Mathematical modelling of HTLV I infection with CTL immune response

Abstract

The thesis work deals with HTLV-I infection models in deterministic, fuzzy, and stochastic environments. The theoretical and numerical findings of HTLV-I infection models are reported according to different biological aspects like viral latency, activation in the target cells, immune response cells, intracellular delay, and immune response delay. Here, a four-dimensional HTLV-I infection model has been investigated into consideration that includes cytotoxic T-lymphocytes. By considering the biologically feasible parameter, the basic mathematical properties of the proposed model are examined to demonstrate uniform persistence, stability, and sensitivity analysis. Then, we consider a mathematical model for HTLV-I infection that includes delayed cytotoxic T-cells (CTLs) immune response. The very rich dynamics of the proposed model have been studied by considering the intracellular time delay for the CTLs immune response. In reality, biological parameters are not precise. From this point of view, we present an HTLV-I infection model by assuming the role of imprecise essence of the biological parameters. We study the dynamics of the fuzzy HTLV-I infection model using the utility function method. After that, in order to introduce randomness and uncertainty in the model description, we proposed and analyzed a stochastic epidemic model for HTLV-I virus transmission dynamics in a fluctuating environment. The dynamics of the HTLV-I infection model is disturbed by white noise. Finally, we have taken an HTLV-I infection model with two control variables. The main aim of this study is to model mathematically, analyze, and investigate computationally potentially optimal strategies that can minimize an HTLV-I virus and treatment cost. Finally, the thesis ends with the conclusions of our work and the scope for future development.