Table 1.
Parameters and values for 4-serotype dengue model.
Figure 1.
Epidemiological dynamics of a multi-strain system with homogeneous mixing.
(A) The simulated time series of an agent-based, multi-strain model of a directly transmitted pathogen show irregular oscillations in total (black lines, top graphs) and strain-specific (coloured lines, bottom graphs) even in the absence of immunological interactions or asymmetries between pathogen strains. (B) Changing the system to describe a vector-transmitted pathogen, including intrinsic and extrinsic incubation periods, results in an overall increase in mean incidence and decrease in the risk of stochastic extinction. (C) Further including seasonal variations in mosquito densities results in multi-annual epidemic outbreaks followed by severe transmission bottlenecks. Parameters are given in Materials and Methods (A) and in Table 1 (B and C, with in B).
Figure 2.
Temporal epidemiological patterns of dengue.
(A) Model output. Structuring the host population into a (20 by 20) lattice of smaller sub-communities results in lower epidemic variability in the simulated epidemiological dynamics and higher out-of-season viral persistence. The average level of disease prevalence is per 100000 individuals and the proportion of the population fully susceptible to dengue is
. Parameters as in Table 1 with
. The overall qualitative behaviour in incidence and serotype oscillations are in good agreement with dengue characteristic epidemiologies. (B) Empirical data. Time series of reported cases of DF and DHF in Puerto Rico in the period 1986–2012 (top) showing a clear seasonal signature and multi-annual epidemic outbreaks. Plotting adjusted serotype-specific incidence (bottom) illustrates the sequential replacement of dominant serotypes over time.
Figure 3.
Spatial epidemiological patterns.
(A) Local viral extinction generates a highly heterogeneous immunity landscape, shown as a snapshot (at year = 80) of the population-wide susceptibility level to DENV1 (left). The spatial prevalence of individual serotypes is equally heterogeneous, driven by serotype-specific susceptibility and here shown as the cumulative incidence of DENV1 for the following 3 seasons (middle). Spatial heterogeneity in serotype prevalence and exposure causes a highly variable distribution in the heterologous exposure period (HEP), or timing between consecutive, heterologous infections(right). (B) Significant differences in serotype prevalence can be observed on multiple geographical scales during a single season within endemic regions, which would be hidden by just considering aggregated data: between rural and urban Thailand (left) and within Ho Chi Minh City (middle). Simulation output (right) showing similar patterns in serotype distribution, where a community in the center of the lattice exhibits dissimilar serotype prevalence levels compared to the aggregated meta-population data, taken from the last 2 years of the simulation shown in Figure 2A.
Figure 4.
Effects of population structuring and host mobility.
(A) Increasing host population structure results in a significant reduction in epidemic variability (blue line in left panel), extinction risk (green line, middle panel), longer periods of serotype oscillations (blue line, middle panel) and serotype co-circulation (red line, middle panel). This increase in viral persistence also causes higher mean prevalence (red line, left panel). The age of primary or subsequent infections are not affected by changes to population structuring (right panel). (B) Host mobility, , counteracts the effects of population structure (here using a 20×20 lattice) and leads to an increase in epidemic variability and therefore extinction risk. In both (A) and (B), the average age of infection is not affected as the mean force of infection is maintained. Note, the oscillatory behavior in serotype prevalence is maintained given the parameter variations, with periods between 7 and 10 years in (A) and between 7 and 9 years in (B). Extinction risk is defined as the percent of time individual serotypes remain bellow a critical threshold of 10 infected hosts (human or mosquito). For ease of comparison, epidemiological variables (except age) are normalised to the case of no structuring in (A) and no host mobility in (B), with ratios above 1 representing an increase and below 1 a decrease. Dashed vertical and horizontal lines mark the parameter set of Figure 2. Shown are the means and deviations for 25 stochastic simulations.
Figure 5.
Effects of host mobility on spatial coherence.
(A) Increasing the probability of long-distance transmission, , as a proxy for increased daily (human) mobility, results in a less variable but more patchy immunity landscape across the population, as shown as a snapshot of the DENV1 susceptibility levels across the population. (B) This effect on spatial heterogeneity in population-level immunity is also reflected in terms of spatial coherence between communities, here shown as Pearson's r between communities along the diagonal. Whereas predominantly local transmission results in a sharp decrease in spatial coherence with distance (
, blue line), high host mobility leads to a generally low and homogeneous degree of coherence across the population (
, red line), due to the nature of mobility here assumed to be stochastic both in time and space.
Figure 6.
Effects of serotype immune interactions within structured populations.
(A) The epidemiological effects of temporary cross-immunity, , on mean prevalence level, epidemic variability or average age of infection only become apparent when the period of immunity increases beyond 12–24 months. Longer periods hamper variant transmission and lead to a decrease in mean disease prevalence and significant increase in the age of heterologous infection. (B) Antibody-dependent enhancement,
, which simultaneously increases susceptibility to and transmissibility of secondary, heterologous infections causes an overall increase in the force of infection and more variable epidemic behaviour. Due to higher susceptibility and co-circulation this also leads to a drop in the age of primary and particularly secondary infection. The oscillatory behavior in serotype prevalence is maintained given the parameter variations, with periods between
8 and
12 years in (A) and between
6 and
9 years in (B). For ease of comparison, epidemiological variables (except age) are normalised to the case of no cross-immunity, with ratios above 1 representing an increase and below 1 a decrease. Dashed vertical and horizontal lines mark the parameter set of Figure 2. Shown are the means and deviations for 25 stochastic simulations.