On State-Space Reduction in Multi-Strain Pathogen Models, with an Application to Antigenic Drift in Influenza A
Figure 5
Approximate Dynamics of Antigenic Drift in Influenza A, Based on the Order-1 Interpolation Closure
Parameter values: μ = 0, ν = 1, m = 10−4, and a = 1/ ; the heterogeneous transmission coefficients β(i,j) were drawn from a normal distribution with mean 3 and standard deviation 0.5. The numerical solution for the time interval t ∈ [0,100] was obtained for a strain space given by a 20 × 20 rectangular lattice. The initial condition was given by all state variables being zero except for I(1,1)(0) = 0.01 and ξ(1,1)(0) = 0.01, corresponding to a healthy and fully susceptible host population with 1% of hosts infected with strain (1,1).
(A) Strains whose maximum epidemic size exceeded 0.01 are shown. The gray shade indicates the maximum epidemic size; the number above each shaded square indicates the time when the maximum of the epidemic for that particular strain was reached. Circles indicate strains whose transmission coefficients are less than 3; crosses indicate strains with transmission coefficients greater than 3.
(B) The sum of all proportions of infectious hosts as a function of time.