Optimal control of allocation of resources and the economic growth in HIV-infected communities

The neoclassical model of economic growth is used to model the economic growth of a HIV‐infected community with efforts in controlling the epidemic. An optimal control model with pure‐state constraints is formulated and investigated. It is found that reduction of prevalence for the disease and economic growth agrees in a positive sense in the communities with high rate of population growth and low income. Moreover, the same control strategy will decrease the prevalence even if the capital is not growing for the case of high income communities. However, a disease control strategy with economic growth as its objective will not result in decrease in prevalence if the rate of population growth of the community is very low. Therefore, if the rate of the population growth of a community is nearly the replacement level, then the utility function for the selection of disease control strategies should not be an economic benefit.