Global stability of multi-group SAIRS epidemic models

Autor: Stefania Ottaviano, Mattia Sensi, Sara Sottile
Přispěvatelé: Dipartimento di Matematica [Padova], Università degli Studi di Padova = University of Padua (Unipd), Mathématiques pour les Neurosciences (MATHNEURO), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Trento [Trento]
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Mathematical Methods in the Applied Sciences
Mathematical Methods in the Applied Sciences, 2023, ⟨10.1002/mma.9303⟩
ISSN: 0170-4214
1099-1476
Popis: We study a multi-group SAIRS-type epidemic model with vaccination. The role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission pattern of the disease among the groups in which the population is divided. This is a natural extension of the homogeneous mixing SAIRS model with vaccination studied in Ottaviano et. al (2021) to a network of communities. We provide a global stability analysis for the model. We determine the value of the basic reproduction number $\mathcal{R}_0$ and prove that the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0 < 1$. In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when $\mathcal{R}_0=1$. Moreover, if $\mathcal{R}_0 > 1$, the disease-free equilibrium is unstable and a unique endemic equilibrium exists. First, we investigate the local asymptotic stability of the endemic equilibrium and subsequently its global stability, for two variations of the original model. Last, we provide numerical simulations to compare the epidemic spreading on different networks topologies.
36 pages, 8 figures
Databáze: OpenAIRE
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