title: The effect of seasonal host birth rates on disease persistence.
abstract: In this paper, we add seasonality to the birth rate of an SIR model with density dependence in the death rate. We find that disease persistence can be explained by considering the average value of the seasonal term. If the basic reproductive ratio R(0)>1 with this average value then the disease will persist and if R(0)<1 with this average value then the disease will die out. However, if the underlying non-seasonal model displays oscillations towards the equilibrium then the dynamics of the seasonal model can become more complex. In this case, the seasonality can interact with the underlying oscillations, resonate and the population can display a range of complex behaviours including chaos. We discuss these results in terms of two examples, Cowpox in bank voles and Rabbit Haemorrhagic disease in rabbits.
authors.affiliation: Department of Computing Science and Mathematics, University of Stirling, Stirling, Scotland FK9 4LA, UK.
authors.forename: J M
authors.initials: JM
authors.lastname: Ireland
authors.forename: B D
authors.initials: BD
authors.lastname: Mestel
authors.forename: R A
authors.initials: RA
authors.lastname: Norman
mesh_terms: D000465:Algorithms; D000818:Animals; D003411:Arvicolinae; D001723:Birth Rate; D017250:Caliciviridae Infections / Q000401:mortality / Q000635:transmission; D003141:Communicable Diseases / Q000401:mortality / Q000635:transmission*; D003198:Computer Simulation; D015605:Cowpox / Q000401:mortality / Q000635:transmission; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D011817:Rabbits; D012621:Seasons; D015996:Survival Rate