TABLE OF CONTENTS The epidemic model in 6 is suitable for infectious diseases with a uniform spatial distribution. Here we study the effect when this distribution is nonhomogeneous. One may think of diseases penetrating a population via contacts between individuals. Examples are influenza, rabies, pest, and Aids. For convenience, the following assumptions are being made:
The incubation time is negligibly short.
The pathogens can only survive and reproduce themselves while residing in infected individuals.
Every infected individual recovers or dies after some time. Recovered individuals become immune.
The model has to describe the time and space dependence of:
| y 1( t, x): | concentration of individuals not yet infected and thus susceptible individuals, |
| y 2( t, x): | concentration of infected individuals. |
In fact a third class y 3 plays a r le in the model, namely the class of recovered and thus immune individuals. Because of the relation y 1+ y 2+ y 3=1 it is not necessary to introduce separate formulae for y 3.
The concentrations are taken with respect to the population density y , averaged over the region and time period under consideration. In view of the considerations above, we describe the interactions between the two classes y 1 and y 2 by the following equations:
The rationale of the different terms is as follows:
? ?y 1 y 2 with rate of infection ?>
