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

Correspondent author email: hyunyang{at}ime.unicamp.br In order to describe mathematically the transmission of microparasites,especially directly transmitted infections, it is usual to setup differential equations assuming the mass action law and ahomogeneously mixed population. In this paper we analyze sucha model taking into account heterogeneity with respect to theinfectivity, that is, the variability in the evolution of theinteraction between parasite and the human host during the infectiousperiod. The well established biological phenomenon of initialincrease in parasite abundance followed by its decrease, dueto the interaction between the host's immunological responseand the parasite, has thus been taken into account The variableamount of microparasites eliminated by an infectious individual,and the different (heterogeneous) immunological response buildup by the host when in interaction with parasite are presentin the model. The analytical expression for the basic reproductionratio is derived through stability analysis.