A predator-prey model with disease amongst the prey and ratio-dependent functional response for both infected and susceptible prey is proposed and its features analysed. This work is based on previous mathematical models to analyse the important ecosystem of the Salton Sea in Southern California and New Mexico where birds (particularly pelicans) prey on fish (particularly tilapia). The dynamics of the system around each of the ecologically meaningful equilibria are presented. Natural disease control is considered before studying the impact of the disease in the absence of predators, the interaction of predators and healthy prey and the disease effects on predators in the absence of healthy prey. Our theoretical results are confirmed by numerical simulation.
|Number of pages||21|
|Journal||Mathematical Methods in the Applied Sciences|
|Early online date||16 Jun 2016|
|Publication status||Published - 15 Jan 2017|
- differential equations
- Hopf bifurcation