Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Global dynamics of compartmental models for the spread of ectoparasite-borne diseases
Attila Dénes, Gergely Röst

Last modified: 2014-03-31


A family of mathematical models is presented to simultaneously study the transmission dynamics of ectoparasite infestation and infectious diseases spread by those ectoparasites in a population. The system has four potential equilibria. We identify three reproduction numbers which determine whether the infectious or the non-infectious parasites can invade the population, and whether a population already infested by non-infectious parasites can be invaded by the infection. By using Lyapunov-LaSalle theory, Dulac-Poincaré type arguments and persistence theory, we show that the solutions always converge to one of the equilibria, depending on the reproduction numbers. We completely characterize the global dynamics in terms of the reproduction numbers. We also provide a detailed description of the structure of the global attractor in all possible cases. Joint work with Gergely Röst.

This research was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP 4.2.4. A/2-11-1-2012-0001 'National Excellence Program'.