Table 1. Summary of the transition rates.
| Transition | Description |
|---|---|
| ψ12 = βj | Susceptible juvenile acquires B. burgdorferi infection |
| ψ13 = αs | Susceptible juvenile develops into a susceptible adult |
| ψ14 = δ | Susceptible juvenile develops into an infected adult |
| ψ21 = 0 | Infected juvenile recovers from B. burgdorferi infection |
| ψ23 = 0 | Infected juvenile develops into a susceptible adult |
| ψ24 = αi | Infected juvenile develops into an infected adult |
| ψ31 = 0 | Susceptible adult regresses into a susceptible juvenile |
| ψ32 = 0 | Susceptible adult regresses into an infected juvenile |
| ψ34 = βa | Susceptible adult acquires B. burgdorferi infection |
| ψ41 = 0 | Infected adult regresses into a susceptible juvenile |
| ψ42 = 0 | Infected adult regresses into an infected juvenile |
| ψ43 = 0 | Infected adult recovers from B. burgdorferi infection |
The multistate model contained four states for the Peromyscus leucopus mice: (1) susceptible juveniles, (2) Borrelia burgdorferi-infected juveniles, (3) susceptible adults, and (4) B. burgdorferi-infected adults. The type of transition is indicated by the subscripts on the transition rate parameter (ψ). For example, ψ12 indicates that a susceptible juvenile (state 1) transitioned into an infected juvenile (state 2). We we modeled five of the twelve theoretical transitions; the other seven transitions, which are not biologically possible, were set to zero. For example, adult mice cannot develop into juvenile mice. The transition from the uninfected to the infected state was symbolized with the infection rate parameter (β). The transition from the juvenile to the adult state was symbolized with the developmental rate parameter (α). The two-step transition from the uninfected juvenile to the infected adult state was symbolized with the delta rate parameter (δ). The subscripts of the infection rates (β) and developmental rates (α) refer to the identity of the other state. Thus, βj and βa refer to the infection rates of juveniles and adults whereas αs and αi refer to the developmental rates of susceptible and infected individuals, respectively.