In this paper, a three-species system consisting of two predators which are in mutual- ism with each other and preying on the same single prey is considered. Also, the prey and first predator are harvested under optim...In this paper, a three-species system consisting of two predators which are in mutual- ism with each other and preying on the same single prey is considered. Also, the prey and first predator are harvested under optimal conditions. The values of the biological parameters depend on the collection of data from the experts as well as on the nature of the environment in which prey predator system are considered. So the biological para- meters are not precise in reality. This paper presents a different approach to study the prey-predator model with imprecise biological parameters. All the possible equilibrium points are identified and the local as well as global stability criteria under imprecise- ness are discussed. The possibility of existence of bionomic equilibrium is discussed. The optimal harvesting policy is studied using Pontryagin＇s maximum principle. Numerical examples are provided to support the proposed approach.展开更多
In this paper, we have introduced a six-compartmental epidemic model with hand, foot and mouth disease （HFMD） infection. The total population is divided into six subclasses, namely susceptible, exposed, infective in...In this paper, we have introduced a six-compartmental epidemic model with hand, foot and mouth disease （HFMD） infection. The total population is divided into six subclasses, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase, quarantined and recovered class. Some basic properties such as boundedness and non-negativity of solutions are discussed. The basic reproduction number （R0） of the system is obtained using next generation matrix method. Then the deterministic dynamical behaviors of the system are studied. Our study includes the existence and stability analysis of equilibrium points of the system. The sensitivity analysis of our system helps us to find out the parameters of greater interest. Next, we deal with the epidemic model with three controls （two treatment controls with quarantine control）. We show that there exists an optimal control, which is effective in controlling the disease outbreak in a cost effective way. Numerical simulation is presented with the help of MATLAB, which shows tile reliability of our model from the practical point of view.展开更多
文摘In this paper, a three-species system consisting of two predators which are in mutual- ism with each other and preying on the same single prey is considered. Also, the prey and first predator are harvested under optimal conditions. The values of the biological parameters depend on the collection of data from the experts as well as on the nature of the environment in which prey predator system are considered. So the biological para- meters are not precise in reality. This paper presents a different approach to study the prey-predator model with imprecise biological parameters. All the possible equilibrium points are identified and the local as well as global stability criteria under imprecise- ness are discussed. The possibility of existence of bionomic equilibrium is discussed. The optimal harvesting policy is studied using Pontryagin＇s maximum principle. Numerical examples are provided to support the proposed approach.
文摘In this paper, we have introduced a six-compartmental epidemic model with hand, foot and mouth disease （HFMD） infection. The total population is divided into six subclasses, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase, quarantined and recovered class. Some basic properties such as boundedness and non-negativity of solutions are discussed. The basic reproduction number （R0） of the system is obtained using next generation matrix method. Then the deterministic dynamical behaviors of the system are studied. Our study includes the existence and stability analysis of equilibrium points of the system. The sensitivity analysis of our system helps us to find out the parameters of greater interest. Next, we deal with the epidemic model with three controls （two treatment controls with quarantine control）. We show that there exists an optimal control, which is effective in controlling the disease outbreak in a cost effective way. Numerical simulation is presented with the help of MATLAB, which shows tile reliability of our model from the practical point of view.
