Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

COEXISTENCE FOR MULTIPLE LARGEST REPRODUCTION RATIOS OF A MULTI-STRAIN SIS EPIDEMIC MODEL

In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.

Assess Medical Screening and Isolation Measures Based on Numerical Method for COVID-19 Epidemic Model in Japan

This study aims to improve control schemes for COVID-19 by a numerical model with estimation of parameters.We established a multi-level and multi-objective nonlinear SEIDR model to simulate the virus transmission.The early spread in Japan was adopted as a case study.The first 96 days since the infection were divided into five stages with parameters estimated.Then,we analyzed the trend of the parameter value,age structure ratio,and the defined PCR test index(standardization of the scale of PCR tests).It was discovered that the self-healing rate and confirmed rate were linear with the age structure ratio and the PCR test index using the stepwise regression method.The transmission rates were related to the age structure ratio,PCR test index,and isolation efficiency.Both isolation measures and PCR test medical screening can effectively reduce the number of infected cases based on the simulation results.However,the strategy of increasing PCR test medical screening would encountered a bottleneck effect on the virus control when the index reached 0.3.The effectiveness of the policy would decrease and the basic reproduction number reached the extreme value at 0.6.This study gave a feasible combination for isolation and PCR test by simulation.The isolation intensity could be adjusted to compensate the insufficiency of PCR test to control the pandemic.

New Fuzzy Fractional Epidemic Model Involving Death Population

In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-Infected-Recovered-Susceptible(SIRS)include the death rate as one of the parameters to estimate the change in susceptible,infected and recovered populations.Actually,because of the deficiencies in immunity,even the ordinary flu could cause death.If people’s disease resistance is strong,then serious diseases may not result in mortalities.The classical model always assumes a closed system where there is no new birth or death,no immigration or emigration,while in reality,such assumptions are not realistic.Moreover,the classical epidemic model does not report the change in population due to death caused by a disease.With this study,we try to incorporate the rate of change in the population of death caused by a disease,where the model is framed to reduce the curve of death along with the susceptible and infected populations.Since the rate of change turned out to be very small,we have tried to estimate it fractionally.Thus,the model is defined using fuzzy logic and is solved by two different methods:a Laplace Adomian decomposition method(LADM)and a differential transform method(DTM)for an arbitrary order α.To test its accuracy,we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method(RKM-4)at α=1.

Stability Analysis of SIQS Epidemic Model with Saturated Incidence Rate

A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.

Analysis of SDEs Applied to SEIR Epidemic Models by Extended Kalman Filter Method

A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a system of nonlinear stochastic differential equations (SDEs). The numerical simulation of the resulting SDEs is done by Euler-Maruyama scheme and the parameters are estimated by adaptive Markov chain Monte Carlo and extended Kalman filter methods. The stochastic results are discussed and it is observed that with the SDE type of modeling, the parameters are also identifiable.

Study on the Dynamics of an SIR Epidemic Model with Saturated Growth Rate

In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.

Extinction and Stationary Distribution of a Stochastic SIR Epidemic Model with Jumps

A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.

Structure-Preserving Dynamics of Stochastic Epidemic Model with the Saturated Incidence Rate

The structure-preserving features of the nonlinear stochastic models are positivity,dynamical consistency and boundedness.These features have a significant role in different fields of computational biology and many more.Unfortunately,the existing stochastic approaches in literature do not restore aforesaid structure-preserving features,particularly for the stochastic models.Therefore,these gaps should be occupied up in literature,by constructing the structure-preserving features preserving numerical approach.This writing aims to describe the structure-preserving dynamics of the stochastic model.We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling.The usual explicit stochastic numerical approaches are time-dependent.We have developed the implicitly driven explicit approach for the stochastic epidemic model.We have proved that the newly developed approach is preserving the structural,dynamical properties as positivity,boundedness and dynamical consistency.Finally,convergence analysis of a newly developed approach and graphically illustration is also presented.

A Stochastic SIVS Epidemic Model Based on Birth and Death Process

A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.

The Effect of State-Dependent Control for an SIRS Epidemic Model with Varying Total Population

Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.

Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate

Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>1.This approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using that.In addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)<1 and linearly stable if R_(c)=1;while V^(0)is unstable if R_(c)>1.

Vaccination effect on a stochastic epidemic model with healing and relapse

In this work,we consider a stochastic epidemic model with vaccination,healing and relapse.We prove the existence and the uniqueness of the positive solution.We establish sufficient conditions for the extinction and the persistence in mean of the stochastic system.Moreover,we also establish sufficient conditions for the existence of ergodic stationary distribution to the model,which reveals that the infectious disease will persist.The graphical illustrations of the approximate solutions of the stochastic epidemic model have been performed.

The global stability and optimal control of the COVID-19 epidemic model

This paper considers stability analysis of a Susceptible-Exposed-Infected-Recovered-Virus(SEIRV)model with nonlinear incidence rates and indicates the severity and weakness of control factors for disease transmission.The Lyapunov function using Volterra-Lyapunov matrices makes it possible to study the global stability of the endemic equilibrium point.An optimal control strategy is proposed to prevent the spread of coronavirus,in addition to governmental intervention.The objective is to minimize together with the quantity of infected and exposed individuals while minimizing the total costs of treatment.A numerical study of the model is also carried out to investigate the analytical results.

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.

A regime-switching stochastic SIR epidemic model with a saturated incidence and limited medical resources

The stochastic switching SIR epidemic model with saturated incidence and limited medical treatment is investigated in this paper.By using Lyapunov methods and Ito formula,we first prove that the system has a unique global positive solution with any positive initial value.Then combining inequality technique and the ergodic property of Markov switching,the suficient conditions for extinction and persistence in the mean of the disease are established.The results demonstrate that increasing medical resources and improving supply efficiency can accelerate the transition from the persistent state to the extinct state.Meanwhile,the high incidence rate will slow down the extinction of the disease.Specially,the switching noise can induce the system to toggle between the extinct and persistent states.Finally,some numerical simulations are carried out to confirm the analytical results.

Backward bifurcation,basic reinfection number and robustness of an SEIRE epidemic model with reinfection

Recent evidences show that individuals who recovered from COVID-19 can be reinfected.However,this phenomenon has rarely been studied using mathematical models.In this paper,we propose an SEIRE epidemic model to describe the spread of the epidemic with reinfection.We obtain the important thresholds R_(0)(the basic reproduction number)and R_(c)(a threshold less than one).Our investigations show that when R_(0)>1,the system has an endemic equilibrium,which is globally asymptotically stable.When R_(c)<R_(0)<1,the epidemic system exhibits bistable dynamics.That is,the system has backward bifurcation and the disease cannot be eradicated.In order to eradicate the disease,we must ensure that the basic reproduction number R_(0) is less than R_(c).The basic reinfection number is obtained to measure the reinfection force,which turns out to be a new tipping point for disease dynamics.We also give definition of robustness,a new concept to measure the dificulty of completely eliminating the disease for a bistable epidemic system.Numerical simulations are carried out to verify the conclusions.

Intelligent computing networks for nonlinear influenza-A epidemic model

The differential equations having delays take paramount interest in the research community due to their fundamental role to interpret and analyze the mathematical models arising in biological studies.This study deals with the exploitation of knack of artificial intelligence-based computing paradigm for numerical treatment of the functional delay differential systems that portray the dynamics of the nonlinear influenza-A epidemic model(IA-EM)by implementation of neural network backpropagation with Levenberg-Marquardt scheme(NNBLMS).The nonlinear IA-EM represented four classes of the population dynamics including susceptible,exposed,infectious and recovered individuals.The referenced datasets for NNBLMS are assembled by employing the Adams method for sufficient large number of scenarios of nonlinear IA-EM through the variation in the infection,turnover,disease associated death and recovery rates.The arbitrary selection of training,testing as well as validation samples of dataset are utilizing by designed NNBLMS to calculate the approximate numerical solutions of the nonlinear IA-EM develop a good agreement with the reference results.The proficiency,reliability and accuracy of the designed NNBLMS are further substantiated via exhaustive simulations-based outcomes in terms of mean square error,regression index and error histogram studies.

Traveling wave solutions for a discrete diffusive epidemic model with asymptomatic carriers

This paper mainly concerns about the traveling wave solution(TwS)for a discrete diffusive epidemic model with asymptomatic carriers.Analysis of the model shows that the minimum wave speed c*exists if a threshold is greater than one.With the help of sub-and super-solutions,we find that the condition for the existence of TWS is R>1 and wave speed c>c^(*).Further,we prove that the TwS connects two different boundary steady states.Through the arguments with Laplace transform,we show there is no TWS for the model if R>1 and o<c<c^(*)or R≤1.