Ecological and immunological determinants of dengue epidemics

Abstract

The management of infectious diseases is an increasingly important public health issue, the effective implementation of which is often complicated by difficulties in teasing apart the relative roles of extrinsic and intrinsic factors influencing transmission. Dengue, a vector-borne strain polymorphic disease, is one such infection where transmission dynamics are affected by environmental variables as well as immune-mediated serotype interactions. To understand how alternative hypotheses concerning dengue infection and transmission may explain observed multiannual cycles in disease incidence, we adopt a theoretical approach that combines both ecological and immunological mechanisms. We demonstrate that, contrary to perceived wisdom, patterns generated solely by antibody-dependent enhancement or heterogeneity in virus virulence are not consistent with serotype-specific notification data in important ways. Furthermore, to generate epidemics with the characteristic signatures observed in data, we find that a combination of seasonal variation in vector demography and, crucially, a short-lived period of cross-immunity is sufficient. We then show how understanding the persistence and eradication of dengue serotypes critically depends on the alternative assumed mechanisms.

Fig. 1.

Comparison of annual dengue data for Thailand with model output. (A and B) Annual serotype-specific [each serotype is denoted by a different color (Den-1, blue; Den-2, green; Den-3, red; and Den-4, cyan) (Left)] and aggregate dengue fever and DHF case report (Right) data for Thailand (taken from ref. 8). The remaining time series are generated by the deterministic model with four serotypes: temporary cross-immunity (C and D); ADE (E and F); asymmetry in virulence (G and H); temporary cross-immunity and ADE (I and J); temporary cross-immunity and asymmetry in virulence (K and L); and temporary cross-immunity, ADE and asymmetry in virulence (M and N). Spectral analysis of the detrended aggregated output (B, D, F, H, J, L, and N) reveals a dominant period of 3.4 (data), 3.4, 15.5, 1, 2.1, 5.2, and 2.1 years, respectively. Model parameters (symmetric for all serotypes i): N_H = 20 million, μ_H = 0.02 per year, k = 2, μ_V = 26.1 per year, a = 0.05, σ_H = 73 per year, σ_V = 36.5 per year, γ_i = 60.8 per year, β_i = α_i = 70 per year (R_0i = 3.5), ρ₁ = ρ₃ = ρ₄ = ρ_x = 0, ξ_i = 0, ϕ_i = 0. (C and D) δ_i = 3 per year, χ_i = 1, ρ₂ = 0. (E and F) δ_i = 365 per year, χ_i = 3, ρ₂ = 0. (G and H) δ_i = 365 per year, χ_i = 1, ρ₂ = 0.05. (I and J) δ_i = 3 per year, χ_i = 3, ρ₂ = 0. (K and L) δ_i = 3 per year, χ_i = 1, ρ₂ = 0.05. (M and N) δ_i = 3 per year, χ_i = 3, ρ₂ = 0.05. Nonzero initial conditions: S₀ = 0.29N_H, S₁₂₃₄ = 0.71N_H, V_Si = kN_H, λ_H1 = β₁, λ_H2 = 2β₂, λ_H3 = 3β₃, λ_H4 = 4β₄.

Fig. 2.

ADE or variation in virulence; the dominant period and correlation of two dengue serotypes from deterministic model simulations. A, D, and G explore the effects of permanent ADE, as defined by increased susceptibility to one serotype after a primary infection with the other, whereas B, E, and H fix χ and explore the effects of a temporary period of ADE. C, F, and I show the effects of increasing the mortality due to infection with only one of the serotypes. In all cases, these effects are studied as the temporary period of cross-immunity (after infection with one serotype and before infection with the other) is lengthened. A–C present the dominant period of incidence of a single serotype, D–F present the dominant period of aggregated dengue incidence (black represents annual cycles), and G–I illustrate the correlation between the dynamics of the two serotypes. See Fig. 8, which is published as supporting information on the PNAS web site, for significance associated with the dominant period. Model parameters are as in Fig. 1, except: N_H = 1 million, δ₁ = δ₂ = δ, χ₁ = χ₂ = χ, in B, E, and H, χ = 2, and in C, F, and I, χ = 1 and ρ₁ = 0. It is interesting to note that if ADE is asymmetric, i.e., primary infection with only one of the serotypes induces ADE (38) (χ₁ = 1, χ₂ ≥ 1), then for short periods of temporary cross-immunity ADE does not result in the multiannual cycles shown here; instead, only annual fluctuations are generated by the model.

Fig. 3.

Consequences of alternative assumptions about serotype interaction for dengue persistence and eradication. (A) Critical community size. Comparison of results from stochastic realizations with monthly DHF incidence from Thai provinces (Inset). Simulations where there is strong ADE (χ = 3) and virtually no cross-immunity (δ = 365 per year) demonstrate high extinction probabilities over all population sizes ≤2 million. Simulations where there is moderate ADE (χ = 1.5) and a 4-month period of cross-immunity (δ = 3 per year) show decreasing extinction probabilities as the population size increases above 1 million; consistent with the Thai data (7). (The black line denotes the least-squares best-fit exponential curve.) Other model parameter values are as in Fig. 1, and results are averages of 50 realizations with standard error bars. (B) Effects of ADE and difference in virulence on vaccination thresholds. If two serotypes have slightly different R₀, then the serotype with the smaller R₀ is either more or less difficult to eradicate in the presence of the other serotype depending on whether there is ADE or increased mortality from the other serotype. Critical vaccination level is given by the following expression, 1 − ((R₀₂/R₀₁ − 1)/c + 1)/R₀₂, where c ≈ χ(1 − ρ₂).