|Budget Amount *help
¥2,500,000 (Direct Cost : ¥2,500,000)
Fiscal Year 1997 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1996 : ¥1,600,000 (Direct Cost : ¥1,600,000)
I developed mathematical models for the evolution of pathogen antigen genotypes under the host immune response. For the patten of evolution of the pathogen antigen genes, I found that the outbreak of a pathogen antigen type will enhance the host immune response against neighboring pathogen genotypes, forcing the next outbreak occurring at a genotype suffciently distant from the currently prevalent one. The condition for this kind of episodic antigen evolution is detailed - it is required that the width of cross-immunity is larger than the mean genetic distance among the offspring antigen types produced by mutation. Another topics of host-pathogen coevolution explored in this project is the arms race between resistance and virulence, as exemplified in the plant-pathogen gene-for-gene interaction extensively studied in rice-fungus and wheat-fungus systems, and in host-parasitoid encapsulation interaction. It is widely known that the host's ability to encapsulate parasitoid eggs and parasitoid's ability to overcome host encapsulation varies between species and between geographical regions in the same species. I developed a mathematical model which deals with the coevolution of host encapsulation ability and parasitoid anti-encapsulation. The model reveals that the stable coevolutionary equilibrium with intermediate arms levels in both species is very difficult to be maintained, and the evolutionary cycles, which characterized with the escalation of arms levels followed by the break down toward no ams level in host, is the likely outcome of coevolution. A number of new studies have been started in this project, which include the mathematical study for the optimal eradication program of polioviruses, which takes into account the emergence of virulent virus from the vaccination strain.