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.

A Hybrid SIR-Fuzzy Model for Epidemic Dynamics:A Numerical Study

This study focuses on the urgent requirement for improved accuracy in diseasemodeling by introducing a newcomputational framework called the Hybrid SIR-Fuzzy Model.By integrating the traditional Susceptible-Infectious-Recovered(SIR)modelwith fuzzy logic,ourmethod effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model parameters.The main aim of this research is to provide a model for disease transmission using fuzzy theory,which can successfully address uncertainty in mathematical modeling.Our main emphasis is on the imprecise transmission rate parameter,utilizing a three-part description of its membership level.This enhances the representation of disease processes with greater complexity and tackles the difficulties related to quantifying uncertainty in mathematical models.We investigate equilibrium points for three separate scenarios and perform a comprehensive sensitivity analysis,providing insight into the complex correlation betweenmodel parameters and epidemic results.In order to facilitate a quantitative analysis of the fuzzy model,we propose the implementation of a resilient numerical scheme.The convergence study of the scheme demonstrates its trustworthiness,providing a conditionally positive solution,which represents a significant improvement compared to current forward Euler schemes.The numerical findings demonstrate themodel’s effectiveness in accurately representing the dynamics of disease transmission.Significantly,when the mortality coefficient rises,both the susceptible and infected populations decrease,highlighting the model’s sensitivity to important epidemiological factors.Moreover,there is a direct relationship between higher Holling type rate values and a decrease in the number of individuals who are infected,as well as an increase in the number of susceptible individuals.This correlation offers a significant understanding of how many elements affect the consequences of an epidemic.Our objective is to enhance decision-making in public health by providing a thorough quantitative analysis of the Hybrid SIR-Fuzzy Model.Our approach not only tackles the existing constraints in disease modeling,but also paves the way for additional investigation,providing a vital instrument for researchers and policymakers alike.

Stability Analysis of Predator-Prey System with Consuming Resource and Disease in Predator Species

The present study is concerned with formulating a predator-prey eco-epidemiological mathematical model assuming that an infection exists in the predator species.The two classes of predator species(susceptible and infected)compete for the same sources available in the environment with the predation option.It is assumed that the disease does not spread vertically.The proposed model is analyzed for the stability of the coexistence of the predators and prey.The fixed points are carried out,and the coexisting fixed point is studied in detail by constructing the Lyapunov function.The movement of species in search of food or protection in their habitat has a significant influence,examined through diffusion.The ecological influences of self-diffusion on the population density of both species are studied.It is theoretically proved that all the under consideration species can coexist in the same environment.The coexistence fixed point is discussed for both diffusive and non-diffusive cases.Moreover,a numerical scheme is constructed for solving time-dependent partial differential equations.The stability of the scheme is given,and it is applied for solving presently modified eco-epidemiological mathematical model with and without diffusion.The comparison of the constructed scheme with two exiting schemes,Backward in Time and Central in Space(BTCS)and Crank Nicolson,is also given in the form of plots.Finally,we run a computer simulation to determine the effectiveness of the proposed numerical scheme.For readers’convenience,a computational code for the proposed discrete model scheme may be made available upon request.