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.

Epidemiological investigation of bovine tuberculosis herd breakdowns in Spain 2009/2011

We analyzed the most likely cause of 687 bovine tuberculosis (bTB) breakdowns detected in Spain between 2009 and 2011 (i.e., 22% of the total number of breakdowns detected during this period). Seven possible causes were considered: i) residual infection; ii) introduction of infected cattle from other herds; iii) sharing of pastures with infected herds; iv) contiguous spread from infected neighbor herds; v) presence of infected goats in the farm; vi) interaction with wildlife reservoirs and vii) contact with an infected human. For each possible cause a decision tree was developed and key questions were included in each of them. Answers to these key questions lead to different events within each decision tree. In order to assess the likelihood of occurrence of the different events a qualitative risk assessment approach was used. For this purpose, an expert opinion workshop was organized and ordinal values, ranging from 0 to 9 (i.e., null to very high likelihood of occurrence) were assigned. The analysis identified residual infection as the most frequent cause of bTB breakdowns (22.3%; 95%CI: 19.4-25.6), followed by interaction with wildlife reservoirs (13.1%; 95%CI: 10.8-15.8). The introduction of infected cattle, sharing of pastures and contiguous spread from infected neighbour herds were also identified as relevant causes. In 41.6% (95%CI: 38.0-45.4) of the breakdowns the origin of infection remained unknown. Veterinary officers conducting bTB breakdown investigations have to state their opinion about the possible cause of each breakdown. Comparison between the results of our analysis and the opinion from veterinary officers revealed a slight concordance. This slight agreement might reflect a lack of harmonized criteria to assess the most likely cause of bTB breakdowns as well as different perceptions about the importance of the possible causes. This is especially relevant in the case of the role of wildlife reservoirs.