Study On Non-Smooth Biosystem Of Theory And Application Under Resource Limitation

Resource limitation does not only make the prevention and control of emerging infectious disease and agricultural pest face serious challenges, but also is highly con-cerned by the department of public health and ecological agriculture. What kind of difficulties and challenges can resource limitation bring for the prevention and con-trol of emerging infectious disease and agricultural pest? What are the best control measures and how to implement then? For these problems, the non-smooth biologi-cal models have been established to describe the phenomena of limited resources in this article. According to the process of the disease spreads and the pest outbreaks, the important indexes to make the disease and pest eradicate are predicted and evaluated through theoretical derivations and numerical simulations Conditional upon resource limitation, the purpose of this study is to examine the impacts of possible state intervenes on disease outbreak or pest outbreaks. Meanwhile, the optimal strategies for the prevention and control of emerging infectious disease and agricultural pest have been obtained, which may provide some suggestions for public health experts and agriculture ecologists.Emerging infectious disease including SARS, H1N1, H7N9, Ebola etc. are often accompanied by other viral diseases such as common flu. In the early stages of SARS outbreak, as the small numbers of cases and adequate medical resource, and there is no effective way to identify the infected, patients infected with different viruses can be get treatment in different areas of the hospital at the same time. With the increasing number of infected cases, and the shortage of medical resources such as doctors, facilities, vaccines etc., the hospital will treat severe cases only. Based on this, this article proposes a non-smooth Pilippov infectious disease model with threshold policy control and selection pressures under limited resources. Analyses of this model include sliding domains, sliding mode dynamics, the existence of all types of equilibria, the sufficient conditions of boundary equilibrium bifurcations. Codimension-1 local and global sliding bifurcations of proposed Filippov model are investigated by employing numerical techniques. Further, one of the main proposed is to show the selective strategy for various diseases under limited resource, the best threshold policy is derived to make the emerging infectious disease be eradicated.In consideration of vaccine shortage in the prevention of emerging infectious dis-ease, we propose a SIR infectious disease model with limited vaccine to examine how a limited vaccine resource affects the transmission and control of emerging infectious diseases. As vaccines are treated only in the part of susceptible people, the threshold condition for eradicating diseases is given, and the effects of the limited vaccine re-source on the threshold have been studied. Latin hypercube sampling/partial rank correlation coefficient uncertainty and sensitivity analysis techniques are employed to determine the key factors which are most significantly related to the threshold value, a viable proposal about how to implement control strategy effectively under limited resources as vaccines, medical facilities etc. is provided. Meanwhile, the conditions for existence and stability of the endemic periodic solution are given, the numerical results reveal that the nonlinear impulse will result in the dynamical behaviors of the system more complicated.Involving the nonlinear factors which affect agriculture resource limitation into the model, in view of the fatality rate of pesticides on pests is a nonlinear function with saturation effect, a general pest-nature enemy model with periodic control strategy is proposed. The existence and stability of pest-free periodic solution are investigated with the threshold conditions by impulsive differential equation theory and Lambert W function. In order to address how the limited resources affect the pest control, as an example the pest-nature enemy model with Holling II functional response function is chosen. The theoretical and numerical results reveal that the system has complex dynamical behaviors, and the initial densities of pest and nature enemy populations are crucial for pest control. According to the detailed analyses of the outbreak of pest and its control strategies on limited resources, some biological conclusions with practical significance are discussed.In this article, it focuses on the proposed novel mathematical models arising from biology, medicine and life sciences etc. The modeling ideals, analytical tech-niques and numerical methods developed in this article can not only be used to study the general infectious disease models and pest control models with IPM strategy, but also may help in the design of an optimal control strategy for department of public health or ecological agriculture.