, asymptomatic infected, asymptomatic recovered, symptomatic infected, quarantined, symptomatic recovered and dead. We study the dynamics of the infected, asymptomatic. Dead classes in 4 different networks: households, workplaces, agglomeration places and the general community, showing that the dynamics of the three compartments have the exact nature in each layer and that the speed of the disease considerably increases in the networks with the highest weight of contacts. The reproduction number, R0, is greater than 1 in all networks conforming to the theory. The variants of the SARS-Cov-2 virus are not taken into account, so the S-HI model would fit a situation similar to the first wave of contagion after the mandatory lockdown. Copyright: © 2022 by the authors.
ABSTRACT
In this paper, we develop and analyse a modified susceptible-infected-recovered (SIR) compartment model by integrating the vaccination factor as a model parameter to investigate the effect of vaccination parameter on the long-term outcomes of the COVID-19 pandemic. Mathematical analysis is used to determine the disease-free equilibrium, the endemic equilibrium, and the basic reproduction number of the developed model. The stability of the model is studied using the Routh-Hurwitz criterion, and numerical simulations are conducted to assess the impact of vaccination on the disease at different rates. The findings suggest that vaccination rate influences the transmission dynamics, and the vaccine can speed up the COVID-19 recovery and contain the outbreak. © 2023 Inderscience Enterprises Ltd.