In this paper, we introduce two perturbations in the classical deterministic susceptible-infected-susceptible epidemic model with two correlated Brownian motions. We consider two perturbations in the deterministic SIS model and formulate the original model as a stochastic differential equation with two correlated Brownian motions for the number of infected population, based on the previous work from Gray et al. (SIAM J Appl Math 71(3):876–902, 2011) and Hening and Nguyen (J Math Biol 77:135–163, 2017. https://doi.org/10.1007/s00285-017-1192-8
 ). Conditions for the solution to become extinction and persistence are then stated, followed by computer simulation to illustrate the results.

/pdf/a-stochastic-differential-equation-sis-epidemic-model-with-2w2fc9yyp0.pdf

A stochastic differential equation SIS epidemic model with two correlated Brownian motions

This manuscript is involved in the study of stability of the solutions of functional differential equations (FDEs) with random coefficients and/or stochastic terms We focus on the study of different types of stability of random/stochastic functional systems, specifically, stochastic delay differential equations (SDDEs) Introducing appropriate Lyapunov functionals enables us to investigate the necessary conditions for stochastic stability, asymptotic stochastic stability, asymptotic mean square stability, mean square exponential stability, global exponential mean square stability, and practical uniform exponential stability Some examples with numerical simulations are presented to strengthen the theoretical results Using our theoretical study, important aspects of epidemiological and ecological mathematical models can be revealed In ecology, the dynamics of Nicholson’s blowflies equation is studied Conditions of stochastic stability and stochastic global exponential stability of the equilibrium point at which the blowflies become extinct are investigated In finance, the dynamics of the Black–Scholes market model driven by a Brownian motion with random variable coefficients and time delay is also studied

/pdf/lyapunov-stability-analysis-for-nonlinear-delay-systems-3h5027vg68.pdf

Lyapunov stability analysis for nonlinear delay systems under random effects and stochastic perturbations with applications in finance and ecology

In this paper, considering the proven role of exosomes and the inevitable randomization within-host, we establish a hepatitis B virus (HBV) model with cell-to-cell transmission and CTL immune response from a deterministic framework to a stochastic differential equation (SDE). By introducing the reproduction number $ R_0 $, we prove that $ R_0 $ can be used to govern the stochastic dynamics of the SDE HBV model. Under certain assumptions, if $ R_{0}\leq1 $, the solution of the SDE model always fluctuates around the infection-free equilibrium of the deterministic model, which indicates that the HBV will eventually disappear almost surely; if $ R_{0} > 1 $, under extra conditions, the solution of the SDE model fluctuates around endemic equilibrium of the corresponding deterministic model, which leads to the stochastic persistence of the HBV with probability one. One of the most interesting findings is that the fluctuation amplitude is positively related to the intensity of the white noise, which can provide us some useful control strategies to regulate HBV infection dynamics.

https://www.aimspress.com/data/article/export-pdf?id=5fd89e34ba35de5526613dc0

Dynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response.

In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to fin...

/pdf/stochastic-delay-foraging-arena-predator-prey-system-with-4eve53v00r.pdf

Stochastic delay foraging arena predator–prey system with Markov switching

Releasing Wolbachia-infected mosquitos to mitigate the transmission of Zika virus

A stochastic differential equation SIS epidemic model with two independent Brownian motions

In this paper, we combined the previous model in [ 2 ] with Gray et al.'s work in 2012 [ 8 ] to add telegraph noise by using Markovian switching to generate a stochastic SIS epidemic model with regime switching. Similarly, threshold value for extinction and persistence are then given and proved, followed by explanation on the stationary distribution, where the \begin{document}$ M $\end{document} -matrix theory elaborated in [ 20 ] is fully applied. Computer simulations are clearly illustrated with different sets of parameters, which support our theoretical results. Compared to our previous work in 2019 [ 2 , 3 ], our threshold value are given based on the overall behaviour of the solution but not separately specified in every state of the Markov chain.

https://www.aimsciences.org/article/exportPdf?id=dd9cb6e3-6464-40e6-9d3c-b96b9fbda0cc

A stochastic differential equation SIS epidemic model with regime switching

This paper focuses on a predator-prey system with foraging arena scheme incorporating stochastic noises. This SDE model is generated from a deterministic framework by the stochastic parameter pertu...

/pdf/analysis-of-a-stochastic-predator-prey-system-with-foraging-2s5uo2lt1g.pdf

Siyang Cai

Papers

A stochastic differential equation SIS epidemic model with two independent Brownian motions

A stochastic differential equation SIS epidemic model with two correlated Brownian motions

Stochastic delay foraging arena predator–prey system with Markov switching

A stochastic differential equation SIS epidemic model with regime switching

Analysis of a stochastic predator-prey system with foraging arena scheme