In this work,we have introduced an eco-epidemiological model of an infected predator prey system.Incorporation of prey refuge gives that a fraction of the infected prey is available to the predator for consumption.Mor...In this work,we have introduced an eco-epidemiological model of an infected predator prey system.Incorporation of prey refuge gives that a fraction of the infected prey is available to the predator for consumption.Moreover,to make the model more realistic to the environment,we have introduced strong Allee effect in the susceptible population.Boundedness and positivity of the solution have been established.Local stability conditions of the equilibrium points have been found with the help of Routh-Hurwitz criterion and it has been observed that if a prey population is infected with a lethal disease,then both the prey(susceptible and infected)and predator cannot survive simultaneously in the system for any parametric values.The disease transmission rate and the attack rate on the susceptible have an important role to control the system dynamics.For different values of these two key parameters,we have got only healthy or disease-free or predation-free or a fluctuating disease-free or even a fluctuating predator-free system with some certain parametric conditions.展开更多
New offspring due to sexual reproduction is not an instantaneous process from its birth,it takes time to be sexually mature.On the other hand,harvesting of commercially profitable fish population before the perfect si...New offspring due to sexual reproduction is not an instantaneous process from its birth,it takes time to be sexually mature.On the other hand,harvesting of commercially profitable fish population before the perfect size or weight is reached is not only a commercial loss but also risks the extinction of the population.Now,we discuss the issue of Ganges-Brahmaputra-Meghna basin,northern Bay of Bengal for the age-selective harvesting of Hilsa shad(Tenualosa ilisha)which lays eggs after its sexual maturation.Harvesting of hilsa before its sexual maturation risks its extinction and due to lamer body weight,it is not a commercially profitable policy.This is a reality of Sundarban estuary for hilsa fish harvesting,therefore,biologically and economically both India and Bangladesh are facing several problems.Empirical data of Frasergunje Fishing Harbor shows a clear picture as the supporting document of this mathematical problem.展开更多
Exploring the predator prey linkage in food chain system is the most familiar research work in population biology.Recently,some research experiments show that predator-prey interaction not only governed by direct hunt...Exploring the predator prey linkage in food chain system is the most familiar research work in population biology.Recently,some research experiments show that predator-prey interaction not only governed by direct hunting but also influenced by some indirect effect such as fear effect(felt by prey)that may change the physiological behavior of prey.Based upon this fact,we consider a tritrophic food chain model incorporating with anti-predation response(fear effect)and multiple time delays for biomass conversion from prey to middle predator and middle to top predator.We analyze the resulting delay differential equations and explore how the anti-predation response level affects the population dynamics.We also investigate the effect of delay parameters,for which the model system switches its stability through Hopf-bifurcation.We compare all of our results between two different food chain models consisting of two different functional responses.Some numerical simulations are performed to validate the effectiveness of the derived theoretical results.展开更多
文摘In this work,we have introduced an eco-epidemiological model of an infected predator prey system.Incorporation of prey refuge gives that a fraction of the infected prey is available to the predator for consumption.Moreover,to make the model more realistic to the environment,we have introduced strong Allee effect in the susceptible population.Boundedness and positivity of the solution have been established.Local stability conditions of the equilibrium points have been found with the help of Routh-Hurwitz criterion and it has been observed that if a prey population is infected with a lethal disease,then both the prey(susceptible and infected)and predator cannot survive simultaneously in the system for any parametric values.The disease transmission rate and the attack rate on the susceptible have an important role to control the system dynamics.For different values of these two key parameters,we have got only healthy or disease-free or predation-free or a fluctuating disease-free or even a fluctuating predator-free system with some certain parametric conditions.
文摘New offspring due to sexual reproduction is not an instantaneous process from its birth,it takes time to be sexually mature.On the other hand,harvesting of commercially profitable fish population before the perfect size or weight is reached is not only a commercial loss but also risks the extinction of the population.Now,we discuss the issue of Ganges-Brahmaputra-Meghna basin,northern Bay of Bengal for the age-selective harvesting of Hilsa shad(Tenualosa ilisha)which lays eggs after its sexual maturation.Harvesting of hilsa before its sexual maturation risks its extinction and due to lamer body weight,it is not a commercially profitable policy.This is a reality of Sundarban estuary for hilsa fish harvesting,therefore,biologically and economically both India and Bangladesh are facing several problems.Empirical data of Frasergunje Fishing Harbor shows a clear picture as the supporting document of this mathematical problem.
文摘Exploring the predator prey linkage in food chain system is the most familiar research work in population biology.Recently,some research experiments show that predator-prey interaction not only governed by direct hunting but also influenced by some indirect effect such as fear effect(felt by prey)that may change the physiological behavior of prey.Based upon this fact,we consider a tritrophic food chain model incorporating with anti-predation response(fear effect)and multiple time delays for biomass conversion from prey to middle predator and middle to top predator.We analyze the resulting delay differential equations and explore how the anti-predation response level affects the population dynamics.We also investigate the effect of delay parameters,for which the model system switches its stability through Hopf-bifurcation.We compare all of our results between two different food chain models consisting of two different functional responses.Some numerical simulations are performed to validate the effectiveness of the derived theoretical results.
