Dynamics of Stochastic Zika Virus with Treatment Class in Human Population via Spectral Method

Abstract

The Zika virus model (ZIKV) is mathematically modeled to create the perfect control strategies. The main characteristics of the model without control strategies, in particular reproduction number, are specified. Based on the basic reproduction number, if R00, then ZIKV satisfies the disease-free equilibrium. If R0>1, then ZIKV satisfies the endemic equilibrium. We use the maximum principle from Pontryagin’s. This describes the critical conditions for optimal control of ZIKV. Notwithstanding, due to the prevention and treatment of mosquito populations without spraying, people infected with the disease have decreased dramatically. Be that as it may, there has been no critical decline in mosquitoes contaminated with the disease. The usage of preventive treatments and insecticide procedures to mitigate the spread of the proposed virus showed a more noticeable centrality in the decrease in contaminated people and mosquitoes. The application of preventive measures including treatment and insecticides has emerged as the most ideal way to reduce the spread of ZIKV. Best of all, to decrease the spread of ZIKV is to use avoidance, treatment and bug spraying simultaneously as control methods. Moreover, for the numerical solution of such stochastic models, we apply the spectral technique. The stochastic or random phenomenons are more realistic and make the model more informative with the additive information. Throughout this paper, the additive term is assumed as additive white noise. The Legendre polynomials and applications are implemented to transform the proposed system into a nonlinear algebraic system.

Keywords

• Zika Virus model
• Legendre spectral collocation method
• stochastic asymptotic stability
• Legendre–Gauss–Lobatto points