Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species. 2011

Mainul Haque, and Sahabuddin Sarwardi, and Simon Preston, and Ezio Venturino
School of Mathematical Science, University of Nottingham, University Park, Nottingham NG7 2RD, UK. pmxmh1@nottingham.ac.uk

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.

UI MeSH Term Description Entries
D008954 Models, Biological Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment. Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D011157 Population Dynamics The pattern of any process, or the interrelationship of phenomena, which affects growth or change within a population. Malthusianism,Neomalthusianism,Demographic Aging,Demographic Transition,Optimum Population,Population Decrease,Population Pressure,Population Replacement,Population Theory,Residential Mobility,Rural-Urban Migration,Stable Population,Stationary Population,Aging, Demographic,Decrease, Population,Decreases, Population,Demographic Transitions,Dynamics, Population,Migration, Rural-Urban,Migrations, Rural-Urban,Mobilities, Residential,Mobility, Residential,Optimum Populations,Population Decreases,Population Pressures,Population Replacements,Population Theories,Population, Optimum,Population, Stable,Population, Stationary,Populations, Optimum,Populations, Stable,Populations, Stationary,Pressure, Population,Pressures, Population,Replacement, Population,Replacements, Population,Residential Mobilities,Rural Urban Migration,Rural-Urban Migrations,Stable Populations,Stationary Populations,Theories, Population,Theory, Population,Transition, Demographic,Transitions, Demographic
D011235 Predatory Behavior Instinctual behavior pattern in which food is obtained by killing and consuming other species. Predation,Behavior, Predatory,Predatory Behaviors
D003141 Communicable Diseases An illness caused by an infectious agent or its toxins that occurs through the direct or indirect transmission of the infectious agent or its products from an infected individual or via an animal, vector or the inanimate environment to a susceptible animal or human host. Infectious Diseases,Communicable Disease,Disease, Communicable,Disease, Infectious,Diseases, Communicable,Diseases, Infectious,Infectious Disease
D003198 Computer Simulation Computer-based representation of physical systems and phenomena such as chemical processes. Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D000835 Animals, Wild Animals considered to be wild or feral or not adapted for domestic use. It does not include wild animals in zoos for which ANIMALS, ZOO is available. Animals, Nondomestic,Animals, Nondomesticated,Animals, Feral,Stray Animals,Animal, Feral,Animal, Nondomestic,Animal, Nondomesticated,Animal, Stray,Animal, Wild,Animals, Stray,Feral Animal,Feral Animals,Nondomestic Animal,Nondomestic Animals,Nondomesticated Animal,Nondomesticated Animals,Stray Animal,Wild Animal,Wild Animals
D020387 Food Chain The sequence of transfers of matter and energy from organism to organism in the form of FOOD. Food chains intertwine locally into a food web because most organisms consume more than one type of animal or plant. PLANTS, which convert SOLAR ENERGY to food by PHOTOSYNTHESIS, are the primary food source. In a predator chain, a plant-eating animal is eaten by a larger animal. In a parasite chain, a smaller organism consumes part of a larger host and may itself be parasitized by smaller organisms. In a saprophytic chain, microorganisms live on dead organic matter. Food Web,Parasite Chain,Predator Chain,Saprophytic Chain,Chain, Food,Chain, Parasite,Chain, Predator,Chain, Saprophytic,Chains, Food,Chains, Parasite,Chains, Predator,Chains, Saprophytic,Food Chains,Food Webs,Parasite Chains,Predator Chains,Saprophytic Chains,Web, Food,Webs, Food

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