TY - JOUR
T1 - A predator-prey model with disease in the predator species only
AU - Haque, Mainul
N1 - Funding Information:
I am very grateful to the referees for their comments. I am greatly indebted to John R. King (editor of IMA Journal of Mathematics in Medicine and Biology, associate editor of SIAM Journal of Applied Mathematics), from whom I have learned applications of mathematics to biology and medicine. Finally, I am also thankful to Professor Philip Maini, Mathematical Institute(CMB), University of Oxford, who saw the earlier version of the manuscript. Finally, thanks go to the UK-IERI for financial support.
PY - 2010/8
Y1 - 2010/8
N2 - In this paper we propose a predator-prey model with logistic growth in the prey population that includes an SIS parasitic infection in the predator population, with the assumption that the predator has an alternative source of food. For simplicity we initially work with a model involving the fractions of the predator which are susceptible and those infected and then translate the results back to the model with absolute numbers. Important thresholds R01, R02, R03 and R04 are identified and their implications have been explained. Our theoretical study indicates that the absence of prey may be beneficial for predator when a transmissible disease runs among the predator population. One important conclusion is that infection in the predator species may save the prey from extinction even if R02, the basic reproduction number for the prey to be able to invade the predator-only equilibrium, is less than one. Therefore infection in the predator species may be taken as biological control. Finally, analytical results have been supported by numerical simulations with the help of experimental data.
AB - In this paper we propose a predator-prey model with logistic growth in the prey population that includes an SIS parasitic infection in the predator population, with the assumption that the predator has an alternative source of food. For simplicity we initially work with a model involving the fractions of the predator which are susceptible and those infected and then translate the results back to the model with absolute numbers. Important thresholds R01, R02, R03 and R04 are identified and their implications have been explained. Our theoretical study indicates that the absence of prey may be beneficial for predator when a transmissible disease runs among the predator population. One important conclusion is that infection in the predator species may save the prey from extinction even if R02, the basic reproduction number for the prey to be able to invade the predator-only equilibrium, is less than one. Therefore infection in the predator species may be taken as biological control. Finally, analytical results have been supported by numerical simulations with the help of experimental data.
KW - Eco-epidemiological model
KW - Infected predator
KW - SIS epidemic model
KW - Stability and bifurcation analysis
UR - http://www.scopus.com/inward/record.url?scp=77955631693&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2009.06.012
DO - 10.1016/j.nonrwa.2009.06.012
M3 - Article
AN - SCOPUS:77955631693
SN - 1468-1218
VL - 11
SP - 2224
EP - 2236
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
IS - 4
ER -
