Mathematical modelling of the effects of peer-educators’ campaign on the dynamics of HIV/AIDS in Rwanda

Abstract

In this paper, we analyse the effects of peer-educator’s campaign on the dynamics of HIV. We present a sex-structured model for heterosexual transmission of HIV/AIDS in a community. The model is formulated using integro-differential equations, which help to account for a time delay due to incubation period of infective before developing AIDS. The sex-structured HIV/AIDS model divides the population into two subpopulations, namely; females and males. Both disease Free equilibrium and the endemic equilibrium points for the model are determined and their stability are examined. The model is extended to assess the effect of peer- educational campaigns in slowing or eradicating the epidemic. The exposure risk of infection after each intervention is obtained. Basic reproductive numbers for these models are computed and compared to assess the effectiveness of each intervention in a community. The models are numerically analyzed to assess the effectiveness of the treatment free measure, namely; peer educational campaign on the transmission dynamics of HIV/AIDS using demographic and epidemiological parameters of Rwanda. The study demonstrates the use of sex-structured HIV/AIDS models in assessing the effectiveness of educational campaigns as a preventive strategy in a heterosexually active population

Mathematics Subject classifications (MSC 2010): 34D20, 34K60, 92D25, 34K25, 34K28

Keywords: Population dynamics, Stability, Basic reproductive numbers, Equilibrium