Abstract
A modified SIRS model is developed as a framework for the study of epizootiological dynamics in an insect-pathogen system. Linearized stability analysis reveals that the system with one immune and one susceptible host class can exhibit stable, periodic or unstable behavior depending on model parameters. In general, high pathogenicity, short pathogen propagule lifespan and high host reproductive rate are stabilizing influences. Pathogen transmissibility and propagule production/host do not influence local stability. The effect of seasonal host reproduction is studied because most insect hosts are seasonal in temperate climates. The basic stability dependence on model parameters holds except as modified by the length of the reproduction interval. The results of this study are compared with the recent work of Anderson and May.
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Scientific paper No. 82-7-179 of the Kentucky Agricultural Experiment Station, Lexington. This research has been financed in part with Federal funds from the USDA under grant number 82-CRSR-2-1000. The contents do not necessarily reflect the views and policies of the USDA.
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Brown, G.C. Stability in an insect-pathogen model incorporating age-dependent immunity and seasonal host reproduction. Bltn Mathcal Biology 46, 139–153 (1984). https://doi.org/10.1007/BF02463727
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DOI: https://doi.org/10.1007/BF02463727