Role of harvesting and allee in a predator-prey model with disease in the both populations

Jai Prakash Tripathi; Krishna Pada Das; Sarita Bugalia; Heena Choudhary; Devendra Kumar; Jagdev Singh

Jai Prakash Tripathi Central University of Rajasthan, \\ Bandar Sindri, Kishangarh-305817, Ajmer, Rajasthan, India.
Krishna Pada Das Mahadevananda Mahavidyalaya Department Of Mathematics Monirampore P.O.-Barrackpore Kol-120
Sarita Bugalia Central University of Rajasthan, \\ Bandar Sindri, Kishangarh-305817, Ajmer, Rajasthan, India
Heena Choudhary Central University of Rajasthan, \\ Bandar Sindri, Kishangarh-305817, Ajmer, Rajasthan, India.
Devendra Kumar University of Rajasthan, Jaipur-302004, Rajasthan, India
Jagdev Singh JECRC University, Jaipur-303905, Rajasthan, India

Abstract

The key aim of the present work is to examine the role of harvesting and Allee effect in a diseased eco-epidemiological systems. We propose a four species eco-epidemiological model system having four compartments, namely, susceptible prey, infected prey, susceptible predator, and infected predator. We consider harvesting on infected prey and infected predator. We also incorporate weak Allee effect on the growth of susceptible prey. Moreover, in nature, species do not exist lonely. Therefore, in order to investigate the persistence and extinction thresholds of each population in eco-epidemiological systems is of more biological significant. We derive the ecological and epidemiological basic reproduction number. Reproduction number is helpful to determine extinction and persistent of species. Reproduction number also allows us to classify the community composition of disease, prey and predators. The results reveal that the harvesting and Allee effect can be a very efficient strategy for controlling the spread of disease.