PROPER PREDATION MAKES THE SYSTEM DISEASE FREE — CONCLUSION DRAWN FROM AN ECO-EPIDEMIOLOGICAL MODEL

In the present paper, an eco-epidemiological model consisting of susceptible prey, infected prey and predator has been proposed and analyzed. We have obtained conditions for the existence and persistence of all the three populations. To study the global dynamics of the system, numerical simulations have been performed. Our simulation results show that the system enters into quasi-periodic solutions or chaotic depending upon the choice of system parameters. To confirm the chaotic behavior of the system, we have calculated Lyapunov exponent and constructed Poincare section. Our analysis reveals that the infection and predation rates specially on the infected prey population are the key parameters that play crucial roles for controlling the chaotic dynamics of the system.

[1]  A. Hastings,et al.  Chaos in a Three-Species Food Chain , 1991 .

[2]  Mark A. McPeek,et al.  Predation, Competition, and Prey Communities: A Review of Field Experiments , 1985 .

[3]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[4]  Joydev Chattopadhyay,et al.  A predator—prey model with disease in the prey , 1999 .

[5]  R M May,et al.  The invasion, persistence and spread of infectious diseases within animal and plant communities. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[6]  Marjorie J. Wonham,et al.  An epidemiological model for West Nile virus: invasion analysis and control applications , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[7]  Rolf O. Peterson,et al.  THE EFFECT OF PREY AND PREDATOR DENSITIES ON WOLF PREDATION , 2002 .

[8]  Thomas G. Hallam,et al.  Persistence in food webs—I Lotka-Volterra food chains , 1979 .

[9]  T. O. Carroll,et al.  Modeling the role of viral disease in recurrent phytoplankton blooms , 1994 .

[10]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[11]  C. Packer,et al.  Keeping the herds healthy and alert: implications of predator control for infectious disease , 2003 .

[12]  J. Sprott.  Chaos and time-series analysis , 2001 .

[13]  Yang Kuang,et al.  Basic Properties of Mathematical Population Models , 2002 .

[14]  Shigui Ruan,et al.  Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling , 1993 .

[15]  R M May,et al.  Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos , 1974, Science.

[16]  Sunita Gakkhar,et al.  On a Food Web Consisting of a Specialist and a Generalist Predator , 2003 .

[17]  Joydev Chattopadhyay,et al.  Infection in prey population may act as a biological control in ratio-dependent predator?prey models , 2004 .

[18]  G. T. Vickers,et al.  A criterion for permanent coexistence of species, with an application to a two-prey one-predator system , 1983 .

[19]  Zhien Ma,et al.  A predator-prey model with infected prey. , 2004, Theoretical population biology.

[20]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[21]  M. Biendo,et al.  Regional dissemination of Salmonella enterica serovar Enteritidis is season dependent. , 2003, Clinical microbiology and infection : the official publication of the European Society of Clinical Microbiology and Infectious Diseases.

[22]  Somdatta Sinha,et al.  The role of virus infection in a simple phytoplankton zooplankton system. , 2004, Journal of theoretical biology.

[23]  Shanmuganathan Rajasekar,et al.  Nonlinear dynamics : integrability, chaos, and patterns , 2003 .

[24]  W M Schaffer,et al.  Chaos in ecological systems: The coals that Newcastle forgot. , 1986, Trends in ecology & evolution.

[25]  H. I. Freedman,et al.  Predator-prey populations with parasitic infection , 1989, Journal of mathematical biology.

[26]  W. Schaffer,et al.  Chaos reduces species extinction by amplifying local population noise , 1993, Nature.

[27]  Lee A. Segel,et al.  Modeling Dynamic Phenomena in Molecular and Cellular Biology , 1984 .