On a discrete SEIR epidemic model with exposed infectivity, feedback vaccination and partial delayed re-susceptibility
De la Sen, Manuel (Universidad del País Vasco. Instituto de Investigación y Desarrollo de Procesos)
Alonso-Quesada, Santiago (Universidad del País Vasco. Instituto de Investigación y Desarrollo de Procesos)
Ibeas, Asier (Universitat Autònoma de Barcelona. Departament de Telecomunicació i Enginyeria de Sistemes)

Data:	2021
Resum:	A new discrete Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is proposed, and its properties of non-negativity and (both local and global) asymptotic stability of the solution sequence vector on the first orthant of the state-space are discussed. The calculation of the disease-free and the endemic equilibrium points is also performed. The model has the follow-ing main characteristics: (a) the exposed subpopulation is infective, as it is the infectious one, but their respective transmission rates may be distinct; (b) a feedback vaccination control law on the Susceptible is incorporated; and (c) the model is subject to delayed partial re-susceptibility in the sense that a partial immunity loss in the recovered individuals happens after a certain delay. In this way, a portion of formerly recovered individuals along a range of previous samples is incorporated again to the susceptible subpopulation. The rate of loss of partial immunity of the considered range of previous samples may be, in general, distinct for the various samples. It is found that the endemic equilibrium point is not reachable in the transmission rate range of values, which makes the disease-free one to be globally asymptotically stable. The critical transmission rate which confers to only one of the equilibrium points the property of being asymptotically stable (respectively below or beyond its value) is linked to the unity basic reproduction number and makes both equilibrium points to be coincident. In parallel, the endemic equilibrium point is reachable and globally asymptotically stable in the range for which the disease-free equilibrium point is unstable. It is also discussed the relevance of both the vaccination effort and the re-susceptibility level in the modifi-cation of the disease-free equilibrium point compared to its reached component values in their absence. The influences of the limit control gain and equilibrium re-susceptibility level in the reached endemic state are also explicitly made viewable for their interpretation from the endemic equilibrium components. Some simulation examples are tested and discussed by using disease parameterizations of COVID-19.
Ajuts:	Agencia Estatal de Investigación RTI2018-094336-B-I00 Instituto de Salud Carlos III COV 20/01213
Nota:	Altres ajuts: Basque Government for Grant IT1207-19
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	COVID-19 pandemic ; Delayed re-susceptibility (or immunity loss) ; Discrete epidemic model ; Feedback vaccination control ; Transmission rate of the ex-posed ; Transmission rate of the infectious ; SDG 3 - Good Health and Well-being
Publicat a:	Mathematics, Vol. 9, Issue 5 (March 2021) , art. 520, ISSN 2227-7390

DOI: 10.3390/math9050520

32 p, 4.9 MB

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