Role of additional food in eco-epidemiological system with disease in the prey

• An eco-epidemiological model supplying additional food is proposed.
• The dynamics of the system is studied both analytically and numerically.
• Optimal control problem is formulated and solved.
• Bifurcation is carried out with respect to additional food.
• Results show that disease free system can be obtained supplying additional food.

An eco-epidemiological system with disease in the prey incorporating additional food to predator is proposed. The main objective of this study is to show the role of additional food in an eco-epidemiological system. We analyze the proposed system by calculating two reproduction numbers. The dynamical behavior of the system is investigated from the point of view of stability and persistence both analytically and numerically. Using Pontryagin’s Maximum Principle, an optimal control problem is formulated and solved in presence of additional food to achieve the control of disease. Numerical results illustrate that there exists a critical infection rate above which disease free system can not be reached in absence of additional food. On the other hand suitable additional food has the capability to obtain a disease free system up to certain infection level. The system becomes disease free also in presence of seasonally varying infection rate providing suitable additional food to predator. This study introduces a new non-chemical method for controlling disease in eco-epidemiological system.