Statistical mechanical considerations in the theory of the spread of the Hantavirus

Calculations in the theory of the spread of epidemics are described with particular focus on the estimation of motion parameters describing rodents that are the carriers of the Hantavirus epidemic. The data considered are of the “mark-recapture” kind, i.e., those collected by capturing, tagging and recapturing the animals in a prescribed finite region of space. The theoretical tool used is the Fokker-Planck equation, its characteristic quantities being the diffusion constant which describes the motion of the rodents, and the attractive potential which addresses their tendency to live near their burrows. The measurements are addressed through simple analytical calculations of the mean squared displacement of the animals relevant to the specific probing window in space corresponding to the trapping region. A Fourier prescription is provided to extract the home range of the animals from the observations. Applications of the theory to rodent movement in Panama and New Mexico are mentioned and several on-going generalizations of current models of Hantavirus epidemic spread are introduced.