Epidemiological Model of Tetanus and its Use in the Planning of Immunization Programmes

Vaccination against rubella and measles: Quantitative investigations of different policies

“…In any such work, the accuracy and appropriateness of the numerical methods used to generate sequences of temporal changes must be carefully understood. As discussed earlier, this point may be illustrated by comparing our results with those reported by Knox (1981) and Cvjetanovic et al (1982). Immunization on a very large scale is a relatively recent phenomenon, and country-wide vaccination programmes against many common viral and bacterial infections are currently only in their second or third decade of operation.…”

“…These and other related questions have recently been examined by Knox (1980), Dietz (1981), Hethcote (1983) and Cvjetanovic, Dixon & Grab (1982). Three ofthese 260 Vaccination against rubella and measles studies are concerned with vaccination against rubella: Knox (1980) examines the long-term effect on disease incidence of various vaccination policies, and also uses computer models to explore the short-term, 'transient' effects attendant upon the initiation ofvaccination; Dietz (1981) and Hethcote (1983) give analytic treatments of long-term effects, taking some account of economic cost-benefit considerations.…”

“…Although these studies are seminal, they concentrate on formal results and do not present any explicit comparison between theoretical results and observed epidemiological data. Cvjetanovic et al (1982) examine measles, and give results for a complex study of various vaccination policies, based on computer simulations; these authors omit description of some important details of their methods and assumptions (it is not clear, for example, how they estimate the rate of infection in communities under different levels of vaccination uptake). The simulation models of both Knox and Cvjetanovic and colleagues are complex in structure; this has the advantage that the models can embrance more biological detail, and the associated disadvantage that it is not always clear how particular conclusions follow from particular initial assumptions.…”

“…Two significant exceptions are the recent studies of rubella by Knox (1980) and of measles by Cvjetanovic et al (1982), both of which present computer studies of the impact of immunization on the population dynamics of infection. We believe that both these studies offer important and new insights, but that some of their conclusions may be in error (as a result of faults in the mathematics).…”

“…All this can be read as a cautionary tale: the time steps used in approximating the partial differential equations (3)-(6) need to be chosen carefully. Cvjetanovic et al (1982) also employed a set of difference equations to examine the impact of various levels of vaccination coverage on the dynamics of measles within large populations. Making extensive use of public health data for measles in Britain, Germany and elsewhere, they concluded that immunization of 60-70 % of successive cohorts of infants could eventually (in 10-20 years) eradicate measles.…”