On the Use of the Leslie Matrix in the Analysis of Prevalence Data for General Epidemic Processes

Abstract

The idea of the Leslie matrix, introduced into the analysis of age prevalence data, is extended to cover prevalence data for general epidemic processes. The use of the projection matrix in such situations is discussed, focusing on model construction and estimation of parameters of the projection matrices that arise. Applications of the technique to data covering varous epidemiological situations (vector-borne disease and virus infection) are illustrated. It is also shown how the technique can be of use in evolving an immunization strategy for arresting the spread of virus infection. dS dt = -(:3IS with initial conditions 1(0) = Q and S(o) = Nand 1(1) + S(I) = N + Q.This is the simplest basic epidemic model called an SI-model. There are others, discussed in Bailey (1975) and Hethcote (1989), named according to the model assumptions adopted, e.g.(a) the SIS-model, in which an individual is susceptible, becomes infective on being infected and returns to the susceptible class again after recovery and (b) the SIR-model, where the recovered infectives are permanently immune and so are classified as removed, R.The system of equations which arises for the continuous time treatment (stochastic or deterministic) is usually mathematically intractable because the equations involve non-linear systems of differential equations. tAddress

Interacting populations : hosts and pathogens, prey and predators

“…Another way is to use matrix models. Apart the applications in the analysis of age-prevalence data (Saporu, 1990(Saporu, , 1996, and description of the contact and transmission processes (e. g., Pugliese, 1991;Keeling & Grenfell, 1997), the matrix approach hasn't commonly been used in epidemiology.…”