A Study on Fuzzy Mathematical Modelling and Applications

Abstract

This thesis deals with fuzzy SIR mathematical models exploring the transmission dynamics newlineof three dangerous viruses (Malaria, TB, and HIV). Models are represented by ordinary newlinenonlinear differential equations. We take two models based on the basic Susceptible- newlineInfectious-Recovered model and another model based on the Uninfected-Infected-Free Virus newlineParticle-Magnitude of CTL model discussed. We analyzed a fuzzy mathematical model for newlinethe transmission, recovery, treatment, and control of the infectious diseases. Disease-free newlineequilibrium, endemic equilibrium, and the basic reproduction number are obtained for stability newlineanalysis. The fuzzy basic reproduction number and fuzzy control system are calculated using newlinethe fuzzy membership function with various virus loads. Bifurcation and Sensitivity analysis newlineof basic reproduction number is performed.We find the solution by using some analytical and newlinenumerical methods to predict the transmission of infectious diseases newline