Stochastic Lattice gas Cellular Automata Model for Epidemics

The aim of this study was to develop and explore a stochastic lattice gas cellular automata （LGCA） model for epidemics. A computer program was development in order to implement the model. An irregular grid of cells was used. A susceptible-infected-recovered （SIR） scheme was represented. Stochasticity was generated by Monte Carlo method. Dynamics of model was explored by numerical simulations. Model achieves to represent the typical SIR prevalence curve. Performed simulations also show how infection, mobility and distribution of infected individuals may influence the dynamics of propagation. This simple theoretical model might be a basis for developing more realistic designs.

Dynamic Modelling of Dengue Epidemics in Function of Available Enthalpy and Rainfall

In this work, we present results of an investigation of environmental precursors of infectious epidemic of dengue fever in the Metropolitan Area of Rio de Janeiro, RJ, Brazil, obtained by a numerical model with representation of infection and reinfection of the population. The period considered extend between 2000 and 2011, in which it was possible to pair meteorological data and the reporting of dengue patients worsening. These data should also be considered in the numerical model, by assimilation, to obtain simulations of Dengue epidemics. The model contains compartments for the human population, for the vector Aedes aegypti and four virus serotypes. The results provide consistent evidence that worsening infection and disease outbreaks are due to the occurrence of environmental precursors, as the dynamics of the accumulation of water in the breeding and energy availability in the form of metabolic activation enthalpy during pre-epidemic periods.

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.

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.

Projecting the Dynamic Trends of Human Immunodeficiency Virus/Acquired Immunodeficiency Syndrome:Modeling the Epidemic in Sichuan Province, China

Objective Our study aimed to provide a comprehensive overview of the current status and dynamic trends of the human immunodeficiency virus(HIV)prevalence in Sichuan,the second most heavily affected province in China,and to explore future interventions.Methods The epidemiological,behavioral,and population census data from multiple sources were analyzed to extract inputs for an acquired immunodeficiency syndrome(AIDS)epidemic model(AEM).Baseline curves,derived from historical trends in HIV prevalence,were used,and the AEM was employed to examine future intervention scenarios.Results In 2015,the modeled data suggested an adult HIV prevalence of 0.191%in Sichuan,with an estimated 128,766 people living with HIV/AIDS and 16,983 individuals with newly diagnosed infections.Considering current high-risk behaviors,the model predicts an increase in the adult prevalence to 0.306%by 2025,projecting an estimated 212,168 people living with HIV/AIDS and 16,555 individuals with newly diagnosed infections.Conclusion Heterosexual transmission will likely emerge as the primary mode of AIDS transmission in Sichuan.Furthermore,we anticipate a stabilization in the incidence of AIDS with a concurrent increase in prevalence.Implementing comprehensive intervention measures aimed at high-risk groups could effectively alleviate the spread of AIDS in Sichuan.

A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential EquationModel for HIV/AIDS with Treatment Compartment

In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.

Stochastic Bifurcation of an SIS Epidemic Model with Treatment and Immigration

In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. .

Traveling Wave Solutions of a SIR Epidemic Model with Spatio-Temporal Delay

In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when R0>1and c>c*, the model has a non-negative and non-trivial traveling wave solution. However, for R01and c≥0or R0>1and 0cc*, the model does not have a traveling wave solution.

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.

Asymptotic Analysis of a Stochastic Model of Mosquito-Borne Disease with the Use of Insecticides and Bet Nets

Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic model based only on the class of human infectious. The consistency of the model is established by proving that the stochastic delay differential equation describing the model has a unique positive global solution. The extinction of the disease is studied through the analysis of the stability of the disease-free equilibrium state and the persistence of the model. Finally, we introduce some numerical simulations to illustrate the obtained results.

Dynamical analysis for a malware propagation model in wireless sensor network

The threat of malware in wireless sensor network has stimulated some activities to model and analyze the malware prevalence.To understand the dynamics of malware propagation in wireless sensor network,we propose a novel epidemic model named as e-SEIR(susceptible-exposed-infectious-recovered)model,which is a set of delayed differential equations,in this paper.The model has taken into account the following two factors:1 Multi-state antivirus measures;2 Temporary immune period.Then,the stability and Hopf bifurcation at the equilibria of linearized model are carefully analyzed by considering the distribution of eigenvalues of characteristic equations.Both mathematical analysis and numerical simulations show that the dynamical features of the proposed model rely on the basic reproduction number R0 and time delayτ.This novel model can help us to better understand and predict the propagation behaviors of malware in wireless sensor networks.

GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA

An SIS epidemic model with a simple vaccination is investigated in this article, The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two threshold R0 and Rc （Rc may not exist）. There is a unique endemic equilibrium for R0 〉 1 or Rc = R0; there are two endemic equilibria for Rc 〈 R0 〈 1; and there is no endemic equilibrium for Rn 〈 Rc 〈 1. When Rc exists, there is a backward bifurcation from the disease-free equilibrium for R0 = 1. They analyze the stability of equilibria and obtain the globally dynamic behaviors of the model. The results acquired in this article show that an accurate estimation of the efficiency of vaccine is necessary to prevent and controll the spread of disease.

GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.

ANALYSIS OF AN SI EPIDEMIC MODEL WITH NONLINEAR TRANSMISSION AND STAGE STRUCTURE

A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.

GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION

In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].

GLOBAL ANALYSIS OF SOME EPIDEMIC MODELS WITH GENERAL CONTACT RATE AND CONSTANT IMMIGRATION

An epidemic models of SIR type and SIRS type with general contact rate and constant immigration of each class were discussed by means of theory of limit system and suitable Liapunov functions. In the absence of input of infectious individuals, the threshold of existence of endemic equilibrium is found.For the disease-free equilibrium and the endemic equilibrium of corresponding SIR model, the sufficient and necessary conditions of global asymptotical stabilities are all obtained.For corresponding SIRS model, the sufficient conditions of global asymptotical stabilities of the disease-free equilibrium and the endemic equilibrium are obtained. In the existence of input of infectious individuals, the models have no disease-free equilibrium. For corresponding SIR model, the endemic equilibrium is globally asymptotically stable; for corresponding SIRS model, the sufficient conditions of global asymptotical stability of the endemic equilibrium are obtained.

The Changing Trends of HIV/AIDS in An Ethnic Minority Region of China: Modeling the Epidemic in Liangshan Prefecture, Sichuan Province

Objective This study was to investigate the HIV current situation in Liangshan prefecture, in order to predict prevalence and transmission trends. Methods Region-specific population, behavior, serosurveillence, and policy/program data （from 1995 to 2020） were gathered from various local and national organizations and applied to the Asian Epidemic Model （AEM） and used to derive estimates of future HIV prevalence, epidemic trends, and outcomes of intervention strategies. Results The AEM projections for 2020 included increased number of people living with HIV （PLHIV; to 136 617）, increased HIV prevalence （2.51%）, and 8037 deaths from acquired immunodeficiency syndrome （AIDS） in this region. However, the overall HIV incidence rate （per 10 000） was projected to decline from 27 in 2015 to 22 in 2020, largely due to a predicted decrease in HIV infection rate （per 10 000） from 658 in 2013 to 621 in 2020 among intravenous drug users. In contrast, the cases of HIV infection per i0 000 was projected to increase from 420 in 2010 to 503 in 2020 among men who have sex with men, and from 8 in 2010 to 15 in 2020 among the general population. The predominant risk factor for HIV transmission over the next decade in Liangshan was casual sex. Community-based outreach strategies to reduce injected drug use and casual sex, and to promote condom use, were predicted as effective interventions to decrease HIV transmission. Conclusion Implementation of a comprehensive public health program, with targeting to the region-specific at-risk populations, will help to mitigate HIV/AIDS spread in Liangshan.

GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.

Turing pattern selection in a reaction-diffusion epidemic model

We present Turing pattern selection in a reaction-diffusion epidemic model under zero-flux boundary conditions. The value of this study is twofold. First, it establishes the amplitude equations for the excited modes, which determines the stability of amplitudes towards uniform and inhomogeneous perturbations. Second, it illustrates all five categories of Turing patterns close to the onset of Turing bifurcation via numerical simulations which indicates that the model dynamics exhibits complex pattern replication： on increasing the control parameter v, the sequence ＂H0 hexagons → H0-hexagon-stripe mixtures →stripes → Hπ-hexagon-stripe mixtures → Hπ hexagons＂ is observed. This may enrich the pattern dynamics in a diffusive epidemic 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.