Dynamical behavior of HIV infection in fuzzy environment

Abstract

The fuzziness of the parameters of any mathematical model is a major concern today in the field of epidemiology. In this article we apply the technique of Hukuhara derivative for mathematical formulation of HIV infection with CD4+T cell. We formulate a two species four dimensional Fuzzy differential equation (FDE), with uncertain behavior of susceptible CD4+T-cells and infected CD4+T-cells. We formulate the FDE when both the populations i.e. susceptible CD4+T cell (x(t)) and infected CD4+T cell (y(t)) are i-gH differentiable, x(t) is i-gH and y(t) is ii-gH differentiable, x(t) is ii-gH and y(t) is i-gH differentiable and finally we present the model when both the population are in ii-gH differentiable. Stability criteria of the equilibrium points are described analytically. Analytic result are verified by numerical simulation. We perform our numerical simulations of the different fuzzy differential equations when all the parameters are imprecise in nature. Here we observed that the dynamical behavior of the HIV infection in CD+T cell depends on the fuzziness of the parameter. From our study, we can conclude that the dynamical behavior of the mathematical model depends on the imprecise nature of the parameters, which is more realistic scenario in the epidemiology. This study opened a new dimension in epidemiological study.

Keywords

• HIV/AIDS
• CD4+T
• Hukuhara derivative
• FDE
• Imprecise