This work presents a novel HIV epidemic model where the infected population is described by a continuous-distributed system with an infection progression coordinate. This coordinate can represent heterogeneities of the infected population which results in a more suitable HIV characterization than the one used in multi-compartmental models. Transition rates and treatment parameters commonly defined for compartmental models are replaced by a diffusion term based on the progression coordinate. The diffusion coefficient is a function of the disease treatment strategies that affect the infection progression rate. The resulting PDE that describes the infected class dynamics is solved by standard numerical techniques. The proposed model is used to evaluate potential treatment strategies for HIV and can be extended to other infectious diseases without major modifications.
Proceedings of the 2011 IFAC World Congress, Milano, Italy, pp. 14159-14164 (2011)