I know that b= l / (k *x0) (That is a lowercase L not a one) 3.7.6 (Model of an

Question

I know that b= l / (k *x0)

(That is a lowercase L not a one)

3.7.6 (Model of an epidemic) In pioneering work in epidemiology, Kermack and McKendrick (1927) proposed the following simple model for the evolution of an epidemic. Suppose that the population can be divided into three classes: x(t) number of healthy people; y(t) number of sick people; z(t) number of dead people. Assume that the total population remains constant in size, except for deaths due to the epidemic. (That is, the epidemic evolves so rapidly that we can ignore the slower changes in the populations due to births, emigration, or deaths by other causes.) Then the model is kxy kxy where k and l are positive constants. The equations are based on two assump- tions (i) Healthy people get sick at a rate proportional to the product of x and y. This would be true if healthy and sick people encounter each other at a rate propor- tional to their numbers, and if there were a constant probability that each such encounter would lead to transmission of the disease. (ii) Sick people die at a constant rate l The goal of this exercise is to reduce the model, which is a third-order system, to a first-order system that can analyzed by our methods. (In Chapter 6 we will see

Explanation / Answer

j. The node is infectious in the sense that it is capable of transmitting the infection to its neighbors. Note that each such state will have a transmissibility parameter. Thus this can include models with transmissibility parameter = 0 i.e. they are ‘exposed’ but not infectious (e.g. the E state in the SEIR model is a state which is in the Infected class in the sense that it can potentially cause infections but is not by itself infectious.

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