We formulate two models for the Caprine Arthritis Encephalitis virus disease (CAEV), a disease first reported in 1974 affecting mainly goats, [1]. Among dis- ease symptoms we find arthritis, pneumonia, mastitis, encephalitis, encephalomyeli- tis, from which the name. This causes an economic burden for the breeding because the infected goats are more vulnerable to further pathologies and produce less milk.

Several viral strains cause this pathology, belonging to the Small Ruminant Lentivirus group (SRLV). These are members of the genus Lentivirus of the fam- ily Retroviridae, [3]. Their name is lentiviruses, because they develop very slowly in time. Clinical signs appear only after several years of incubation. The most common of the 5 genotypes of SRLVs are genotypes A and B, with well-known associated diseases. Genotype B is pathogenic and can be transmitted both verti- cally and horizontally, through the blood or the saliva of infectious adult goats. The lentivirus genotype E can just be vertically transmitted. Its prototype is named the Roccaverano strain, from the place where it was first discovered. Goats infected by this genotype do not harm the breedings.

We present and investigate a basic CAEV system for modeling just the geno- type B situation, and a further one in which both strains are present. The models allow only the endemic, the genotype E-free and the disease-free equilibria, con- nected via transcritical bifurcations. Eradication of the pathogenic genotype is possible by reversing the actual policy used nowadays by the farmers to combat the spread of this disease.