In this article, we develop a new age-structured stochastic delayed toxicant-population model with Lévy noise. Some novel criteria for the existence of a global positive solution and the mean square h-stability of the addressed model are given. The key technique used to prove the results is the Lyapunov functional approach and Itô’s formula. Finally, two numerical examples are provided to illustrate the effectiveness of our criteria.
AkimenkoV, KřivanV. Asymptotic stability of delayed consumer age-structured population models with an allee effect. Math Biosci, 2018; 306(1):170–179.
2.
AmaniAZ. Studies on the population dynamics of some common weeds under the stress of environmental pollution. J Dent, 1983; 41(3):195–206.
3.
DengS, FeiW, LiangY, et al.Convergence of the split-step θ-method for stochastic age-dependent population equations with markovian switching and variable delay. Applied Numerical Mathematics, 2019; 139(1):15–37.
4.
FreedmanHI, ShuklaJB. Models for the effect of toxicant in single-species and predator-prey systems. J Math Biol, 1991; 30(1):15–30.
5.
HallamTG, ClarkCE, JordanGS. Effects of toxicants on populations: A qualitative approach II. First order kinetics. J Math Biol, 1983; 18(1):25–37.
6.
HeJ, WangK. The survival analysis for a single-species population model in a polluted environment. Applied Mathematical Modelling, 2007; 31(10):2227–2238.
7.
LiW, YeM, ZhangQ, et al.Numerical approximation of a stochastic age-structured population model in a polluted environment with markovian switching. Numerical Methods Partial, 2020; 36(6):1460–1491.
8.
LiW, YeM, ZhangQ, et al.A periodic averaging method for impulsive stochastic age‐structured population model in a polluted environment. Math Methods in App Sciences, 2022; 45(12):7760–7779.
9.
LiuH, MaZ. The threshold of survival for system of two species in a polluted environment. J Math Biol, 1991; 30(1):49–61.
10.
LiuJW, GeritzFSA. Effects of a toxicant on a single-species population with partial pollution tolerance in a polluted environment. Annals of Applied Mathematics, 2016; 32(3):266–274.
11.
LiuM, WangK, WuQ. Survival analysis of stochastic competitive models in a polluted environment and stochastic competitive exclusion principle. Bull Math Biol, 2011; 73(9):1969–2012.
12.
LiuM, WangK. Survival analysis of stochastic single-species population models in polluted environments. Ecol Modell, 2009; 220(9–10):1347–1357.
13.
LuoZ, HeZR. Optimal control for age-dependent population hybrid system in a polluted environment. Appl Math Comput, 2014; 228:68–76.
14.
LuoZ. Optimal control for an age-dependent predator-prey system in a polluted environment. J Appl Math Comput, 2014; 44(1–2):491–509.
15.
MaW, LuoX, ZhuQ. Practical exponential stability of stochastic age-dependent capital system with levy noise. Systems and Control Letters, 2020; 144(1):104759.
16.
MaoX. Almost sure polynomial stability for a class of stochastic differential equations. Q J Math, 1992; 43(3):339–348.
17.
MoR, WuX, WeiF. Population-toxicant models with stage structure and the psychological effects. Int J Biomath, 2024; 17(1):2450075.
RohrJR, KerbyJL, SihA. Community ecology as a framework for predicting contaminant effects. Trends Ecol Evol, 2006; 21(11):606–613.
20.
TanJ, MenW, PeiY, et al.Construction of positivity preserving numerical method for stochastic age-dependent population equations. Appl Math Comput, 2017; 293:57–64.
21.
TomásC, MchiriL, MohsenB, et al.p-th moment exponential stability of neutral stochastic pantograph differential equations with markovian switching. Communications in Nonlinear Science and Numerical Simulation, 2021; 102(1):105916.
22.
WeiF, ChenL. Psychological effect on single-species population models in a polluted environment. Math Biosci, 2017; 290(1):22–30.
23.
WeiF, GeritzSAH, CaiJ. A stochastic single-species population model with partial pollution tolerance in a polluted environment. Appl Math Lett, 2017; 63(1):130–136.
24.
WuJ. Dynamics of a two-predator one-prey stochastic delay model with lévy noise. Physica A: Statistical Mechanics and Its Applications, 2020; 539:122910.
25.
YangB, LiJ. An almost periodic solution for an impulsive two-species logarithmic population model with time-varying delay. Math Comput Model, 2012; 55(7–8):1963–1968.
26.
YuZX, RongY. Traveling waves of a nonlocal dispersal delayed age-structured population model. Japan J Indust Appl Math, 2013; 30(1):165–184.
27.
ZhaoY, YuanS, ZhangQ. Numerical solution of a fuzzy stochastic single-species age-structure model in a polluted environment. Appl Math Comput, 2015; 260(1):385–396.