疟疾的两种带菌体之间的竞争对其共存的影响

在能够传染疟疾病的蚊子中引入对此病原体有抵抗力的蚊子，基于随机配对法则和一个描述竞争的死亡率矩阵，建立起疟疾传染过程的数学模型．在假设两种蚊子能够共存的情况下，证明了此模型的两个无病平衡点的稳定性，同时发现蚊子之间的竞争并不会影响两平衡点所对应基本再生率的大小关系，进一步找出了这两种蚊子的共存条件和共存状态的稳定条件．

Influence of Competition among Vectors on the Disease Dynamics of Malaria

In this paper, the authors introduce a pathogen-resistant strain into vectors of malaria. Then they formulate a mathematical model on the basis of random pair formations and competition mortalities among vectors. The stability of four disease-free equilibria is analyzed and the basic reproduction numbers are calculated by means of the next generation method. It is found that the competition does not influence the relationship between these two reproduction numbers. Furthermore, the authors find that only when the reproduction probability of the mating between two resistant vectors is bigger than that of the interbreeding between a wild and resistant vector, can two strain vectors coexist stably.