Qualitative study of Kermack and Mckendrick's epidemic model

Abstract

In this paper, we carry out a qualitative study of Kermack and Mckendrick's epidemic model. We derive a special case of this model for recurrent diseases (relapse – recovery model). Using the new model, we investigate the severity of the epidemic and then test the stability of the original model. It is then shown that the number of invectives after a very long time from the inception of the epidemic is a constant. It is also shown that the steady state is unstable. Trajectories that help to know the extent of the severity are also presented. Through these trajectories it is shown that the severity of this epidemic can be estimated when the rate of infectiousness (r) and the removal rate (δ.) are estimated.

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 477-480