The effects of tertiary and quaternary infections on the epidemiology of dengue

Abstract

The epidemiology of dengue is characterised by irregular epidemic outbreaks and desynchronised dynamics of its four co-circulating virus serotypes. Whilst infection by one serotype appears to convey life-long protection to homologous infection, it is believed to be a risk factor for severe disease manifestations upon secondary, heterologous infection due to the phenomenon of Antibody-Dependent Enhancement (ADE). Subsequent clinical infections are rarely reported and, since the majority of dengue infections are generally asymptomatic, it is not clear if and to what degree tertiary or quaternary infections contribute to dengue epidemiology. Here we investigate the effect of third and subsequent infections on the transmission dynamics of dengue and show that although the qualitative patterns are largely equivalent, the system more readily exhibits the desynchronised serotype oscillations and multi-annual epidemic outbreaks upon their inclusion. More importantly, permitting third and fourth infections significantly increases the force of infection without resorting to high basic reproductive numbers. Realistic age-prevalent patterns and seroconversion rates are therefore easier reconciled with a low value of dengue's transmission potential if allowing for more than two infections; this should have important consequences for dengue control and intervention measures.

Figure 1. Dengue epidemiology in South Vietnam.

The total annual number of dengue cases (blue bars) and relative serotype prevalence (lines) over the period 1994–2008 in the southern 20 provinces of Viet Nam show the characteristic fluctuation in disease incidence and sequential replacements of dominant serotypes. Source of data: Vietnamese Ministry of Health Dengue passive surveillance scheme and kindly provided by the Pasteur Institute, HCMC, Viet Nam. The Hospital for Tropical Diseases is a tertiary referral hospital for infectious diseases.

Figure 2. General model dynamics under parameter changes.

Here we observe the fluctuations in the total proportion of the population that has been infected by each serotype against time for different levels of transmissibility enhancement (from left to right: , , , ; no enhancement is represented by ; increasing corresponds to augmented levels of enhancement). The top panel is for the model with the assumption of total immunity after two infections only (model (i)) whilst the bottom is for the model which allows for infection with all four serotypes (model (ii)). The individual serotype dynamics seem to become ever more desynchronised as increases in both models, though this effect appears stronger in model (ii).

Figure 3. Comparison of synchronisation and single-serotype dominance between model (i) (top) and model (ii) (bottom).

(a) The synchronisation pattern between serotypes 1 and 2 indicates that, for both models, most of parameter space is characterised by desynchronised behaviour i.e. the dynamics of the two serotypes are not ‘locked’ together. (b) Using a measure of single serotype dominance (where 0 corresponds to at least two serotypes being simultaneously dominant and higher values indicate a greater tendency for one serotype to be dominating at any given time), one can observe that in both models the trend is for increasing levels of dominance with increasing enhancement; this trend is more pronounced in model (ii) than model (i).

Figure 4. Comparison of inter-epidemic period and serotype persistence between model (i) (top) and model (ii) (bottom).

(a) As enhancement increases so too does the epidemic period observed in each model. There is also a trend towards longer periods at lower . However, these trends both appear to be stronger in model (ii). (b) The risk of stochastic extinction within the model is shown as the proportion of time in each model that the prevalence of a particular serotype exists above a specific threshold. In both models there is a low risk of extinction but the risk increases with enhancement; again, this trend is stronger in model (ii).

Figure 5. Comparison of age structured dynamics between model (i) and model (ii).

(a) The lines show the proportion of the population at each age (for model (i) (top) and model (ii) (bottom)) who have suffered one (solid dark blue line), two (solid red), three (solid green), four (solid magenta) and any (solid black) dengue infections. For model (ii) the proportion of the population that is at risk of disease (defined as having seen 1, 2 or 3 serotypes) is also plotted (dotted black) for comparison to the equivalent in model (i) (solid dark blue). Generally, in model (ii) people are exposed to dengue at an earlier age, experience heterologous infections younger, and take much longer to become completely immune. (b) For model (i) ((ii)), the blue (green) bar shows how the average age of disease (DHF), determined as heterologous infection, changes with the number of serotypes present whilst the small bars show the change in age of first infection. The increase in the total force of infection with the number of serotypes is shown as dotted lines (model (i): blue, and model (ii): green). (c) For model (i) (blue line) and model (ii) (green line) we observe that increasing acts to decrease the average age of first infection (here estimated as 1/total force of infection) and that for all levels of this value is significantly lower when allowing for third and fourth infection (model (ii)). Parameter values: ((a), (b) and (c)) and (a), (b).