Analysis of a time-delayed HIV/AIDS epidemic model with education campaigns

TL;DR

This paper analyzes a time-delayed HIV/AIDS epidemic model incorporating education campaigns, demonstrating how increased information dissemination can reduce infection levels and potentially eradicate the disease.

Contribution

It introduces a novel HIV/AIDS model with time delay and education effects, providing theoretical analysis and data fitting to show the impact of information dissemination.

Findings

Disease eradication when R0 ≤ 1

Infected population size decreases linearly with education

Model fitted to real HIV/AIDS data and validated through simulations

Abstract

We consider a time-delayed HIV/AIDS epidemic model with education dissemination and study the asymptotic dynamics of solutions as well as the asymptotic behavior of the endemic equilibrium with respect to the amount of information disseminated about the disease. Under appropriate assumptions on the infection rates, we show that if the basic reproduction number is less than or equal to one, then the disease will be eradicated in the long run and any solution to the Cauchy problem converges to the unique disease-free equilibrium of the model. On the other hand, when the basic reproduction number is greater than one, we prove that the disease will be permanent but its impact on the population can be significantly minimized as the amount of education dissemination increases. In particular, under appropriate hypothesis on the model parameters, we establish that the size of the component of the infected population of the endemic equilibrium decreases linearly as a function of the amount of information disseminated. We also fit our model to a set of data on HIV/AIDS in order to estimate the infection, effective response, and information rates of the disease. We then use these estimates to present numerical simulations to illustrate our theoretical findings.