Dynamic behavior of a stochastic SIRS model with two viruses
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Jiandong Zhao
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Tonghua Zhang
Abstract
To study the effect of environmental noise on the spread of the disease, a stochastic Susceptible, Infective, Removed and Susceptible (SIRS) model with two viruses is introduced in this paper. Sufficient conditions for global existence of positive solution and stochastically asymptotic stability of disease-free equilibrium in the model are given. Then, it is shown that the positive solution is stochastically ultimately bounded and the moment average in time of the positive solution is bounded. Our results mean that the environmental noise suppresses the growth rate of the individuals and drives the disease to extinction under certain conditions. Finally, numerical simulations are given to illustrate our main results.
Funding source: Department of Education and Training
Award Identifier / Grant number: 5395-2016
Funding source: Ludong University
Funding source: National Statistics Bureau of China
Award Identifier / Grant number: 2020LY016
Acknowledgments
The first author would like to thank Department of Mathematics at Swinburne University of Technology and Department of Mathematics and Statistics at Memorial University of Newfoundland for kindly hosting during his visiting.
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Article note: Supported by Endeavor Research Fellowship (5395-2016) (Granted by Department of Education and Training, Australian Government), National Statistical Science Research Project of China (2020LY016) and the Visiting Scholar Program of Ludong University.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: Supported by Endeavor Research Fellowship (5395-2016) (Granted by Department of Education and Training, Australian Government), National Statistical Science Research Project of China (2020LY016) and the Visiting Scholar Program of Ludong University.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Dynamic behavior of a stochastic SIRS model with two viruses
- Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems
- Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system
- Positive periodic solution for inertial neural networks with time-varying delays
- Stability analysis of almost periodic solutions for discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays
- Analysis of (α, β)-order coupled implicit Caputo fractional differential equations using topological degree method
- A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space
- Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps
- Stress wave propagation in different number of fissured rock mass based on nonlinear analysis
- Analytical predictor–corrector entry guidance for hypersonic gliding vehicles
- Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space
- Anthropogenic climate change on a non-linear arctic sea-ice model of fractional Duffing oscillator
- Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation
- Invariant solutions of fractional-order spatio-temporal partial differential equations
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Dynamic behavior of a stochastic SIRS model with two viruses
- Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems
- Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system
- Positive periodic solution for inertial neural networks with time-varying delays
- Stability analysis of almost periodic solutions for discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays
- Analysis of (α, β)-order coupled implicit Caputo fractional differential equations using topological degree method
- A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space
- Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps
- Stress wave propagation in different number of fissured rock mass based on nonlinear analysis
- Analytical predictor–corrector entry guidance for hypersonic gliding vehicles
- Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space
- Anthropogenic climate change on a non-linear arctic sea-ice model of fractional Duffing oscillator
- Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation
- Invariant solutions of fractional-order spatio-temporal partial differential equations
