Compartmental model analysis for disease dynamics of tuberculosis in fuzzy environment

Abstract

This study presents a compartmental model analysis for disease dynamics of tuberculosis in fuzzy environment. The objective behind this study is to see the impact of two different control strategies namely protective antiviral treatment for active tuberculosis population and vaccination for susceptible population. The use of fuzzy parameters aids in addressing the difficulties associated with measuring uncertainty in the mathematical representation of disease dynamics of tuberculosis. Fuzzy theory is the most effective strategy for managing these uncertainties. The disease dynamics of tuberculosis in fuzzy environment is discussed by considering the tuberculosis transmission rate as fuzzy parameter. Forward Euler's scheme, Runge-Kutta method and non-standard finite difference (NSFD) scheme have been used to solve the model. The basic characteristics of the proposed model including positivity and boundedness are investigated. This study also includes the convergence and consistency analysis of NSFD scheme. The fuzzy reproduction number and fuzzy equilibrium points are obtained by using a model relevant to a specific group described by the triangular membership function. Numerical simulations are also performed to support the analytical results. Despite the uncertainty and heterogeneity, the computational findings show that the suggested NSFD scheme accurately captures the disease dynamics of tuberculosis.