Global stability of SAIRS epidemic models

Ottaviano, Stefania; Sensi, Mattia; Sottile, Sara

doi:10.1016/j.nonrwa.2021.103501

Cited by 39 publications

(63 citation statements)

References 31 publications

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“…As in [28], we conjecture that some, if not all, these technical assumptions could be relaxed, as our numerical simulations suggest. However, the techniques we use in this paper require such assumptions on the parameters in order to reach a result, and multigroup models often require cumbersome hypotheses [9,16,32].…”

Section: Local Asymptotic Stabilitymentioning

confidence: 63%

“…The primary criterion for parameter selection is the clarity of the resulting plot. Hence, the simulations were carried out with a set of parameters considered in [28]. These parameters, summarized in Table 1, ensure that R 0 > 1 in all the networks we consider, whose shapes are represented in Figure 3.…”

Section: Numerical Analysismentioning

confidence: 99%

“…In this paper, we present a multi-group model, as extension of the SAIRS-type model proposed in [28], where the role of asymptomatic and symptomatic infectious individuals in the disease transmission has been explicitly considered. Asymptomatic cases often remain unidentified and possibly have more contacts than symptomatic individuals, allowing the virus to circulate widely in the population [3,24,25,11].…”

Section: Introductionmentioning

confidence: 99%

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Global stability of multi-group SAIRS epidemic models

Ottaviano¹,

Sensi²,

Sottile³

2022

Preprint

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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). We provide a global stability analysis for the model. We determine the value of the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable if R0 < 1. In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when R0 = 1. Moreover, if R0 > 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.

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Section: Local Asymptotic Stabilitymentioning

confidence: 63%

Section: Numerical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Global stability of multi-group SAIRS epidemic models

Ottaviano¹,

Sensi²,

Sottile³

2022

Preprint

Self Cite

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“…In this paper, we consider a ten parameters SAIR (also called SEIR in the classic literature [51]) epidemic model inspired by [24,31,34,48,10,37,16,40], which we call SAIR/V+S (or SAIR for short), since it groups together immunized people in an R/V compartment. The letter A (from asymptomatic) stands for the fact that the individuals in this compartment may infect the susceptibles.…”

Section: The Sairs Model With Linear Birth Ratementioning

confidence: 99%

“…The goal of our paper is to draw attention to two interesting open problems , for the SIR-PH, SIR-PH-FA, and also for a second, more refined "intermediate approximation" SIR-PH-IA. We illustrate the current status-quo by presenting new results on a generalization of the SAIRS epidemic model of [44,40].…”

Section: Introductionmentioning

confidence: 99%

New results and open questions for SIR-PH epidemic models with linear birth rate, loss of immunity, vaccination, and disease and vaccination fatalities

Avram¹,

Rim²,

Halanay³

2022

Preprint

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Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the "R0 alternative" of [52,51], which states that the local stability condition of the disease free equilibrium may be expressed as R0 < 1, where R0 is the famous basic reproduction number, which plays also a major role in the theory of branching processes. The literature suggests that it is impossible to find general laws concerning the endemic points. However, it is quite common that

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Threshold dynamics of SAIRS epidemic model with semi‐Markov switching

Ottaviano

2023

Math Methods in App Sciences

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We study the threshold dynamics of a stochastic SAIRS-type model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the epidemic dynamics. In the model, the values of the disease transmission rate may switch between different levels under the effect of a semi-Markov process. We provide sufficient conditions ensuring the almost surely epidemic extinction and persistence in time mean. In the case of disease persistence, we investigate the omega-limit set of the system and give sufficient conditions for the existence and uniqueness of an invariant probability measure.

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Global stability of SAIRS epidemic models

Cited by 39 publications

References 31 publications

Global stability of multi-group SAIRS epidemic models

Global stability of multi-group SAIRS epidemic models

New results and open questions for SIR-PH epidemic models with linear birth rate, loss of immunity, vaccination, and disease and vaccination fatalities

Threshold dynamics of SAIRS epidemic model with semi‐Markov switching

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