Multi-stage Dynamic Model Research Articles

Study of the brucellosis transmission with multi-stage

In this paper, based on characteristics of brucellosis infection in some regions in China, a multi-stage dynamic model is proposed for sheep brucellosis transmission. The birth rate is related to the adult and vaccinated sheep. More realistically, the immigration from other place is also considered. Firstly, the basic reproduction number $ R_{0}$ is determined and the dynamical properties of the model is discussed. It is concluded that the unique endemic equilibrium exists when $ R_{0}>1$. By constructing suitable Lyapunov function, the global stability of the endemic equilibrium is verified. By carrying out sensitivity analysis of the basic reproduction number in term of the parameters, it is concluded that increasing the sheep vaccination rate and elimination rate of infected sheep is important for the control brucellosis.

Modeling sheep brucellosis transmission with a multi-stage model in Changling County of Jilin Province, China

Brucellosis is one of the major public health problems in Jilin Province of China, especially in Changling County of Jilin Province where at least 95 % of the human brucellosis cases are caused by sheep, which attribute to the large number of sheep kept there and the high positive rate of sheep. In this paper, based on the monitoring data and the characteristics of brucellosis infection in Changling County of Jilin Province, a multi-stage dynamic model is proposed for sheep brucellosis transmission, involving young sheep population and adult sheep population. Firstly, the basic reproduction number $$R_0$$ is determined and then the dynamic properties of the model is further discussed. By carrying out sensitivity analysis of the basic reproduction number in terms of some parameters, it concluded that the birth rate of sheep, sheep vaccination rate, and the elimination rate of infectious sheep play an important roles in the transmission of brucellosis. After investigating and comparing the effect of vaccination and culling strategies is completed, the results show that vaccinating sheep and culling infectious sheep are two effective and feasible strategies to control the spread of brucellosis in Changling County of Jilin Province, but the latter is more effective than the former.

A new multistage dynamic model for biological control exemplified by the host–parasitoid system Spodoptera exigua–Chelonus oculator

Over the last few decades, important advances have been made in understanding of host–parasitoid relations and their applications to biological pest control. Not only has the number of agent species increased, but new manipulation techniques for natural enemies have also been empirically introduced, particularly in greenhouse crops. This makes biocontrol more complex, requiring a new mathematical modeling approach appropriate for the optimization of the release of agents. The present paper aimed at filling this gap by the development of a temperature- and stage-dependent dynamic mathematical model of the host–parasitoid system with an improved functional response. The model is appropriate not only for simulation analysis of the efficiency of biocontrol agents, but also for the application of optimal control methodology for the optimal timing of agent releases, and for the consideration of economic implications. Based on both laboratory and greenhouse trials, the model was validated and fitted to the data of Chelonus oculator (F.) (Hym.: Braconidae) as a biological control agent against the beet armyworm, Spodoptera exigua Hubner (Lep.: Noctuidae). We emphasize that this model can be easily adapted to other interacting species involved in biological or integrated pest control with either parasitoid or predator agents.

Dynamic determination of vessel speed and selection of bunkering ports for liner shipping under stochastic environment

In this work, we study a liner shipping operational problem which considers how to dynamically determine the vessel speed and refueling decisions, for a single vessel in one service route. Our model is a multi-stage dynamic model, where the stochastic nature of the bunker prices is represented by a scenario tree structure. Also, we explicitly incorporate the uncertainty of bunker consumption rates into our model. As the model is a large-scale mixed integer programming model, we adopt a modified rolling horizon method to tackle the problem. Numerical results show that our framework provides a lower overall cost and more reliable schedule compared with the stationary model of a related work.