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Sex pheromone, aiming at mating disruption (MD), being species specific and leaving no toxic residues in the produce grown, offers an attractive alternative to conventional pesticides. In this paper, by incorporating the gestation delay and sex pheromone, we explore the impact of MD control on the dynamic behaviors of pest system. Firstly, the boundness, stability and bifurcation of system are deliberated. Secondly, an optimal control problem based on sex pheromone and pesticide is transformed into an equivalent optimal parameter selection problem by introducing the constrain violation function. Additionally, the gradients of the cost function with respect to the dose of sex pheromone and the killing rate are given. Furthermore, simulations are executed to validate the validity of our method. Meanwhile, our results indicate that gestation delay increases the extinction risk of the population and liberating sex pheromone destroys the stability of equilibrium states. [ABSTRACT FROM AUTHOR]

We propose and study a predator-prey model with state-dependent delay where the prey population is assumed to have an age structure. The state-dependent delay appears due to the mature condition that the prey must spend an amount of time in the immature stage sufficient to accumulate a threshold amount of food. We perform a qualitative analysis of the solutions, which includes studying positivity and boundedness, existence and local stability of equilibria. For the global dynamics of the system, we discuss an attracting region which is determined by solutions, and the region collapses to the interior equilibrium in the constant delay case. [ABSTRACT FROM AUTHOR]

Abstract: Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, two SIR epidemic models with different patterns of recruitment and difference in immunity are investigated. When the recruitment rate is less than some threshold value, the disease will be eradicated. Furthermore, for the continuous recruitment model, according to the Poincare–Bendixson theorem, the global asymptotical stability of a unique positive equilibrium is obtained. For the pulse recruitment model, we investigated the existence of nontrivial periodic solutions via a supercritical (subcritical) bifurcation. From a biological point of view, our results indicate that (1) the disease can be eradicated if the recruitment rate is controlled under some threshold; (2) the number of the infected increases as the difference in immunity increases; (3) fewer individuals are infected as the pulse recruitment is taken, displaying its effect on the control of the disease. [Copyright &y& Elsevier]

Abstract: In compared with specialist predators which feed almost exclusively on a specific species of prey, generalist predators feed on many types of species. Consequently, their dynamics is not coupled to the dynamics of a specific prey population, and the generalist predators has itself growth function which be extended a well-known logistic growth term. We develop a generalist predator–prey model with diffusion and study the effect of harvesting and delay under Neumann conditions. The stability of the equilibria is firstly investigated, and the existence of traveling wave solutions is then established by constructing a pair of upper–lower solutions and using the cross iteration method and Schauder’s fixed point theorem. [Copyright &y& Elsevier]

Abstract: Considering that over exploitation would result in the extinction of the population, we propose and investigate a Holling II functional response prey-predator model with harvesting for fishery resource in a two-patch environment: a free fishing zone (patch 1) and a reserve zone (patch 2) where fishing is strictly prohibited. First, the presence of harvesting can impact the existence of equilibria. Further, stability criteria of the model is analyzed both from local and global point of view. Our results indicate that so long as the prey population in the reserved zone does not extinct, the both prey always exist, that is marine reserves should ensure the sustainability of system. Thus, marine reserves not only protect species inside the reserve area but they can also increase fish abundance in adjacent areas. Next, the existence of bionomic equilibrium and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle. It is established that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results. [Copyright &y& Elsevier]