New Trends in Fuzzy Modeling Through Numerical Techniques

Amoebiasis is a parasitic intestinal infection caused by the highly pathogenic amoeba Entamoeba histolytica. It is spread through person-to-person contact or by eating or drinking food or water contaminated with feces. Its transmission rate depends on the number of cysts present in the environment. The traditional models assumed a homogeneous and contradictory transmission with reality. The heterogeneity of its transmission rate is a significant factor when modeling disease dynamics. The heterogeneity of disease transmission can be described mathematically by introducing fuzzy theory. In this context, a fuzzy SEIR Amoebiasis disease model is considered in this study. The equilibrium analysis and reproductive number are studied with fuzziness. Two numerical schemes forward Euler method and a nonstandard finite difference (NSFD) approach, are developed for the learned model, and the results of numerical simulations are presented. The numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease despite the uncertainty and heterogeneity. Moreover, the obtained method generates plausible predictions that regulators can use to support decision-making to design and develop control strategies.