Controlling disease in migratory bird population: a probable solution through mathematical study

摘要

The role of migratory birds in an eco-system cannot be ignored. It becomes more important if they carry a disease. Chatterjee and Chattopadhyay proposed and analysed a three component one season eco-epidemiological model consisting of susceptible migratory birds, infective migratory birds and their predator population (see Chatterjee, S. and Chattopadhyay, J., Role of migratory bird populations in a simple eco-epidemiological model, Mathematical and Computer Modelling of Dynamical systems, in press). They assumed that the recovered infective birds become susceptible again. But, it is observed that in diseases like salmonella and WNV, the recovered birds develop a permanent immunity. Keeping this in mind we modify the model of Chatterjee and Chattopadhyay by adding a recovered class. The main objective of this work is to observe the role of recovery and immunity in such a system. Numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings. It is observed that to obtain a disease free system proper vaccination and proper predation are necessary. The second factor was mentioned in the paper of Chatterjee and Chattopadhyay.