Farkas JZ & Calsina A (2016) On a strain-structured epidemic model. Nonlinear Analysis: Real World Applications, 31, pp. 325-342. https://doi.org/10.1016/j.nonrwa.2016.01.014
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.
Structured populations; epidemiology; super-spreaders; global existence; positive operators; steady states
Nonlinear Analysis: Real World Applications: Volume 31