Immunological serotype interactions and their effect on the epidemiological pattern of dengue

Abstract

Long-term epidemiological data reveal multi-annual fluctuations in the incidence of dengue fever and dengue haemorrhagic fever, as well as complex cyclical behaviour in the dynamics of the four serotypes of the dengue virus. It has previously been proposed that these patterns are due to the phenomenon of the so-called antibody-dependent enhancement (ADE) among dengue serotypes, whereby viral replication is increased during secondary infection with a heterologous serotype; however, recent studies have implied that this positive reinforcement cannot account for the temporal patterns of dengue and that some form of cross-immunity or external forcing is necessary. Here, we show that ADE alone can produce the observed periodicities and desynchronized oscillations of individual serotypes if its effects are decomposed into its two possible manifestations: enhancement of susceptibility to secondary infections and increased transmissibility from individuals suffering from secondary infections. This decomposition not only lowers the level of enhancement necessary for realistic disease patterns but also reduces the risk of stochastic extinction. Furthermore, our analyses reveal a time-lagged correlation between serotype dynamics and disease incidence rates, which could have important implications for understanding the irregular pattern of dengue epidemics.

Figure 1

Dengue epidemiology in South Viet Nam. (a) The total annual number of dengue cases (blue bars) over the period 1994–2007 shows the characteristic fluctuation in disease incidence, whereas the relative serotype prevalence (1996–2007) clearly demonstrates the sequential replacements of dominant types (dark blue line, DEN-1; red line, DEN-2; yellow line, DEN-3; green line, DEN-4). (b) Monthly data of hospitalized dengue patients reveal a strong seasonal component in total disease burden (blue bars), which is not reflected in the relative frequency of the individual serotypes (dark blue line, DEN-1; red line, DEN-2; yellow line, DEN-3; green line, DEN-4).

Figure 2

Model output showing the proportion of the population infected over time under changes of the degrees of enhancement. Each colour represents one of the four dengue serotypes. As the degree of enhancement increases (transmissibility enhancement from left to right and susceptibility enhancement from top to bottom), the system exhibits a rich catalogue of dynamical behaviours, from stable endemic equilibrium (γ=1, φ=1) to synchronized oscillations (e.g. γ=1, φ=1.9) and desynchronized and chaotic fluctuations with increased inter-epidemic periods (e.g. γ=1.8, φ=1.9). The inter-epidemic periods, π, also increase as the level of enhancement increases ((a) π=inf, (b) π=4y, (c) π=5y, (d) π=4y, (e) π=3y, (f) π=5y, (g) π=3y, (h) π=4y and (i) π=8y). Parameter values: (a) φ=1, γ=1; (b) φ=1.9, γ=1; (c) φ=2.4, γ=1; (d) φ=1, γ=2; (e) φ=1.9, γ=1.8; (f) φ=2.4, γ=1.7; (g) φ=1, γ=2.4; (h) φ=1.9, γ=2.4; and (i) φ=2.4, γ=2.4. Other parameter values: β=400, σ=100 and μ=1/70.

Figure 3

Qualitative comparison between model output and epidemiological data. (a) Data showing long-term record of total disease incidence (blue bars) and relative serotype prevalence in Thailand, taken from Nisalak et al. (2003) (dark blue line, DEN-1; red line, DEN-2; yellow line, DEN-3; green line, DEN-4). (b) Typical model outcome for a moderate degree of ADE (γ=2.1, ϕ=1.8) showing desynchronized oscillations in serotype prevalence and chaotic fluctuations in total disease prevalence (blue bars, arbitrary units; green line, serotype1; yellow line, serotype2; dark blue line, serotype3; red line, serotype4). Other parameter values: β=400, σ=100 and μ=1/70.

Figure 4

Analysis of the parameter space of enhancement. The (ϕ,γ)-parameter space can be qualified with respect to (a) synchronization patterns between two individual serotypes, (b) single-serotype prevalence, (c) major inter-epidemic period, and (d) serotype persistence. (a) The four synchronization patterns between serotypes (i) 1 and 2, (ii) 1 and 3, (iii) 2 and 3, and (iv) 3 and 4 reveal that the majority of the parameter space is occupied by desynchronized (blue) behaviour. Complete synchronization (red) indicates that after some initial transient, the time series of the two serotypes coincide and stay locked for the rest of the time interval; partial synchronization (green) is defined as a regime in which the time series are not fully synchronized, but throughout their 1000-year integration period have intervals of more than 100 years of synchronized behaviour. (b) Within the regime of desynchronized oscillation, we also find the system's behaviour being characterized by single-serotype replacement and dominance, where 0 indicates that at least two types are simultaneously dominant. (c) As the respective degrees of enhancement increase, we find the periods between epidemic outbreaks becoming longer, with a typical 3–5 year cycle occupying a large part of the parameter space and longer cycles (5–15 years) occurring towards the higher end of the enhancement spectrum. (d) The proportion of time a particular serotype persists above a persistence-threatening threshold level of 10⁻⁸ drops sharply as the level of enhancement increases, but remains high throughout a large region of the parameter space occupied by desynchronized, chaotic oscillations. Other parameter values: β=400, σ=100 and μ=1/70.

Figure 5

Cross-correlation analysis between serotype diversity and disease prevalence. (a) Time series of the relative frequency of the four dengue serotypes (red line, DEN-1; green line, DEN-2; yellow line, DEN-3; dark blue line, DEN-4) with (b) total disease prevalence (P, dark blue) and corresponding serotype diversity (H, red line); (c) the rates of change in prevalence and diversity, dP/dt and dH/dt, respectively. (d) The cross-correlation, r(Δ), between prevalence and diversity, P×H (black line), over a 100-year period reveals a bimodal distribution with two significant peaks at time lags Δ_P and Δ_−P and a ‘dip’ at lag Δ=0. This dip can be explained by the negative correlation at this point between the rates of change in prevalence and diversity, dP/dt×dH/dt (red line). The bimodal shape of the cross-correlation between the rates of change also reveals the negative feedback between prevalence and diversity. Parameter values: γ=2.1, ϕ=1.8, β=400, σ=100 and μ=1/70.