Using mathematical and economic epidemiology tools for modelling HIV infection in serodiscordant couples.
We investigate the appropriate strategies that reduce the HIV transmission rate amongst the serodiscordant married couples. In particular, we formulate two discrete sub-models, the formation of married serodiscordant couples through marriage of single individuals and the formation of married serodiscordant couples through infection of HIV concordant negative married couples. We incorporate a constant treatment rate and solve these sub-models analytically. Our results showed that the formation of married serodiscordant couples through marriage of single individuals sub-model has no disease free equilibrium point because the serodiscordant couples are always present in the population. We computed the invasion reproductive number and showed that the endemic equilibrium point is stable when the invasion reproduction number is greater than one. In the formation of serodiscordant couples through infection of HIV concordant negative married couples, our results revealed that there exist a disease free equilibrium point and the endemic equilibrium point. We use the fixed point theory to determine the existence of the endemic equilibrium. We showed that when the basic reproduction number is less than unity, then it will be possible to control the HIV epidemic in serodiscordant couples otherwise the infection will persist. Sensitivity analysis revealed that for the disease to be controllable, intervention strategies must target to increase the treatment rate to reduce the HIV transmission rate. We then formulated the main model combining the dynamics of the two sub-models and incorporate treatment rate as the price-dependent demand function. We use the main model to explore the effects of treatment under eight different intervention strategic scenarios. Our results showed that out of the eight strategies only six were capable of reducing the HIV transmission rate amongst the serodiscordant married couples. The most effective intervention strategy was to treat directly the serodiscordant married couples. This strategy is expected to be cost efficient and could be implemented in poor resource setting.