Exponential growth in age-structured two-sex populations.
We consider a continuous age-structured two-sex population model which is given by a semilinear system of partial differential equations with nonlocal boundary conditions and is a simpler case of Fredrickson-Hoppensteadt model. The non-linearity is introduced by a source term, called from its physical meaning, the marriage function. The explicit form of the marriage function is not known; however, there is an understanding among the demographers about the properties it should satisfy. We have shown that the homogeneity property of the non-linearity leads to the fact that the system supports exponentially growing persistent solutions using a general form of the marriage function and its properties. This suggests that the model can be viewed as a possible extension of the one-sex stable population theory to monogamously mating two-sex populations.
Martcheva
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Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA. mayam@magnus.poly.edu
D000367:Age Factors; D001723:Birth Rate; D005260:Female; D006801:Humans; D016014:Linear Models; D008297:Male; D008393:Marriage; D008954:Models, Biological; D009026:Mortality; D011157:Population Dynamics