Theiler murine encephalomyelitis virus (TMEV) infection of a mouse's central nervous system is biphasic: first the virus infects motor neurons (acute phase), and this is followed by a chronic phase in which the virus infects glial cells (primarily microglia and macrophages [Mϕ]) of the spinal cord white matter, leading to inflammation and demyelination. As such, TMEV-induced demyelinating disease in mice provides a highly relevant experimental animal model for multiple sclerosis. Mathematical models have proven valuable in understanding the in vivo dynamics of persistent virus infections, such as HIV-1, hepatitis B virus, and hepatitis C virus infections. However, viral dynamic modeling has not been used for understanding TMEV infection. We constructed the first mathematical model of TMEV-host kinetics during acute and early chronic infections in mice and fit measured viral kinetic data with the model. The data fitting allowed us to estimate several unknown parameters, including the following: the rate of infection of neurons, 0.5 × 10−8 to 5.6 × 10−8 day−1; the percent reduction of the infection rate due to the presence of virus-specific antibodies, which reaches 98.5 to 99.9% after day 15 postinfection (p.i.); the half-life of infected neurons, 0.1 to 1.2 days; and a cytokine-enhanced macrophage source rate of 25 to 350 Mϕ/day into the spinal cord starting at 10.9 to 12.9 days p.i. The model presented here is a first step toward building a comprehensive model for TMEV-induced demyelinating disease. Moreover, the model can serve as an important tool in understanding TMEV infectious mechanisms and may prove useful in evaluating antivirals and/or therapeutic modalities to prevent or inhibit demyelination.