Effects of sexual and vertical transmission on Zika virus dynamics under environmental fluctuations

Zika is a mosquito-transmitted viral disease which may spread directly by the vector or sexual transmission. Zika virus may persist in semen and urine for a long time after disappearance from the blood, those persons are known as the convalescent humans. It can also be transmitted vertically among mosquitoes. In this paper, we have considered an eight-compartment Zika model to study the effect of all the said aspects on the virus dynamics in deterministic as well as stochastic environment. In analytic part, we have computed basic reproduction number and discussed stability of different equilibria. We have shown the proposed model undergoes through transcritical bifurcation when the reproduction number is unity and validate the model with real infection data of Dominican Republic in 2016. To study the model in stochastic environments, the additive noise is taken into consideration which is formulated considering the standard Brownian white noises proportional to each class. We have obtained the condition for disease extinction and persistence in mean. All theoretical findings are justified by numerical simulations. Lastly, the paper is ended with some conclusions.