Reproduction number for yellow fever dynamics between primates and human beings

Abstract

Vector borne diseases are spreading very rapidly in the populations all over the World. Thus, there is need to mobilize people about transmission of the disease in order to eradicate it. In this paper we propose a deterministic mathematical model through non-linear ordinary differential equations in order to gain an insight into dynamics of yellow fever between primates, human beings and Aedes mosquito for the purpose of controlling the disease. In the analysis of the model we investigate the basic reproduction number, $R_{0}$, between primates, vectors and human host. The disease threshold parameter is obtained using next generation matrix approach and is of the form $R_{0}^{2}=R_{h}+R_{m}$, where $R_{h}$ and $R_{m}$ are the reproduction number of human-vector and vector-primate compartments respectively. It is proved that the global transmission dynamics of the disease are completely determined by the basic reproduction number. In order to study the effect of model parameters to $R_{0}$, the sensitivity analysis of basic reproductive number, $R_{0}$, with respect to epidemiological and parameters is performed. Results call attention to parameters regarding to daily bitting rate of mosquitoes, birth rate of vectors, probability of transmission from infectious vector to susceptible human and vice versa, recruitment of human host which includes unvaccinated immigrants as well as the incubation period for both vector and humans. Thus, quick and focused interventions, like personal protection and destruction of breeding sites, may be effective for controlling the disease transmission.