DETERMINISTIC MODEL OF ZIKA-VIRUS WITH CARRIER MOTHER AND RESERVOIRS: A MATHEMATICAL ANALYSIS APPROACH
Abstract
In this paper, a mathematical model for the Zika virus is suggested to investigate the transmission dynamics of infection based on humans, pregnant carrier mother, infected children and the reservoir (primates) in three connected populations. Vertical and direct transmissions from all people to primates are considered in the proposed model. The Zika virus then spreads from this reservoir of infection via the nonhuman primate population (infected mosquitoes) to other entities. This virus can be passed on to the human population through an infected mosquito. Therefore, the new model with ten compartmental models has been normalized as follows: The normalized model is analyzed in depth to explore linkages between mosquitoes, humans, and primates on the dynamics of Zika-Virus transmission. The mathematical analysis comprises positivity and boundedness of solutions, determination of the basic reproduction number R0 via next-generation matrix approach, existence and stability of all equilibria as well as sensitivity analysis. Local and Global Stability of the Disease-free Equilibrium. Finally, numerical simulations are performed to verify the analytical results obtained and exhibit the contribution of different model parameters on disease transmission dynamics. The results prove that the interaction of forest mosquitoes with primates has a significant effect on human-Zika-Virus transmission dynamics among the susceptible population due to transitions to forested areas. Moreover, the findings suggest that the transmission probabilities and biting rates of mosquitoes on humans and primates are major parameters in transmitting the disease.
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