A mathematical model of the ecology of Lyme disease

A mathematical model of enzootic Lyme-disease transmission in a natural focus is presented. This model is based on the life history of the vector tick Ixodes scapularis Say and the primary reservoir host Peromyscus leucopus. Using this model, the threshold condition for the disease to be able to invade a nonenzootic region is determined as a function of the various possible transmission chains operating throughout the year. These expressions show that the transmission chain in which ticks acquire the disease from mice in the fall and transmit it back to mice as nymphs in the spring is the most important chain (contributing approximately 87% of the elasticity of the threshold for the parameter choices examined). Equilibrium disease levels were examined under the assumption of a constant tick population; these levels were determined as a function of tick and mouse density, the vertical transmission rate, the infectivity of mice, and the survivorship parameters of the ticks and of the tick-host contact rates. Vertical transmission has a disproportionately large effect, since unfed infected larval ticks have two opportunities to feed on mice, rather than only one opportunity (as for a newly infected unfed nymph). Finally, a global sensitivity analysis based on Latin hypercube sampling is performed, in which is shown the importance of quantifying the natural history of infection in mice, and of elucidating the contribution of other hosts for I. scapularis than mice.