On vaccination strategies for a SISV epidemic model guaranteeing the nonexistence of endemic solutions
type: Item
instance of: scholarly article
title: On vaccination strategies for a SISV epidemic model guaranteeing the nonexistence of endemic solutions
zbMATH Open document ID: 1417.92088
DOI: 10.1155/2018/9484121
author: S. Alonso-Quesada
author: M. De la Sen
author: Raúl Nistal
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: A vaccination strategy based on the state feedback control theory is proposed. The objective is to fight against the propagation of an infectious disease within a host population. This propagation is modelled by means of a SISV (susceptible-infectious-susceptible-vaccinated) epidemic model with a time-varying whole population and with a mortality directly associated with the disease. The vaccination strategy adds four free-design parameters, with three of them being the feedback gains of the vaccination control law. The other one is used to switch off the vaccination if the proportion of susceptible individuals is smaller than a prescribed threshold. The paper analyses the positivity of such a model under the proposed vaccination strategy as well as the conditions for the existence of the different equilibrium points of its normalized model. The fact that an appropriate adjustment of the control gains avoids the existence of endemic equilibrium points in the normalized SISV model while guaranteeing the existence of a unique disease-free equilibrium point being globally exponentially stable is proved. This is a relevant novelty dealt with in this paper. The persistence of the infectious disease within a host population irrespective of the growing properties of the whole population can be avoided in this way. Such theoretical results are mathematically proved and, also, they are illustrated by means of simulation examples. Moreover, the performance of the proposed vaccination strategy in several real situations is studied in some simulation examples. One of them deals with the presence of uncertainties, which affects the synthesis of the vaccination control law, in the measures of the subpopulations of the model.
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 7026730
Wikidata QID: Q57674416
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9484121
OpenAlex ID: W2895019296
cites work: Q5425001
cites work: Q4255467
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description: scientific article; zbMATH DE number 7026730