A MATHEMATICAL MODEL FOR THE RURAL AMPLIFICATION OF MURRAY VALLEY ENCEPHALITIS VIRUS IN SOUTHERN AUSTRALIA

Abstract

The exacerbation of epidemics of Murray Valley encephalitis in southern Australia during 1951 and 1974 was studied retrospectively to determine when viral introduction may have occurred. Data from studies spanning over 30 years were utilized 1) to determine the number of infective Culex annulirostris necessary to cause one clinical case, based on known host-feeding patterns and the subclinical infection rate in man, and 2), using mathematical modeling, to calculate the likely duration of the rural amplification phase. Generalized tables were generated which demonstrated that mosquito longevity, extrinsic incubation period, and duration of the feeding cycle were the most important variables predisposing rapid amplification. Although Murray Valley encephalitis transmission may still occur during adverse conditions when the reproduction rate Z < 1.0, subtraction of the durations of incubation in man prior to clinical onset and the most likely rural amplification period from the dates of onset of clinical infections during January 1951 and 1974 suggested that amplification commenced around October 9–30 and that any Murray Valley encephalitis introduction had occurred by then. Examination of bird and mosquito dispersal prior to this time suggests that long-range dissemination of the virus from endemic northern Australia was unlikely.