Stationary distribution and extinction of a stochastic influenza virus model with disease resistance
Open Access
- 1 January 2022
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Biosciences and Engineering
- Vol. 19 (9), 9125-9146
- https://doi.org/10.3934/mbe.2022424
Abstract
Influenza is a respiratory infection caused influenza virus. To evaluate the effect of environment noise on the transmission of influenza, our study focuses on a stochastic influenza virus model with disease resistance. We first prove the existence and uniqueness of the global solution to the model. Then we obtain the existence of a stationary distribution to the positive solutions by stochastic Lyapunov function method. Moreover, certain sufficient conditions are provided for the extinction of the influenza virus flu. Finally, several numerical simulations are revealed to illustrate our theoretical results. Conclusively, according to the results of numerical models, increasing disease resistance is favorable to disease control. Furthermore, a simple example demonstrates that white noise is favorable to the disease's extinction.Keywords
This publication has 20 references indexed in Scilit:
- Qualitative study of a stochastic SIS epidemic model with vertical transmissionPhysica A: Statistical Mechanics and its Applications, 2018
- Cumulative and maximum epidemic sizes for a nonlinear SEIR
stochastic model with limited resourcesDiscrete & Continuous Dynamical Systems - B, 2017
- Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidencePhysica A: Statistical Mechanics and its Applications, 2017
- Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidencePhysica A: Statistical Mechanics and its Applications, 2016
- Stability analysis of an influenza virus model with disease resistanceJournal of the Egyptian Mathematical Society, 2016
- Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbationsNonlinear Analysis: Real World Applications, 2012
- Analysis of an influenza A (H1N1) epidemic model with vaccinationArabian Journal of Mathematics, 2012
- Pandemic Potential of a Strain of Influenza A (H1N1): Early FindingsScience, 2009
- A population-dynamic model for evaluating the potential spread of drug-resistant influenza virus infections during community-based use of antiviralsJournal of Antimicrobial Chemotherapy, 2003
- An Algorithmic Introduction to Numerical Simulation of Stochastic Differential EquationsSIAM Review, 2001