Mathematical Analysis of a Zika Model with reservoirs and Human Movement

A mathematical model for Zika virus is proposed describing the spread of the disease in three interacting populations, namely, human, vector (mosquitoes) and non-human primate (monkeys) inhabiting forests area. Human movement between rural and forest areas has been also considered. It is assumed that Zika virus spreads within non-human primate population, which in turn acts as a reservoir of infection, and then transmitted to the human population through infected mosquitoes. The proposed model incorporates vertical transmission and direct transmission in all populations. The proposed model has been first normalized. The normalized model has been then fully analyzed both qualitatively and quantitatively to investigate the role of the interaction between forest mosquitoes and primates on the ZIKV transmission dynamics. The mathematical analysis includes positivity and boundedness of solutions, derivation of the basic reproduction number R0 using the next generation matrix method, sensitivity analysis, existence and stability analysis of all equilibria and bifurcation analysis. Finally, numerical simulations have been carried out to illustrate the obtained theoretical results and to demonstrate the effect of some model parameters in the disease transmission dynamics. The results show that the interaction between forest mosquitoes and primates has a significant impact on the ZIKV transmission dynamics among human population through the fraction of susceptible moving to forest areas. Furthermore, the results highlight that the transmission probabilities are as important as the ratios of population size between vector population and human or primate populations in the disease transmission dynamics.