arXiv subjects

N. N. Nhu

Publications and source records attributed to N. N. Nhu.

2 recordsLinked to original sources

arXiv2021

Permanence and Extinction for the Stochastic SIR Epidemic Model

The aim of this paper is to study the stochastic SIR equation with general incidence functional responses and in which both natural death rates and the incidence rate are perturbed by white noises. We derive a sufficient and almost necessary condition for the extinction and permanence for an epidemic system with multi noises \begin{equation*} \begin{cases} dS(t)=\big[a_1-b_1S(t)-I(t)f(S(t),I(t))\big]dt + σ_1 S(t) dB_1(t) -I(t)g(S(t),I(t))dB_3(t),\\ dI(t)=\big[-b_2I(t) + I(t)f(S(t),I(t))\big]dt + σ_2I(t) dB_2(t) + I(t)g(S(t),I(t))dB_3(t). \end{cases} \end{equation*} Moreover, the rate of all convergences of the solution are also established. A number of numerical examples are given to illustrate our results

math.DS↗

arXiv2019

Stochastic Partial Differential Equation Models for Spatially Dependent Predator-Prey Equations

Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more versatile. To incorporate more qualitative features of the ratio-dependent models, the Beddington-DeAngelis functional response is also used. To analyze the systems under consideration, first existence and uniqueness of solutions of the SPDEs are obtained using the notion of mild solution. Then sufficient conditions for permanence and extinction are derived.

math.DS↗