Models of understanding virus-host dynamics of EIAV infection with free-virus and cell-to-cell transmission in SCID horses

We develop three models of Equine Infectious Anemia Virus infection with free-virus and cell-to-cell transmission in Severe Combined Immunodeficiency Disease horses. Since such horses do not have immune responses, we will conduct studies for EIAV infection with two possible immune responses: the Antibody neutralization and the Cytotoxic T Lymphocyte (CTL) immune response. The first model is the basic model which does not contain immune response. And based on the first model we add the cytotoxic T Lymphocyte immune response to the second model. Thereafter, in the third model we combine both CTL and antibody immune responses. There are two strains of viruses in our models, one is sensitive to the antibody neutralization and the other one is neutralization resistant. For each model there are three types of equilibria: Infection-free equilibrium, single resistant strain equilibrium and both strains coexist equilibrium. We study the values of the basic reproduction number $R_0$ to find how the endemic status changes when $R_0$ changes. Then we examine how the antibody immune response controls the infection by comparing the effects of different impulsive infusion dosages. We also test the minimum dosage of the impulsive antibody that may eradicate the infection. Last we study the sensitivity of $R_0$ on the model parameters. We do the sensitivity analysis by using the Latin hypercube sampling method and the partial rank correlation coefficients method. Then we get the most sensitive parameters of $R_0$ which will change $R_0$ greatly even if they themselves move just a little. We find that the transmission rates of free-virus and the proportion of virions released for free viral transmission of both strains will enlarge $R_0$ if they become larger, the clearance rates of both viral strains will make $R_0$ smaller if they grow.