Introduction to the modelling of venereal disease

Summary

The continually rising trend in the incidence of venereal diseases, especially gonorrhoea, in a large number of countries, both developed and developing is causing considerable public health concern. There is a disquieting volume of human suffering involved, as well as large economic losses in treatment and hospitalization. The present paper reviews the existing state of development in the mathematical modelling of the relevant disease dynamics. The ‘criss-cross’ nature of the infections, which in heterosexual contacts switch between the male and female populations, together with the nonlinear form of the rate of spread normally occurring in infectious diseases, leads to special types of simultaneous nonlinear differential equations.

The simplest deterministic models available entail threshold phenomena connecting the maintenance of endemic states to the contact-rates, the personto-person infection-rates, and the removal-rates. A few stochastic results are also available.

Special attention is given to the aspects of nonhomogeneous mixing, analysis of contact-rates, infection without immunity, allowance for asymptomatic infection, the recognition of many different classes of infected individuals, and the problems of public health forecasting and control. In some cases transient solutions of the equations can be used to forecast future trends in disease incidence, depending on appropriate assumptions about alternative public health interventions.

It is concluded that further mathematical work should be concentrated on relatively simple models comprising no more than three or four district epidemiological groups for each sex. There should be both (i) more intense mathematical investigations, and (ii) new attempts to assimilate the models directly to public health venereal disease control.