Kusumika Kundu

Chaos in eco-epidemiological problem of the Salton Sea and its possible control

Abstract The Salton Sea, which is located in the southeast desert of California, came into the limelight due to deaths of fish and fish catching birds on a massive scale. Recently, Chattopadhyay and Bairagi [J. Chattopadhyay, N. Bairagi, Pelicans at risk in Salton Sea – an eco-epidemiological model, Ecol. Model. 136 (2001) 103–112] proposed and analysed an eco-epidemiological model on Salton Sea. In the present paper, we modified their model by taking into account the bilinear mass action incidence rate and performed extensive numerical simulations. Our studies show that the system exhibits chaotic dynamics when some key parameters attain their critical values. We have tried to explain the unusual deaths of fish and fish eating birds in the Salton Sea using the simulation results. We have also suggested some possible measures to avoid chaos in such natural systems.

CONTROL OF DISEASE IN PREY POPULATION BY SUPPLYING ALTERNATIVE FOOD TO PREDATOR

A simple predator–prey system with disease in prey population and alternative food for the predator is proposed and analyzed. The main objective of the present investigation is to observe the conditions for which the disease in prey population will be controlled. It is observed that supply of alternative food to the predator population can make the system disease free. Enrichment also plays an important role in suppressing the infected population in the presence of alternative food. However, in the absence of predator population, enrichment increases the disease prevalence instead of reducing it. We finally conclude that supply of alternative food to the predator provides a healthy disease free system.

AN ECO-EPIDEMIOLOGICAL STUDY WITH PARASITE ATTACK AND ALTERNATIVE PREY

The present paper deals with the problem of a predator-prey system with disease in the prey population. We observe the dynamics of such a system under the influence of severe as well as unnoticeable parasite attack and also alternative food sources for predator population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Local and global stability of the system around the biological feasible equilibria are studied. The conditions for which all three species will persist are worked out. Our results indicate that in the case of severe parasite attack, the predator population will prefer the alternative food source and not the infected one. But the strategy is reversed in the case of unnoticeable parasite attack.

Role of force of infection in an eco-epidemiological model

In this paper, the model of Chattopadhyay and Bairagi1 has been modified by considering the horizontal incidence as standard incidence in lieu of mass action incidence. Our observations indicate that the modified system around the positive equilibrium is stable for a wider range of force of infection. Numerical experiments are performed to observe the effect of disease transmission on different types of functional responses. We finally conclude that the mechanistic nature of disease transmission should be known for predicting the dynamics of such systems.