On a strain-structured epidemic model

Àngel Calsina, József Z. Farkas

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Resum

© 2016 Elsevier Ltd. All rights reserved. We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the interesting scenario when individuals infected with different strains cause secondary (new) infections at different rates. Therefore, we consider a nonlinear infection process, which generalises the bilinear process arising from the classic mass-action assumption. Our main motivation is to study competition between different strains of a virus/bacteria. From the mathematical point of view, we are interested whether the nonlinear infection process leads to a well-posed model. We use a semilinear formulation to show global existence and positivity of solutions up to a critical value of the exponent in the nonlinearity. Furthermore, we establish the existence of the endemic steady state for particular classes of nonlinearities.
Idioma originalAnglès
Pàgines (de-a)325-342
RevistaNonlinear Analysis: Real World Applications
Volum31
DOIs
Estat de la publicacióPublicada - 1 d’oct. 2016

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