Deterministic and Stochastic Nonlinear Schistosomiasis Model with Delay and Vaccination
Brou Edmond Narcisse YAPI *
Laboratory of Applied Mathematics and Computer Science, University Felix Houphouet Boigny, 22 BP 582 Abidjan 22, Cˆote d’Ivoire.
Modeste N’ZI
Laboratory of Applied Mathematics and Computer Science, University Felix Houphouet Boigny, 22 BP 582 Abidjan 22, Cˆote d’Ivoire.
*Author to whom correspondence should be addressed.
Abstract
A worldwide approach is needed to combat schistosomiasis, one that addresses the disease’s mollusc problem, treats parasitised individuals, and enhances hygienic circumstances by getting rid of human waste. This paper presents a deterministic SIR delayed epidemiological model with vaccination that accounts for the dynamics of parasites in both molluscs and humans. Then, we will alter some of the coefficients to create a new stochastic SIR model that includes vaccination and delay, so expanding the range of possible control tactics. Using the Lyapunov function, we may analyse the above model to determine the necessary and sufficient conditions for the regularity, existence, and uniqueness of a global solution.
Furthermore, we examine the stochastic asymptotic stability of both the endemic and disease-free equilibrium points in this model. Finally, we present applications that highlight our overall findings.
Keywords: Schistosomiasis control strategy, basic reproduction number, local stability, global stability, epidemic model, lyapunov function, ito’s formula