The dynamics of infectious diseases differ in fundamental ways between endemic regions, where infections can exhibit seasonal outbreaks but persist throughout the year, and epidemic regions, where outbreaks occur intermittently punctuating periods of local extinction. The dynamics of cholera has been studied extensively in endemic but not epidemic conditions, despite the relevance of the latter to the current emergence of the disease and to its devastating consequences when large outbreaks occur unexpectedly in unpredictable fashion. The historical cholera data for districts of former British India, that report monthly cholera mortality from 1890 to 1940, provide an opportunity to examine the patterns of outbreaks in epidemic regions. We examine here the frequency distribution of epidemic size in a large number of districts.
Results/Conclusions We show that these distributions are characterized by heavy-tails, exhibiting epidemics of all sizes with no characteristic scale over two to three orders of magnitude and intermittent epidemics of extreme size. These distributions can be approximated by power-laws over a significant range of sizes, with the exponents of these power laws close to those observed for forest fires. In particular, in many districts, the exponents correspond to supercritical behavior. The value and range of variation of these exponents allow us to explain the dynamics of this infectious disease with a simple forest-fire model that exhibits both self-organization and criticality. We discuss the implications of these common patterns between forest fires and cholera epidemics, as well as some measles epidemics. In particular, frequency size distributions allow us infer the values and roles of both the spread of disease and the re-growth of susceptibles. We conclude that stochasticity is essential not just in the dynamics of extinction, as previously recognized, but also in the dynamics of transmission.
