Stability analysis of fuzzy HTLV-I infection model: a dynamic approach

This paper deals with a mathematical model for HTLV-I infection by considering the role of imprecise essence of the biological parameters. The considered imprecise biologically realistic parameters are taken as a form of triangular fuzzy number. Then the imprecise parameters are transformed to the associated intervals and then with the aid of interval mathematics the corresponding differential equations is changed to two equations. Next, by utilizing utility function method the transformed differential equations is converted to a differential equation. The dynamics of fuzzy HTLV-I model is studied with the help of the utility function method. We explored the qualitative features of HTLV-I model including positivity, boundedness, uniform persistence and biologically feasible equilibrium points, namely disease-free equilibrium point, HTLV-I free steady state and an interior equilibrium point. Our theoretical analysis demonstrates that local and global stability are examined by two critical parameters R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} and R1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_1$$\end{document}, basic reproduction numbers due to viral infection and for cytotoxic-T-lymphocytes response, respectively. By using geometric approach, we performed global stability of the endemic equilibrium point which is not only theoretically significant but also important in forecasting the development of HTLV-I infection in the long-run so that involvement strategies can be effectively sketched. Some numerical illustrations are presented to support our theoretical analysis under imprecise biological parameters.