Fig 1.
Number of infected individuals over time for two-population age-structured model using default parameters and varying transmissibility b0.
A) b0 = 0.009, Convergence to stable equilibria; B) b0 = 0.013, 2-point cycle; C) b0 = 0.02, 4-point cycle; D) b0 = 0.021, chaos; E) b0 = 0.0235, 6-pt cycle; F) b0 = 0.025, Collapse.
Fig 2.
Bifurcation diagram of equilibria, oscillatory dynamics, and chaotic behavior as a function of transmissibility b0.
Points in the figure represent sustained long-term results in the model; thus any b0 value with, for example, two corresponding y-axis points represents a sustained oscillation between two values for infected individuals.
Fig 3.
Phase plane of non-zero equilibrium and stability.
Heat maps of dynamic regimes as a function of the relationship between aversion to infection in the youth (α21) and in the elderly (α22). Dynamic regimes are indicated by color and A–F are increasing in transmissibility (b0): A) b0 = 0.009; B) b0 = 0.013; C) b0 = 0.02; D) b0 = 0.021; E) b0 = 0.0235; F) b0 = 0.025.
Fig 4.
Number of infected individuals over time for two-population age-structured model using default parameters and varying between-group contact rate c12.
A) c12 = 0.005, Convergence to stable equilibria; B) c12 = 0.025, 2-point cycle; C) c12 = 0.04, 6-point cycle; D) c12 = 0.05, chaos; E) c12 = 0.08, 6-pt cycle; F) c12 = 0.15, 8-pt cycle for Old and 2-pt cycle for Young.
Fig 5.
Bifurcation diagram of equilibria, oscillatory dynamics, and chaotic behavior as a function of inter-group contact rate c12.
Points in the figure represent sustained long-term results in the model; thus any c12 value with, for example, two corresponding y-axis points represents a sustained oscillation between two values for infected individuals.
Fig 6.
Number of infected individuals for Youth and Elderly populations over time with default parameters, each population size set to N, no between-group contact (i.e., c12 = 0), and varying transmissibility b0.
A) b0 = 0.009; B) b0 = 0.013 =,; C) b0 = 0.02; D) b0 = 0.021; E) b0 = 0.0235; F) b0 = 0.025.
Fig 7.
Number of infected individuals over time in each of three populations using default parameters and varying transmissibility b0.
A) b0 = 0.01, Convergence to stable equilibria; B) b0 = 0.013, 2-point cycle; C)b0 = 0.022, Chaos into a 2-pt cycle cycle; D) b0 = 0.05, Collapse.
Fig 8.
Number of infected individuals over time in each of three populations using default parameters and varying between-group contact rates c12, c13, and c23.
A) c12 = 0.005, c13 = 0.003, c23 = 0.007, Convergence to stable equilibria; B) c12 = 0.008, c13 = 0.01, c23 = 0.01, 2-point cycle; C) c12 = 0.022, c13 = 0.02, c23 = 0.024, 4-point cycle; D) c12 = 0.032, c13 = 0.03, c23 = 0.034, Chaos; E) c12 = 0.05, c13 = 0.048, c23 = 0.052, 5-pt cycle; F) c12 = 0.06, c13 = 0.058, c23 = 0.062, 6-pt cycle.
Fig 9.
Disease dynamics for the 3-population model when delta = 1.
Number of infected individuals over time in each of three populations using default parameters, time-delay Δ = 1, and varying transmissibility b0. A) b0 = 0.01, Damped oscillator; B) b0 = 0.013, Chaos; C) b0 = 0.022, Collapse; D) b0 = 0.05, Collapse.