Dynamics of Leslie-Gower Pest-Predator Model with Disease in Pest Including Pest-Harvesting and Optimal Implementation of Pesticide

We propose a model which describes the interaction between pest and its natural predator. We assume that pest can be infected with diseases or pathogens such as bacteria, fungi, and viruses. The model is constructed by combining the Leslie-Gower model and S-I epidemic model. It is also considered the effects of pest harvesting. Harvesting in this case is intended to take a number of pests as one of the pest population control strategies. The proposed model will be analyzed dynamically to study its qualitative behaviour. The dynamical analysis includes the determination of all possible equilibrium points and their stability properties. Furthermore we also discuss the implementation of pesticide control where its optimal strategy is determined by Pontryagin's maximum principle. To support our analytical studies, we perform some numerical simulations and their interpretation.