A Partition Theorem for a Randomly Selected Large Population

We state and prove a proposition on partitioning of a randomly selected large population into stationary and non-stationary populations by using a property of stationary population identity. Applicability of this theorem for practical purposes is summarized at the end.Comment: 7 pages, a new result in population dynamic

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 on surviving period of people with HIV. We consider previously well-known models in HIV epidemiology where the parameter for 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 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 are also computed.Comment: 53 page