Modeling and optimal control analysis of Zika virus with media impact

Abstract

Zika virus disease is a mosquito-borne disease which is mainly transmitted by the female Aedes mosquitoes. Initially, since the 1950, the Zika virus disease (or Zika fever) was known to occur only in a narrow equatorial belt from Africa to Asia but from 2007 to 2016, the virus spread eastward (i.e. across the Pacific Ocean to the Americas) and that led to the 2015–2016 Zika virus epidemic. Now, it is creating a viral threat to societies all over the World because it spreads very fast in a globally connected world. The Zika virus is a member of the virus family Flaviviridae and its dynamics is governed by the day time activities of Aedes mosquitoes (i.e. A. aegypti and A. albopictus, etc.). However, there also exist new evidences of its transmission dynamics being governed via sexual contact and that has been reported from different nations (i.e. Argentina, Canada, Chile, France, Italy, New Zealand, Peru, Portugal, and USA). This paper introduces a mathematical model to investigate the transmission dynamics of Zika virus disease through the inclusion of the impact of media. Our proposed model involves both the possible routes of transmission (i.e. mosquito borne and sexual transmission). The existence and stability of different equilibria of this model are presented and analyzed in detail. The basic reproduction number $$R_0$$ of the model is computed and it is found that for $$R_0<1$$ , the disease free equilibrium of the model is locally asymptotically stable. When $$R_0>1$$ , the endemic equilibrium point exists and is locally asymptotically stable under some restriction on parameters. For $$R_0<1$$ , backward bifurcation occurs, which suggests that lowering $$R_0$$ below one is not enough to eliminate the disease from the population. Finally, we extend our model to optimal control model by introducing two types of control parameters and compare the results of both the models using numerical simulation. Our presented results highlight the efficacy of the role of media and show that the proposed model is efficient in the analysis of transmission dynamics of the Zika virus disease. The sensitivity analysis of the parameters suggests that the key parameters are the mosquito biting rate and the rate of transmission due to the sexual contact between human to human. A small increase in any of these parameters can lead to great increase in the basic reproduction number $$R_0$$ and this causes a large outbreak of this disease. So, the control policies should aim for controlling both the routes of transmission of this disease.