西南师范大学学报(自然科学版)
西南師範大學學報(自然科學版)
서남사범대학학보(자연과학판)
JOURNAL OF SOUTHWEST CHINA NORMAL UNIVERSITY
2009年
2期
31-38
,共8页
疟疾%免疫的传播向量%竞争%随机配对%基本再生率
瘧疾%免疫的傳播嚮量%競爭%隨機配對%基本再生率
학질%면역적전파향량%경쟁%수궤배대%기본재생솔
malaria%resistant strain%competition%random formation%basic reproduction number
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.
在能夠傳染瘧疾病的蚊子中引入對此病原體有牴抗力的蚊子,基于隨機配對法則和一箇描述競爭的死亡率矩陣,建立起瘧疾傳染過程的數學模型.在假設兩種蚊子能夠共存的情況下,證明瞭此模型的兩箇無病平衡點的穩定性,同時髮現蚊子之間的競爭併不會影響兩平衡點所對應基本再生率的大小關繫,進一步找齣瞭這兩種蚊子的共存條件和共存狀態的穩定條件.
재능구전염학질병적문자중인입대차병원체유저항력적문자,기우수궤배대법칙화일개묘술경쟁적사망솔구진,건립기학질전염과정적수학모형.재가설량충문자능구공존적정황하,증명료차모형적량개무병평형점적은정성,동시발현문자지간적경쟁병불회영향량평형점소대응기본재생솔적대소관계,진일보조출료저량충문자적공존조건화공존상태적은정조건.
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.
