A study for mathematical theory and applications of structured population dynamics

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(l) We have developed a two-sex age-structured population model with homogeneous marriage function as an evolution equation system and constructed its semigroup solution. Existence of persistent solution (exponential solution) has been proved for general marriage function.(2) We have formulated a nonlinear age-structured population model for marine invertebrates with density dependent mortality. We have constructed a positive semigroup solution, and proved the sufficient condition for the stability of the steady state solution. We have also the possibility of unstable steady state solution and oscillatory behavior.(3) We have formulated an epidemic model for type A influenza that takes into account the evolutionary aspects of virus, and examined it as an evolutionary equation. We have established the threshold condition for disease invasion and existence of endemic steady state. The possibility of unstable endemic steady state has been Oalso shown.(4) We have constructed a duration-dependent epidemic model for vector transmitted diseases like as Chagas disease, and shown that a backward bifurcation of endemic steady states can occur if there exists a disease-induced death rate.(5) We have formulated and analyzed an age-duration-structured population model for HIV infection in homogeneous community. We have established the threshold condition for invasion and existence of endemic steady states. It was also shown that a backward bifurcation of endemic steady slates can occur, so multiple endemic steady states are possible.(6) We have analyzed the behavior of a pair formation model for sexually transmitted diseases with subpopulations divided by sexual activity. And we have constructed an individual-based model to simulate sexually transmitted diseases.