Threshold behaviour of a SI epidemiological model with two structuring variables
2015
Perasso, Antoine
In this article, we study a SI epidemic model describing the spread of a disease in a perfectly mixedmanaged population, representing an animal herd in a fattening farm. The epidemic process is characterizedby a non-neglectable and variable incubation period, during which individuals are infectious but cannot beeasily detected. The susceptible and infected populations are structured according to age and, for infected,to time remaining before the end of the incubation, where they show detectable clinical signs. We studythe well posedness and the asymptotic behaviour of the problem and show that in some cases, even if thefarm is fed with healthy animals, disease persistence can occur. We give an explicit formula for the basicreproduction number R0 and the biological interpretation of this threshold on a specific example. We finallyillustrate the asymptotic behaviour of the model by numerical simulations.
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