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A model for HIV transmission with two interacting high-risk groups


We formulate a model of HIV transmission which keeps track of two interacting high-risk groups, namely female sex workers (FSW) and male injecting drug users (IDU), along with a third “bridge” group of male drug-free clients (DFC). To determine the global asymptotic behaviour of the model, we first consider the dynamics of an n<math class="math"><mi is="true">n</mi></math>-group SIR<math class="math"><mi is="true">S</mi><mi is="true">I</mi><mi is="true">R</mi></math> model featuring abstract, unspecified and possibly nonlinear forces of infection utilising the graph theoretic approach of Li and Shuai. It is determined that the basic reproduction number R0<math class="math"><msub is="true"><mrow is="true"><mi is="true">R</mi></mrow><mrow is="true"><mn is="true">0</mn></mrow></msub></math>, computed via the next generation method, is a threshold parameter for the stability of the disease-free and the endemic equilibrium. Global stability results for the model with two interacting high-risk groups are then obtained via suitable particularisations. We obtained partial reproduction numbers for each disease transmission route in the model, via which and our analytical results we are able to establish that if the goal of an intervention measure is to eradicate, significant reduction in transmission between FSW and IDU is needed, in addition to reduction in other routes of transmission. On the other hand, if the aim is to mitigate the disease spread, reduction in any one or more routes of disease transmission will be useful, albeit reduction in transmission between the two high-risk groups will be more impactful than others.