Soc Psychiatry Psychiatr Epidemiol (2004) 39 : 853–856 DOI 10.1007/s00127-004-0867-9 ■ Abstract Background Epidemics can be represented mathematically using a variety of models. One of these, the Kermack-McKendrick model, has been used to sup- port health policy decisions concerning vaccination re- quirements. An unrelated body of literature suggests that some behaviours, including some types of violence, may spread in ways analogous to the contagious spread of infectious diseases, a process that has been character- ized as “behavioural contagion”. Methods Various pa- rameter values reflecting the characteristics of crowds were substituted into the Kermack-McKendrick model. Computer simulations were used to evaluate the impact of these parameter values. Results The simulations re- produced several features of crowd violence: the ten- dency for riots to occur in large groups, the importance of rapid removal of violent individuals from crowds,and the roles of alcohol consumption and social identifica- tion processes. Conclusions Epidemic models may be of relevance to the prevention and control of violent be- haviour as they can assist with the identification of high- risk situations and prevention strategies. Theoretical constructs related to epidemic theory may have broad applicability for modelling the unstable course of some mental disorders. ■ Key words violence – riots – epidemic theory – theoretical models – computer simulation Introduction Diseases may be categorized as endemic or epidemic. Endemic describes the occurrence of a disease within a population at its expected or baseline rate, whereas an epidemic disease is one occurring with a frequency greater than normal expectancy [1]. In epidemiological theory, endemic diseases and epidemic diseases are ad- dressed differently. An endemic disease is characterized by a stable base- line frequency (e. g. incidence or prevalence), and these population proportions can be estimated using a proba- bility sample drawn from the population. Similarly, in analytical research, the frequency of disease can be re- lated to various potential determinants in order to eval- uate etiological hypotheses. Generally, in chronic dis- ease epidemiology,the population frequency is regarded as being fixed, such that the challenges involved in esti- mating the relevant frequencies are those of statistical inference. Statistical methods are used to quantify the impact of random error resulting from sampling vari- ability. The concepts underlying statistical analysis have their mathematical foundations in the “law of large numbers”, sometimes attributed to Jacob Bernoulli [1]. Statistical estimates become more stable as sample sizes increase, such that stable estimates arise out of random samples. Epidemiology, especially as it is applied to endemic chronic diseases, is, therefore, largely oriented towards concepts of stability in estimation and infer- ence. In epidemic diseases, a different set of methodologies are required. Here, there is no stable underlying proba- bility or frequency to be estimated. Rather, the fre- quency of the disease is unstable and the behaviour of epidemic disease is guided by the “mass action princi- ple” [1] whereby the number of future cases is regarded as a function of the number of current cases and the number susceptible to the infection in the population. SPECIAL ISSUE S. B. Patten · J. A. Arboleda-Flórez Epidemic theory and group violence Accepted: 9 June 2004 SPPE 867 S. B. Patten Depts. of Community Health Sciences and Psychiatry University of Calgary 3330 Hospital Drive NW Calgary (AB), Canada Tel.: +1-403/220-8752 Fax: +1-403/270-7307 E-Mail: patten@ucalgary.ca J. A. Arboleda-Flórez Dept. of Psychiatry Queens University Kingston (ON), Canada