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 original | Anglès |
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Pàgines (de-a) | 325-342 |
Revista | Nonlinear Analysis: Real World Applications |
Volum | 31 |
DOIs | |
Estat de la publicació | Publicada - 1 d’oct. 2016 |