Incubation periods under various anti-retroviral therapies in homogeneous mixing and age-structured dynamical models: A theoretical approach

With the launch of second line anti-retroviral therapy for HIV infected individuals, there has been an increased expectation of survival for people with HIV. We consider previously well-known models in HIV epidemiology where the parameter for the incubation period is used as one of the important components to explain the dynamics of the variables. Such models are extended here to explain the dynamics with respect to a given therapy that prolongs the life of an HIV infected individual. A deconvolution method is demonstrated for estimation of parameters in the situations when no-therapy and multiple therapies are given to the infected population. The models and deconvolution method are extended in order to study the impact of therapy in age-structured populations. A generalization for a situation when n-types of therapies are available is given. Models are demonstrated using hypothetical data, and sensitivity of the parameters is also computed.