The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response

Abstract

In order to describe mathematically the transmission of microparasites, especially directly transmitted infections, it is usual to set up differential equations assuming the mass action law and a homogeneously mixed population. In this paper we analyze such a model taking into account heterogeneity with respect to the infectivity, that is, the variability in the evolution of the interaction between parasite and the human host during the infectious period. The well established biological phenomenon of initial increase in parasite abundance followed by its decrease, due to the interaction between the host's immunological response and the parasite, has thus been taken into account. The variable amount of microparasites eliminated by an infectious individual, and the different (heterogeneous) immunological response build up by the host when in interaction with parasite are present in the model. The analytical expression for the basic reproduction ratio is derived through stability analysis.