An illustration of the changing dynamics for both the original deterministic model and our stochastic mean-field approximation model for pathogen populations with two loci (i.e., four strains). Two strains comprising one discordant set are plotted in black; the other discordant set is plotted in gray. Plotted in all simulations is the proportion of the host population immune to each of the four strains. Parameter values [corresponding to the parameter notation of Gupta *et al.* ()] used for the ODE simulations (*A*–*C*) were μ = 0.02, σ = 10, *R*_{0} = 2, α = 1, with the only difference in parameter values being the degree of cross-immunity γ (0.3 in *A*, 0.7 in *B*, 0.9 in *C*). The mean-field approximation of the stochastic IBM (*D*–*F*) used parameter values corresponding to our model's parameter notation in : *C* = 12, *r* = 0.0953, τ = 0.0042, β = 0.2472, 1/μ = 7, 1/σ = 23, *P* = 223, *n* = 2. The degree of cross-immunity γ was 0.01 in *D*, 0.95 in *E*, and 2.00 in *F*. (Note that γ is defined slightly differently in our model compared with its definition in ref. ). *A* and *D*, with the lowest values ofγ, both have no strain structure, with the mean diversity in *D* being 0.9882 and the mean discordance being 0.6723. *B* and *E* have intermediate values of γ, and both exhibit cyclical strain dynamics. Mean diversity in *E* is 0.8733, and mean discordance is 0.7496. *C* and *F* have high values of γ, and both exhibit strong strain structure, with one discordant set being dominant. Mean diversity in *F* is 0.5480, and mean discordance is 0.9720. Simulations were run for 2,000 time steps for the IBM and 500 time steps for the ODE.

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