Stability and sensitivity analysis of Be-CoDiS, an epidemiological model to predict the spread of human diseases between countries. Validation with data from the 2014-16 West African Ebola Virus Disease epidemic.

Ebola virus disease is a lethal human and primate disease that requires a particular attention from the international health authorities due to important recent outbreaks in some Western African countries and isolated cases in European and North-America continents. Regarding the emergency of this situation, various decision tools, such as mathematical models, were developed to assist the authorities to focus their efforts in important factors to eradicate Ebola. In a previous work, we have proposed an original deterministic spatial-temporal model, called Be-CoDiS (Between-Countries Disease Spread), to study the evolution of human diseases within and between countries by taking into consideration the movement of people between geographical areas. This model was validated by considering numerical experiments regarding the 2014-16 West African Ebola Virus Disease epidemic. In this article, we propose to perform a stability analysis of Be-CoDiS. Our first objective is to study the equilibrium states of simplified versions of this model, limited to the cases of one an two countries, and to determine their basic reproduction ratios. Then, in order to give some recommendations for the allocation of resources used to control the disease, we perform a sensitivity analysis of those basic reproduction ratios regarding the model parameters. Finally, we validate the obtained results by considering numerical experiments based on data from the 2014-16 West African Ebola Virus Disease epidemic.

Importance of Ecological Factors and Colony Handling for Optimizing Health Status of Apiaries in Mediterranean Ecosystems

We analyzed six apiaries in several natural environments with a Mediterranean ecosystem in Madrid, central Spain, in order to understand how landscape and management characteristics may influence apiary health and bee production in the long term. We focused on five criteria (habitat quality, landscape heterogeneity, climate, management and health), as well as 30 subcriteria, and we used the analytic hierarchy process (AHP) to rank them according to relevance. Habitat quality proved to have the highest relevance, followed by beehive management. Within habitat quality, the following subcriteria proved to be most relevant: orographic diversity, elevation range and important plant species located 1.5 km from the apiary. The most important subcriteria under beehive management were honey production, movement of the apiary to a location with a higher altitude and wax renewal. Temperature was the most important subcriterion under climate, while pathogen and Varroa loads were the most significant under health. Two of the six apiaries showed the best values in the AHP analysis and showed annual honey production of 70 and 28 kg/colony. This high productivity was due primarily to high elevation range and high orographic diversity, which favored high habitat quality. In addition, one of these apiaries showed the best value for beehive management, while the other showed the best value for health, reflected in the low pathogen load and low average number of viruses. These results highlight the importance of environmental factors and good sanitary practices to maximize apiary health and honey productivity.