It is shown that when the basic reproduction number is less than 1 then the trivial equilibrium is globally asymptotically stable if the basic reproduction number is greater than 1 then the trivial equilibrium is unstable and there is a positive equilibrium which attracts all positive solutions. Then, in Section 3, we modify the model obtained in Section 2 to incorporate lethal control and contraception control. We take into account the seasonal cycle of breeding and non-breeding. In Section 2, we model the population with natural growth.
![plateau pika plateau pika](http://animal.memozee.com/ArchHAN03/1274425678-m.jpg)
investigated the influence of environment change on population dynamics. With this kind of model, Burkey and Stenseth studied the effects of resource patchiness and the effects of a seasonally variable environment on the population dynamics of a herbivore species, and Liu et al. This kind of model can describe the population dynamics in more detail. During the breeding and the non-breeding seasons, the dynamics of plateau pika population satisfies different models. Considered the seasonal reproduction of plateau pika, we proposed several discrete models to understand the dynamics of plateau pika. They have short spring-summer breeding seasons typical to herbivorous small mammals inhabiting alpine environments. Plateau pika is a native herbivorous species inhabiting the Qinghai-Tibetan plateau. Reproduction in mammals is likely affected by the resources available in its habitat to sustain the energy demands of reproduction. In fact, some sterilants can also poison target species. Zhang argued that culling and contraception combined will give better result in controlling population numbers. Now, sterilants have also been used to control plateau pika. The commonly used one to control plateau pika is poisoning, which kills them with botulins of models C and D. In order to manage rodent pests, a variety of methods have been used.
![plateau pika plateau pika](https://live.staticflickr.com/2652/3914885937_726fc8111a.jpg)
Now, plateau pika is regarded as a pest because its competition with livestock for herbage and its burrowing activity which leads to soil erosion and vegetation disturbances. The degraded meadow provides the plateau pika with a better habitat and results in the overabundance of plateau pika. In the recent years, due to overgrazing and the global climate change, the alpine meadow has degraded seriously. Its presence of reasonable size is important for the healthy development and the biodiversity of the alpine meadow.
![plateau pika plateau pika](https://live.staticflickr.com/65535/49397943896_6fba822e22_n.jpg)
The plateau pika ( Ochotona curzoniae) is a keystone species of the Qinghai-Tibet plateau.