Stability of stochastic SIS model with disease deaths and variable diffusion rates
The SIS model is a fundamental model that helps to understand the spread of an infectious disease, in which infected individuals recover without immunity. Because of the random nature of infectious diseases, we can estimate the spread of a disease in population by stochastic models. In this article,...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2019-02-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6300 |
| _version_ | 1797830509859962880 |
|---|---|
| author | Henri Schurz Kursad Tosun |
| author_facet | Henri Schurz Kursad Tosun |
| author_sort | Henri Schurz |
| collection | DOAJ |
| description | The SIS model is a fundamental model that helps to understand the spread of an infectious disease, in which infected individuals recover without immunity. Because of the random nature of infectious diseases, we can estimate the spread of a disease in population by stochastic models. In this article, we present a class of stochastic SIS model with births and deaths, obtained by superimposing Wiener processes (white noises) on contact and recovery rates and allowing variable diffusion rates. We prove existence of the unique, positive and bounded solution of this nonlinear system of stochastic differential equations (SDEs) and examine stochastic asymptotic stability of equilibria. In addition, we simulate the model by considering a numerical approximation based on a balanced implicit method (BIM) on an appropriately bounded domain $\mathbb{D} \subset \mathbb{R}^2$. |
| first_indexed | 2024-04-09T13:37:16Z |
| format | Article |
| id | doaj.art-6072090c51c74648af632a494b310e6b |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:16Z |
| publishDate | 2019-02-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-6072090c51c74648af632a494b310e6b2023-05-09T07:53:09ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752019-02-0120191412410.14232/ejqtde.2019.1.146300Stability of stochastic SIS model with disease deaths and variable diffusion ratesHenri Schurz0Kursad Tosun1Southern Illinois University, Carbondale, IL, USAMugla Sitki Kocman University, Mugla, TurkeyThe SIS model is a fundamental model that helps to understand the spread of an infectious disease, in which infected individuals recover without immunity. Because of the random nature of infectious diseases, we can estimate the spread of a disease in population by stochastic models. In this article, we present a class of stochastic SIS model with births and deaths, obtained by superimposing Wiener processes (white noises) on contact and recovery rates and allowing variable diffusion rates. We prove existence of the unique, positive and bounded solution of this nonlinear system of stochastic differential equations (SDEs) and examine stochastic asymptotic stability of equilibria. In addition, we simulate the model by considering a numerical approximation based on a balanced implicit method (BIM) on an appropriately bounded domain $\mathbb{D} \subset \mathbb{R}^2$.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6300stochastic sis modelvariable diffusion ratesstochastic differential equationspositivity and boundednessbalanced implicit methodsstochastic asymptotic stabilitylyapunov functionsmathematical epidemiology |
| spellingShingle | Henri Schurz Kursad Tosun Stability of stochastic SIS model with disease deaths and variable diffusion rates Electronic Journal of Qualitative Theory of Differential Equations stochastic sis model variable diffusion rates stochastic differential equations positivity and boundedness balanced implicit methods stochastic asymptotic stability lyapunov functions mathematical epidemiology |
| title | Stability of stochastic SIS model with disease deaths and variable diffusion rates |
| title_full | Stability of stochastic SIS model with disease deaths and variable diffusion rates |
| title_fullStr | Stability of stochastic SIS model with disease deaths and variable diffusion rates |
| title_full_unstemmed | Stability of stochastic SIS model with disease deaths and variable diffusion rates |
| title_short | Stability of stochastic SIS model with disease deaths and variable diffusion rates |
| title_sort | stability of stochastic sis model with disease deaths and variable diffusion rates |
| topic | stochastic sis model variable diffusion rates stochastic differential equations positivity and boundedness balanced implicit methods stochastic asymptotic stability lyapunov functions mathematical epidemiology |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6300 |
| work_keys_str_mv | AT henrischurz stabilityofstochasticsismodelwithdiseasedeathsandvariablediffusionrates AT kursadtosun stabilityofstochasticsismodelwithdiseasedeathsandvariablediffusionrates |