Positivity and Boundedness of Solutions for a Stochastic Seasonal Epidemiological Model for Respiratory Syncytial Virus (RSV)

Abstract

In this paper we investigate the positivity and boundedness of the solution of a stochastic seasonal epidemic model for the respiratory syncytial virus (RSV ). The stochasticity in the model is due to fluctuating physical and social environments and is introduced by perturbing the transmission parameter of the seasonal disease. We show the existence and uniqueness of the positive solution of the stochastic seasonal epidemic model which is required in the modeling of populations since all populations must be positive from a biological point of view. In addition, the positivity and boundedness of solutions is important to other nonlinear models that arise in sciences and engineering. Numerical simulations of the stochastic model are performed using the Milstein numerical scheme and are included to support our analytic results.

Keywords

• Seasonal epidemic model
• respiratory syncytial virus
• stochastic differential equation
• Itˆo’s formula
• positive solutions
• brownian motion.