基于价格因素的布鲁氏菌病动力学建模及其控制措施研究

Modeling of Brucellosis Dynamics and Its Control Measures Based on Price Factors

摘要: 随着社会经济发展，羊肉制品的需求量与日俱增，羊养殖规模不断扩大，预防羊疫病工作的难度系数也日渐严峻。目前我国羊养殖业依然受到布鲁氏菌病的威胁，由于羊群养殖量和羊肉价格有直接关系，羊肉价格和羊肉的供需有直接关系，本文在考虑布鲁氏菌病对羊群养殖的影响时加入了羊肉价格和羊肉市场库存量这两个变量进而建立数学模型，给出模型的基本再生数，无病平衡点和正平衡点并分别讨论了稳定性。随后在传染病模型基础上加入三个控制措施，分别为减少易感羊和染病羊的接触；增大对感染羊的捕杀力度；减少布鲁氏菌对环境的排放；以此建立控制模型。以养殖户损失最小为目的建立目标函数，寻求对养殖户最有利的控制策略，利用Pontryagin极小值原理得出最优控制策略的理论结果。以河南羊的活重价格和人间布鲁氏菌病的累计病例数为例，对模型进行数值模拟。最后对上述三个控制措施进行组合，给出七种不同的策略。经研究表明，相比起单一控制策略和双重控制策略，三项措施同时实施对养殖户来说损失最小，控制成本、羊患病数和环境中布病浓度达到最低，故本文给养殖户的建议是综合实施上述三项措施最有利。

Abstract: With the socio-economic development, the demand for sheep meat products is increasing day by day, the scale of sheep farming is expanding, and the difficulty factor of sheep disease prevention work is getting more and more severe. At present, the sheep farming industry in China is still threatened by brucellosis. Since the amount of sheep farming and the price of sheep meat are di-rectly related, and the price of sheep meat and the supply and demand of sheep meat are directly related, this paper adds two variables, the price of sheep meat and the amount of sheep meat mar-ket inventory, when considering the influence of brucellosis on sheep farming and then establishes a mathematical model, gives the basic regeneration number of the model, the disease-free equilib-rium point and the positive equilibrium point and discusses respectively. The stability of the model was discussed. Three control measures were then added to the infectious disease model, namely, reducing contact between susceptible and infected sheep; increasing the culling of infected sheep; and reducing brucellosis emissions to the environment; thus establishing the control model. The objective function was established with the aim of minimizing farmers’ losses, and the most favora-ble control strategy for farmers was sought. The theoretical results of the optimal control strategy were derived using the Pontryagin principle of minimal values. The model is numerically simulated with the live weight price of Henan sheep and the cumulative number of human brucellosis cases. Finally, the three controls mentioned above were combined to give seven different strategies. It was shown that compared to the single control strategy and dual control strategy, the simultaneous im-plementation of the three measures was the least lossy for farmers, with the lowest control cost, number of sheep diseases and brucellosis concentration in the environment, so the recommenda-tion to farmers in this paper is that the combined implementation of the above three measures is the most beneficial.