On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.

Sex-biased differences in the effects of host individual, host population and environmental traits driving tick parasitism in red deer

The interactions between host individual, host population, and environmental factors modulate parasite abundance in a given host population. Since adult exophilic ticks are highly aggregated in red deer (Cervus elaphus) and this ungulate exhibits significant sexual size dimorphism, life history traits and segregation, we hypothesized that tick parasitism on males and hinds would be differentially influenced by each of these factors. To test the hypothesis, ticks from 306 red deer-182 males and 124 females-were collected during 7 years in a red deer population in south-central Spain. By using generalized linear models, with a negative binomial error distribution and a logarithmic link function, we modeled tick abundance on deer with 20 potential predictors. Three models were developed: one for red deer males, another for hinds, and one combining data for males and females and including "sex" as factor. Our rationale was that if tick burdens on males and hinds relate to the explanatory factors in a differential way, it is not possible to precisely and accurately predict the tick burden on one sex using the model fitted on the other sex, or with the model that combines data from both sexes. Our results showed that deer males were the primary target for ticks, the weight of each factor differed between sexes, and each sex specific model was not able to accurately predict burdens on the animals of the other sex. That is, results support for sex-biased differences. The higher weight of host individual and population factors in the model for males show that intrinsic deer factors more strongly explain tick burden than environmental host-seeking tick abundance. In contrast, environmental variables predominated in the models explaining tick burdens in hinds.