Analysis of stochastic SEIR(S) models with random total populations and variable diffusion rates
A stochastic SEIR(S) model with random total population, overall saturation constant K > 0 and general, local Lipschitz continuous diffusion rates is presented. We prove the existence of unique, Markovian, continuous time solutions w.r.t. filtered, complete probability spaces on certain, bounded...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2024
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Sztochasztikus modell, Differenciálegyenlet - sztochasztikus, Markov-folyamat |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2024.1.55 |
| Online Access: | http://acta.bibl.u-szeged.hu/88857 |
| Tartalmi kivonat: | A stochastic SEIR(S) model with random total population, overall saturation constant K > 0 and general, local Lipschitz continuous diffusion rates is presented. We prove the existence of unique, Markovian, continuous time solutions w.r.t. filtered, complete probability spaces on certain, bounded 4D prisms. The total population N(t) is governed by kind of stochastic logistic equations, which allows to have an asymptotically stable maximum population constant K > 0. Under natural conditions on our SEIR(S) model, we establish asymptotic stochastic and moment stability of the disease-free and endemic equilibria. Those conditions naturally depend on the basic reproduction number R0, the growth parameter µ > 0 and environmental noise intensity σ 2 5 coupled with the maximum threshold K 2 of total population N(t). For the mathematical proofs, the technique of appropriate Lyapunov functionals V(S(t), E(t), I(t), R(t)) is exploited. Some numerical simulations of the expected Lyapunov functionals E[V(S, E, I, R)] depending on several parameters and time t support our findings. |
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| Terjedelem/Fizikai jellemzők: | 26 |
| ISSN: | 1417-3875 |