Abstract
A model for parasitic diseases which is described by an infinite system of ordinary differential equations is compared to a related two-dimensional system It is shown that depending on a bifurcation parameter κ the infinite dimensional system can have solutions which asymptotically grow exponentially in time or a unique endemic steady state. The threshold values for κ and the results for the bifurcation branches of exponential solutions and steady states are comparable to similar results for the related two-dimensional system. Finally it is shown that invariant distributions for the infinite dimensional model are overdispersed; i.e., the variance to mean ratio is larger than 1.
Original language | English |
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Pages (from-to) | 235-260 |
Number of pages | 26 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 176 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 1993 |