Fuzzy Uncertainty Analysis of A Fractional Order HIV Dynamic Model with Type-1 and Interval Type-2 Parameters

Abstract

Abstract In recent years, the study of mathematical models for the Human Immunodeficiency Virus (HIV) has attracted considerable interest due to its importance in comprehending and combating the propagation of the virus. Typically, the model's governing equations are a system of ordinary differential equations. In order to explain the inheritance behaviour, fractional order HIV models may be more helpful than integer order models. In addition, the presence of uncertainty in real world phenomena can not be avoided, and fuzzy numbers are of great use in these scenarios. In view of the above, the numerical solution of the fuzzy fractional order HIV model is analysed in this paper. The model takes into account the interactions between susceptible, asymptomatic, and symptomatic populations, as well as the effects of fractional order derivatives and fuzzy uncertainty. Here, the differentiation of the fuzzy parameters is considered in granular sense. The uncertain model parameters are addressed with triangular fuzzy numbers (TFNs) and interval type-2 triangular fuzzy numbers (IT2TFNs). The use of interval type-2 fuzzy numbers rather than type-1 fuzzy numbers to express the imprecise parameters may be helpful in some instances where the membership grade is unclear. The generalised modified Euler method (GMEM) is used to derive the corresponding solutions. Lastly, the behaviour of various populations in crisp as well as uncertain environments is also studied using graphical results.