# Mathematical Modeling and Stability Analysis of HIV with Contact Tracing According to the Changes in the Infected Classes

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1111)

## Abstract

In this paper, we investigate the effect of contact tracing the spread of HIV in a population. The mathematical model is given as a system of differential equations with piecewise constant arguments, where we divide the population into three sub-classes: HIV negative, HIV positive that do not know they are infected and the class with HIV positive that know they are infected. This system is analyzed using the theory of differential and difference equations. The local stability of the positive equilibrium point is investigated by using the Schur-Cohn Criteria, while for the global stability we consider an appropriate Lyapunov function. The system under consideration has shown that it has semi-cycle behaviors, but not a structure of period two. Moreover, we analyze the case for low infection rate by using the Allee effect at time t. Several examples are presented to support our theoretical findings using data from a case study in India.

## Keywords

Logistic differential equations Stability analysis Periodic behavior Allee effect

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