Statistical analysis of the dynamics of antibody loss to a disease-causing agent: plague in natural populations of great gerbils as an example.

We propose a new stochastic framework for analysing the dynamics of the immunity response of wildlife hosts against a disease-causing agent. Our study is motivated by the need to analyse the monitoring time-series data covering the period from 1975 to 1995 on bacteriological and serological tests-samples from great gerbils being the main host of Yersinia pestis in Kazakhstan. Based on a four-state continuous-time Markov chain, we derive a generalized nonlinear mixed-effect model for analysing the serological test data. The immune response of a host involves the production of antibodies in response to an antigen. Our analysis shows that great gerbils recovered from a plague infection are more likely to keep their antibodies to plague and survive throughout the summer-to-winter season than throughout the winter-to-summer season. Provided the seasonal mortality rates are similar (which seems to be the case based on a mortality analysis with abundance data), our finding indicates that the immune function of the sampled great gerbils is seasonal.

Plague dynamics are driven by climate variation.

The bacterium Yersinia pestis causes bubonic plague. In Central Asia, where human plague is still reported regularly, the bacterium is common in natural populations of great gerbils. By using field data from 1949-1995 and previously undescribed statistical techniques, we show that Y. pestis prevalence in gerbils increases with warmer springs and wetter summers: A 1 degrees C increase in spring is predicted to lead to a >50% increase in prevalence. Climatic conditions favoring plague apparently existed in this region at the onset of the Black Death as well as when the most recent plague pandemic arose in the same region, and they are expected to continue or become more favorable as a result of climate change. Threats of outbreaks may thus be increasing where humans live in close contact with rodents and fleas (or other wildlife) harboring endemic plague.

Bayesian population dynamics of interacting species: great gerbils and fleas in Kazakhstan.

We propose a discrete-time Bayesian hierarchical model for the population dynamics of the great gerbil-flea ecological system. The model accounts for the sampling variability arising from data originally collected for other purposes. The prior for the unknown population densities incorporates specific biological hypotheses regarding the interacting dynamics of the two species, as well as their life cycles, where density-dependent effects are included. Posterior estimates are obtained via Markov chain Monte Carlo. The variance of the observed density estimates is a quadratic function of the unknown density. Our study indicates the presence of a density-dependent growth rate for the gerbil population. For the flea population there is clear evidence of density-dependent over-summer net growth, which is dependent on the flea-to-gerbil ratio at the beginning of the reproductive summer. Over-winter net growth is favored by high density. We estimate that on average 35% of the gerbil population survives the winter. Our study shows that hierarchical Bayesian models can be useful in extracting ecobiological information from observational data.

Predictive thresholds for plague in Kazakhstan.

In Kazakhstan and elsewhere in central Asia, the bacterium Yersinia pestis circulates in natural populations of gerbils, which are the source of human cases of bubonic plague. Our analysis of field data collected between 1955 and 1996 shows that plague invades, fades out, and reinvades in response to fluctuations in the abundance of its main reservoir host, the great gerbil (Rhombomys opimus). This is a rare empirical example of the two types of abundance thresholds for infectious disease-invasion and persistence- operating in a single wildlife population. We parameterized predictive models that should reduce the costs of plague surveillance in central Asia and thereby encourage its continuance.