Global stability of SAIRS epidemic models
We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission patterns of the disease. We provide a global stability analysis for the model. We determine the value of the basic reproduction n...
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| Published in | Nonlinear analysis: real world applications Vol. 65; p. 103501 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.06.2022
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| Abstract | We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission patterns of the disease. 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. If R0>1, the disease free equilibrium is unstable and a unique endemic equilibrium exists. We investigate the global stability of the endemic equilibrium for some variations of the original model under study and answer an open problem proposed in Ansumali et al. (2020). In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when R0=1. We provide a thorough numerical exploration of our model to illustrate our analytical results. |
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| AbstractList | We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission patterns of the disease. 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. If R0>1, the disease free equilibrium is unstable and a unique endemic equilibrium exists. We investigate the global stability of the endemic equilibrium for some variations of the original model under study and answer an open problem proposed in Ansumali et al. (2020). In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when R0=1. We provide a thorough numerical exploration of our model to illustrate our analytical results. |
| ArticleNumber | 103501 |
| Author | Sottile, Sara Sensi, Mattia Ottaviano, Stefania |
| Author_xml | – sequence: 1 givenname: Stefania orcidid: 0000-0003-2319-8163 surname: Ottaviano fullname: Ottaviano, Stefania organization: University of Trento, Department of Civil, Environmental and Mechanical Engineering, Via Mesiano, 77, Trento, 38123, Italy – sequence: 2 givenname: Mattia orcidid: 0000-0002-6631-0242 surname: Sensi fullname: Sensi, Mattia email: mattia.sensi@inria.fr organization: TU Delft, Network Architectures and Services Group, Mekelweg 4, Delft, 2628CD, The Netherlands – sequence: 3 givenname: Sara orcidid: 0000-0001-7810-2099 surname: Sottile fullname: Sottile, Sara organization: University of Trento, Department of Mathematics, Via Sommarive 14, Povo - Trento, 38123, Italy |
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| Keywords | Susceptible–asymptomatic infected–symptomatic infected–recovered–susceptible Geometric approach Global asymptotic stability Basic reproduction number Lyapunov functions Vaccination |
| Language | English |
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| SubjectTerms | Basic reproduction number Geometric approach Global asymptotic stability Lyapunov functions Susceptible–asymptomatic infected–symptomatic infected–recovered–susceptible Vaccination |
| Title | Global stability of SAIRS epidemic models |
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