title: Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species.
abstract: We consider a system of delay differential equations modeling the predator-prey ecoepidemic dynamics with a transmissible disease in the predator population. The time lag in the delay terms represents the predator gestation period. We analyze essential mathematical features of the proposed model such as local and global stability and in addition study the bifurcations arising in some selected situations. Threshold values for a few parameters determining the feasibility and stability conditions of some equilibria are discovered and similarly a threshold is identified for the disease to die out. The parameter thresholds under which the system admits a Hopf bifurcation are investigated both in the presence of zero and non-zero time lag. Numerical simulations support our theoretical analysis.
authors.affiliation: School of Mathematical Science, University of Nottingham, University Park, Nottingham NG7 2RD, UK. pmxmh1@nottingham.ac.uk
authors.forename: Mainul
authors.initials: M
authors.lastname: Haque
authors.forename: Sahabuddin
authors.initials: S
authors.lastname: Sarwardi
authors.forename: Simon
authors.initials: S
authors.lastname: Preston
authors.forename: Ezio
authors.initials: E
authors.lastname: Venturino
mesh_terms: D000818:Animals; D000835:Animals, Wild / Q000382:microbiology; D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission*; D003198:Computer Simulation; D020387:Food Chain; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior