Modelling contact spread of infection in host-parasitoid systems: Vertical transmission of pathogens can cause chaos

Katharine F. Preedy (1) , P.G. Pietà G. Schofield (2) , Sijia Liu (3) , Anastasios Matzavinos (3) , Mark A.J. Chaplain (1) , Stephen F. Hubbard (2)

1 Division of Mathematics
2 University of Dundee
3 Department of Mathematics

All animals and plants are, to some extent, susceptible to disease caused by varying combinations of parasites, viruses and bacteria. In this paper, we develop a mathematical model of contact spread infection to investigate the effect of introducing a parasitoid-vectored infection into a one-host-two-parasitoid competition model. We use a system of ordinary differential equations to investigate the separate influences of horizontal and vertical pathogen transmission on a model system appropriate for a variety of competitive situations. Computational simulations and steady-state analysis show that the transient and long-term dynamics exhibited under contact spread infection are highly complex. Horizontal pathogen transmission has a stabilizing effect on the system whilst vertical transmission can destabilize it to the point of chaotic fluctuations in population levels. This has implications when considering the introduction of host pathogens for the control of insect vectored diseases such as bovine tuberculosis or yellow fever.

Mots clés: Insect-pathogen interactions; Population dynamics; Infection; Horizontal transmission; Vertical transmission; Vectored diseases; Competition; Chaotic dynamics

Katharine F. Preedy, P.G. Pietà G. Schofield, Sijia Liu, Anastasios Matzavinos, Mark A.J. Chaplain, et al.. Modelling contact spread of infection in host-parasitoid systems: Vertical transmission of pathogens can cause chaos. Journal of Theoretical Biology, 2009, 262 (3), pp.441. ⟨10.1016/j.jtbi.2009.10.003⟩. ⟨hal-00559161⟩