A two-age-classes dengue transmission model

In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reason to divide the human population into two age classes is for practical purpose, as vaccination is usually concentrated in one age class. We assume that a constant rate of individuals in the child-class is vaccinated. We analyze a threshold number which is equivalent to the basic reproduction number. If there is an undeliberate vaccination to infectious children, which worsens their condition as the time span of being infectious increases, then paradoxically, vaccination can be counter productive. The paradox, stating that vaccination makes the basic reproduction number even bigger, can occur if the worsening effect is greater than a certain threshold, a function of the human demographic and epidemiological parameters, which is independent of the level of vaccination. However, if the worsening effect is to increase virulence so that one will develop symptoms, then the vaccination is always productive. In both situations, screening should take place before vaccination. In general, the presence of class division has obscured the known rule of thumb for vaccination

Protected areas in fisheries: a two-patch, two-species model *

The use of marine protected areas as a fishery management tool has been suggested as a hedge against management failures and variation in harvests. A stochastic bioeconomic model of a hypothetical predator-prey fishery is used to test the performance of protected areas in a fishery with heterogenous environments. Protected areas are analysed under density-dependent and sink-source dispersal relationships between the subpopulations that occur within the fishery. Differing management structures governing resource extraction are analysed. The focus of the study is placed on the biological and management characteristics that yield benefits to both fishers and society. It is shown that the establishment of a protected area improves fishery rent and lowers harvest variation. This result is sensitive to both current management controls and the correlation between species and patches. Copyright Australian Agricultural and Resource Economics Society Inc. and Blackwell Publishing Ltd 2006.