THE IMPACT OF RESOURCE AND TEMPERATURE ON MALARIA TRANSMISSION

In this paper, we extend the famous Ross's model to establish a new model for malaria to incorporate the impact of blood meal resources for mosquitoes and temperature on the transmission of malaria. A dynamical analysis for the new model is provided and it is shown that with the new growth rate for mosquitoes, the transmission dynamics of malaria becomes more complex and the Hopf bifurcation may occur which induces sustained oscillations not only in the mosquito population but also in the infected human population. Our results suggest that the abundance of blood meal resource for mosquitoes can be a factor which is important to characterize the transmission dynamics of malaria in a region. The impact of maturation time delay related to temperature changes is also analyzed which suggests that increasing the temperature exacerbates the transmission of malaria.

Mathematical and Dynamic Analysis of a Gompertz Ecosystem with Impulsive Control Strategy and Stage Structure for Predator

In this paper, on the basis of the theories and methods of ecology and ordinary differential equations, an ecological Gompertz model with Holling III functional response and stage structure for predator is established. By use of the stroboscopic map, a predator extinction periodic solution is obtained, and the global attractivity of the predator extinction periodic solution is analyzed. By using comparison theorem of impulsive differential equation and small amplitude perturbation skills, we get the sufficient condition for permanence of the system under impulsive harvest strategy for the prey and maturation time delay of predator.

Dynamics of a Stage Structure Pest Control Model with Impulsive Effects at Different Fixed Time

Many existing pest control models, which control pests by releasing natural enemies, neglect the effect that natural enemies may get killed. From this point of view, we formulate a pest control model with stage structure for the pest with constant maturation time delay (through-stage time delay) and periodic releasing natural enemies and natural enemies killed at different fixed time and perform a systematic mathematical and ecological study. By using the comparison theorem and analysis method, we obtain the conditions for the global attractivity of the pest-eradication periodic solution and permanence of the system. We also present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is uniformly permanent. We show that maturation time delay, impulsive releasing, and killing natural enemies can bring great effects on the dynamics of the system. Numerical simulations confirm our theoretical results.