The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leone and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method.

A major Ebola outbreak occurs in West Africa since March 2014, being the deadliest epidemic in history. As an infectious disease epidemiology, Ebola is the most lethal and is moving faster than in previous outbreaks. On 8 August 2014, the World Health Organization (WHO) declared the outbreak a public health emergency of international concern. Last update on 7 July 2015 by WHO reports 27,609 cases of Ebola with a total of 11,261 deaths. In this work, we present a mathematical description of the spread of Ebola virus based on the SEIR (Susceptible-Exposed-Infective-Recovered) model and optimal strategies for Ebola control. In order to control the propagation of the virus and to predict the impact of vaccine programmes, we investigate several strategies of optimal control of the spread of Ebola: control infection by vaccination of susceptible; minimize exposed and infected; reduce Ebola infection by vaccination and education.

Timely and accurate identification of cows with intramammary infections is essential for optimal udder health management. Various sensor systems have been developed to provide udder health information that can be used as a decision support tool for the farmer. Among these sensors, the DeLaval Online Cell Counter (DeLaval, Tumba, Sweden) provides somatic cell counts from every milking at cow level. Our aim was to describe and evaluate diagnostic sensor properties of these online cell counts (OCC) for detecting an intramammary infection, defined as an episode of subclinical mastitis or a new case of clinical mastitis. The predictive abilities of a single OCC value, rolling averages of OCC values, and an elevated mastitis risk (EMR) variable were compared for their accuracy in identifying cows with episodes of subclinical mastitis or new cases of clinical mastitis. Detection of subclinical mastitis episodes by OCC was performed in 2 separate groups of different mastitis pathogens, Pat 1 and Pat 2, categorized by their known ability to increase somatic cell count. The data for this study were obtained in a field trial conducted in the dairy herd of the Norwegian University of Life Sciences. Altogether, 173 cows were sampled at least once during a 17-mo study period. The total number of quarter milk cultures was 5,330. The most common Pat 1 pathogens were Staphylococcus epidermidis, Staphylococcus aureus, and Streptococcus dysgalactiae. The most common Pat 2 pathogens were Corynebacterium bovis, Staphylococcus chromogenes, and Staphylococcus haemolyticus. The OCC were successfully recorded from 82,182 of 96,542 milkings during the study period. For episodes of subclinical mastitis the rolling 7-d average OCC and the EMR approach performed better than a single OCC value for detection of Pat 1 subclinical mastitis episodes. The EMR approach outperformed the OCC approaches for detection of Pat 2 subclinical mastitis episodes. For the 2 pathogen groups, the sensitivity of detection of subclinical mastitis episodes was 69% (Pat 1) and 31% (Pat 2), respectively, at a predefined specificity of 80% (EMR). All 3 approaches were equally good at detecting new cases of clinical mastitis, with an optimum sensitivity of 80% and specificity of 90% (single OCC value).