Spatio-temporal patterns resulting from a predator-based disease with immune prey

Propagation of a disease through a spatially varying population poses complex questions about disease spread and population survival. We consider a spatio-temporal predator-prey model in which a disease only affects the predator. Diffusion-driven instability conditions are analytically derived for the spatio-temporal model. We perform numerical simulation using experimental data given in previous studies and demonstrate that travelling waves, periodicity and chaotic patterns are possible. We show that the introduction of disease in the predator species makes the standard Rosenzweig-MacArthur model capable of producing Turing patterns, which is not possible without disease. However, in the absence of infection, both species can coexist in spiral non-Turing patterns. It follows that disease persistence may be predictable, while eradication may not be.

Automated summary

Propagation of disease in a population with spatial variation raises complex questions. We analyze a predator-prey model with a disease affecting only the predator. We derive analytically the instability conditions for this spatio-temporal model. Using numerical simulations and experimental data, we demonstrate the possibility of travelling waves, periodicity, and chaotic patterns. Our findings show that the introduction of disease can produce Turing patterns in the predator population, while coexistence in non-Turing patterns occurs when infection is absent. This implies that disease persistence may be predictable, but eradication may not be.