Dynamics analysis and numerical simulations of a delayed stochastic epidemic model subject to a general response function

• Published in: Computational & applied mathematics Vol. 38; no. 2; pp. 1 - 30
• Main Authors: Li, Fei, Zhang, Shengqiang, Meng, Xinzhu
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2019; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Asymptotic properties; Background noise; Computational mathematics; Computational Mathematics and Numerical Analysis; Computer simulation; Economic models; Epidemics; Liapunov functions; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinear response; Response functions; Simulation; Stochastic models; Time delays; Numerical simulations; Global asymptotics; 65C30; 34E10; 92B05; Nonlinear incidence rate; Stochastic delayed epidemic model
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-019-0857-x

This paper proposes a new delayed stochastic epidemic model with double epidemic hypothesis and a general nonlinear response function. The main purpose is to explore the effects of environmental noise and the general nonlinear response function on stochastic dynamics. By constructing appropriate Lyapunov functions and using some novel differential inequality techniques, we first investigate the long-time asymptotic properties of the stochastic delayed system. Moreover, the threshold conditions for the persistence in mean are established. At last, we carry out a series of numerical simulations to illustrate the performance of the theoretical results. The developed theoretical methods and stochastic inequalities techniques can be applied to explore stochastic differential systems with the general response function.