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Mathematical Medicine and Biology 1999 16(4):319-332; doi:10.1093/imammb/16.4.319
© 1999 by Institute of Mathematics and its Applications
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A Kermack–McKendrick model applied to an infectious disease in a natural population

M. G. ROBERTS{dagger}

AgResearch, Wallaceville Animal Research Centre PO Box 40063, Upper Hutt, New Zealand

{dagger} robertsm{at}agresearch.cri.nz

The dynamics of a fatal infectious disease in a population regulated by density-dependent constraints are represented as a system of nonlinear integral equations. Survival probabilities and disease transmission coefficients may vary with the time elapsed since infection, and horizontal and vertical modes of transmission are allowed for. Criteria for the existence and stability of steady states are derived, and an example based on the dynamics of tuberculosis is presented. Finally, the relative merits of this approach, and the familar compartmental models based on differential equations are discussed.

Keywords: epidemic models; Kermack–McKendrick model; tuberculosis


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