Modelli epidemiologici per l' allevamento caprino

In this thesis we propose and study a basic demographical and several epidemiological models related to goat breeding. The epidemic affecting goats that we analyze is the Viral Arthritis Encephalitis, commonly called CAEV. This is an infectious disease first reported in 1974. As the name suggests, this disease manifests itself through three different forms: as arthritis, the most frequent symptom, as pneumonia, which is rare and it is associated to the first form, or as mastitis, that leads to udder deformation. It is an infectious pathology characterized by a long period of incubation and with a progressive cronic course. No vaccine is able to prevent the insurgence of this pathology. So it is necessary to apply a series of hygienic-sanitary measures to avoid the spread of the virus or to prevent it. Virus eradication is one of the most common technique employed in the last years to fight the disease spreading. Recent veterinary studies have found two different virus genotypes that affect goats and lead to CAEV: they are called the B and the E genotypes. Genotype B lentivirus, known to be pathogenic, can be transmitted in a vertical way from mother to offspring through the colostrum or the milk; it is also trasmitted in an horizontal way, through the blood or the saliva infecting goats adult. The symptoms are not immediately visible, they are connected to the name of lentivirus that characterizes this pathology. In fact there is a quite long period, in which goats are infected by the virus without any apparent symptom. Genotype E lentivirus, known as Roccaverano stock, from the breeding site where it has been discovered for the first time, is particulary important because it is not pathogenic. Studies show that the genotype E lentivirus can be transmitted only vertically. In this work we analyze only CAEV caused by the genotype B lentivirus, in order to study its complexity, severity and different routes of transmission. In this thesis we formulate our descriptions as compartmental models, with the population under study being divided into compartments and with assumptions about the nature and transfer rates from one compartment to another. The independent variable in our compartmental models is the time t and the evolution of compartments sizes are expressed mathematically as derivatives with respect to time. As a result our models are formulated initially as ordinary differential equations. The work is articulated in four principal chapters with a final conclusion. For every model the goal is to understand how to change the replacement rate in order to maintain the total number of goat in the breeding constant. This is a possible strategy that is commonly used by the farmer in order to have always a fixed population. We start our work, in Chapter 2, with the formulation of the simplest model of goat breeding. We introduce the parameters used in our analysis and explain the breeding dynamics. Then, in Chapter 3, we continue our analysis considering a goat breeding affected by CAEV with total vertical and horizontal transmissions. The model is analyzed in order to understand for what size of the population the disease can disappear or it can become endemic. After, Chapter 4 deals with a goat breeding where an eradication policy is employed. Finally, in Chapter 5, a goat breeding where vertical transmission, from mother to offspring, partially occurs is presented.