| Autor: |
Roman Taranets, Nataliya Vasylyeva, Belgacem Al-Azem |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Frontiers in Applied Mathematics and Statistics, Vol 10 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2297-4687 |
| DOI: |
10.3389/fams.2024.1383106 |
| Popis: |
Compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases or in mathematical models of population genetics. In this study, we study a time-dependent Susceptible-Infectious-Susceptible (SIS) Partial Differential Equation (PDE) model that is based on a diffusion-drift approximation of a probability density from a well-known discrete-time Markov chain model. This SIS-PDE model is conservative due to the degeneracy of the diffusion term at the origin. The main results of this article are the qualitative behavior of weak solutions, the dependence of the local asymptotic property of these solutions on initial data, and the existence of Dirac delta function type solutions. Moreover, we study the long-term behavior of solutions and confirm our analysis with numerical computations. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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