Abstract In this paper, we generalise a simple discrete-time stochastic SIR-type model introduced by Tuckwell and Williams. The SIR model by Tuckwell and Williams assumes a homogeneous population, a fixed infectious period, and a strict transition from susceptible to infectious to recovered. In contrast, our model introduces two groups, A and B , where group B has a higher risk of infection due to increased contact rates. Additionally, the duration of the infectious period follows a probability distribution rather than being fixed. Finally, individuals in group B can transition directly to the recovered class R, allowing us to analyse the impact of this preventive measure on the spread of the disease. We then apply this model to the spread of HIV, analysing how risk behaviours, rapid testing, and PrEP-like therapies influence the epidemic dynamics.
Carles Rovira (Thu,) studied this question.