The aim is to describe the distribution of immune status (as captured by antibody level) on the basis of a within-host submodel for continuous waning and occasional boosting. Inspired by Feller's fundamental work and the more recent delay equation formulation of models for the dynamics of physiologically structured populations, we derive, for given force of infection, a linear renewal equation. The solution is obtained by generation expansion, with the generation number corresponding to the number of times the individual became infected. Our main result provides a precise characterization of the stable distribution of immune status.

Campylobacter is the primary agent of human bacterial gastroenteritis worldwide. In contrast to temperate zones, weather effects on Campylobacter prevalence in broilers under tropical conditions are under-researched. We examined the association between weather and Campylobacter prevalence in slaughtered broilers in Sri Lanka, a tropical country with weather variations led by monsoons. Each month (October 2009-July 2011), 20-30 broiler batches referring to two semi-automated slaughterhouses from five Sri Lankan provinces were tested for Campylobacter contamination and analysed in relation to temperature, humidity and rainfall. Overall prevalence was 63.8% (95% CI 59.6-67.9%, n = 542), peaking in September-November. Each 1 °C increase in monthly mean temperature up to 26 °C increased Campylobacter-positive batches by 16.4% (95% CI 0.4-35.1%). For each 10 mm increase in monthly total rainfall up to 300 mm, Campylobacter-positive batches increased significantly by 0.8% (0.1-1.5%) at 1-month lag. For each 1% increase in relative humidity up to 80% at 1- and 2-month lags, Campylobacter-positive batches increased of respectively 4.2% (1.9-6.7%) and 4.0% (1.5-6.5), and decreased by 3.6% (2.6-4.6%) and 4.0% (2.6-5.4%) for unit increases above 80%. These results suggest that even in tropical countries without marked seasons, there are weather effects possibly reflecting Campylobacter potential to colonise its preferred host and/or survive in the environment.