(*a*) Isoperiodic diagram of deterministic model, indicating nature of model dynamics, as a function of degree, φ_{i}, of ADE for each of two strains. Color designates period of epidemic cycle (in years), with black indicating equilibrium coexistence (no cycles). Note that because the system is symmetrical between the strains, φ_{1} is varied between 0 and 3, and φ_{2} only between 1 and 3. No cycles are seen for the case when both φ_{1} and φ_{2} are negative. Parameters: *R*_{01} = *R*_{02} = 2, the recovery rate is σ = 100/yr, and host life span 1/μ = 50 yr. No background force of infection (λ_{0} = 0). For most points where the period is plotted as over 200 yr, the dynamics are chaotic. (*b*) As in *a*, but with λ_{0} = 10^{−5} (5 infectives/million per yr). (*c*) Bifurcation diagram plotting the local maxima of *x*_{1} against φ_{1} (for values of φ_{1} where limit cycles exist), with φ_{1} being varied between 0 and 1. φ_{2} = 2 and other parameters as in *a*. This diagram represents a horizontal slice through the left-hand half of *a* showing a complex cascade of bifurcations, with limit cycle regions interspersed by chaotic regimes. Integration of the deterministic model used the Bulirsch-Stoer method for maximum numerical accuracy, with randomly chosen (nonsymmetrical) initial conditions. Convergence to any equilibrium point or limit cycle was ensured by discarding the first 10,000 yr of each resulting time series.

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