Mortality estimates are central to understanding tsetse fly population dynamics, but are difficult to acquire from wild populations. They can be obtained from age distribution data but, with limited data, it is unclear whether the assumptions required to make the estimates are satisfied and, if not, how violations affect the estimates. We evaluate the assumptions required for existing mortality estimation techniques using long-term longitudinal ovarian dissection data from 144,106 female tsetse, Glossina pallidipes Austen, captured in Zimbabwe between 1988 and 1999. At the end of the hot-dry season each year, mean ovarian ages peaked, and maximum-likelihood mortality estimates declined to low levels, contrary to mark-recapture estimates, suggesting violations of the assumptions underlying the estimation technique. We demonstrate that age distributions are seldom stable for G. pallidipes at our study site, and hypothesize that this is a consequence of a disproportionate increase in the mortality of pupae and young adults at the hottest times of the year. Assumptions of age-independent mortality and capture probability are also violated, the latter bias varying with capture method and with pregnancy and nutritional status. As a consequence, mortality estimates obtained from ovarian dissection data are unreliable. To overcome these problems we suggest simulating female tsetse populations, using dynamical modelling techniques that make no assumptions about the stability of the age distribution.

Although age-related heterogeneity of infection has been addressed in variousepidemic models assuming a demographically stationary population, only a few studies haveexplicitly dealt with age-specific patterns of transmission in growing or decreasing population.To discuss the threshold principle realistically, the present study investigates an age-duration-structured SIR epidemic model assuming a stable host population, as the first scheme toaccount for the non-stationality of the host population. The basic reproduction number R0is derived using the next generation operator, permitting discussions over the well-knowninvasion principles. The condition of endemic steady state is also characterized by usingthe effective next generation operator. Subsequently, estimators of R0 are offered which canexplicitly account for non-zero population growth rate. Critical coverages of vaccination arealso shown, highlighting the threshold condition for a population with varying size. Whenquantifying R0 using the force of infection estimated from serological data, it should beremembered that the estimate increases as the population growth rate decreases. On thecontrary, given the same R0, critical coverage of vaccination in a growing population would behigher than that of decreasing population. Our exercise implies that high mass vaccinationcoverage at an early age would be needed to control childhood vaccine-preventable diseasesin developing countries.

The asymptotic sizes and compositions of critical general branching processes conditioned on non-extinction are treated. First, results are given for processes counted with random characteristics allowed to depend on the whole daughter processes, then these are used to derive conditional limit theorems for the pedigrees of randomly sampled individuals among populations counted with 0–1-valued characteristics. The limiting stable pedigrees have nice independence structures and are easily derived from the original branching laws.

Start a Bellman–Harris branching process from one or several ancestors, whose ages are identically distributed random variables. Assume that the life-length distribution decays more quickly than exponentially and that the distribution of ages at start does not give too much mass to high ages (in a sense to be made precise). Then, if the expected population size is an exponential function of time, the ages must follow the stable age distribution of the process.