Global Dynamics of a Reaction-Diffusion Model of Zika Virus Transmission with Seasonality.

In this paper, we propose a periodic reaction-diffusion model of Zika virus with seasonal and spatial heterogeneous structure in host and vector population. We introduce the basic reproduction ratio [Formula: see text] for this model and show that the disease-free periodic solution is globally asymptotically stable if [Formula: see text], while the system admits a globally asymptotically stable positive periodic solution if [Formula: see text]. Numerically, we study the Zika transmission in Rio de Janeiro Municipality, Brazil, and investigate the effects of some model parameters on [Formula: see text]. We find that the neglect of seasonality underestimates the value of [Formula: see text] and the maximum carrying capacity affects the spread of Zika virus.

Regional climate affects salmon lice dynamics, stage structure and management.

Regional variation in climate can generate differences in population dynamics and stage structure. Where regional differences exist, the best approach to pest management may be region-specific. Salmon lice are a stage-structured marine copepod that parasitizes salmonids at aquaculture sites worldwide, and have fecundity, development and mortality rates that depend on temperature and salinity. We show that in Atlantic Canada and Norway, where the oceans are relatively cold, salmon lice abundance decreases during the winter months, but ultimately increases from year to year, while in Ireland and Chile, where the oceans are warmer, the population size grows monotonically without any seasonal declines. In colder regions, during the winter the stage structure is dominated by the adult stage, which is in contrast to warmer regions where all stages are abundant year round. These differences translate into region-specific recommendations for management: regions with slower population growth have lower critical stocking densities, and regions with cold winters have a seasonal dependence in the timing of follow-up chemotherapeutic treatments. Predictions of our salmon lice model agree with empirical data, and our approach provides a method to understand the effects of regional differences in climate on salmon lice dynamics and management.