Spatial epidemiological patterns.

<p>(<b><i>A</i></b>) Local viral extinction generates a highly heterogeneous immunity landscape, shown as a snapshot (at year = 80) of the population-wide susceptibility level to DENV1 (<i>left</i>). 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 (<i>middle</i>). Spatial heterogeneity in serotype prevalence and exposure causes a highly variable distribution in the heterologous exposure period (HEP), or timing between consecutive, heterologous infections(<i>right</i>). (<b><i>B</i></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 (<i>left</i>) and within Ho Chi Minh City (<i>middle</i>). Simulation output (<i>right</i>) 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 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003308#pcbi-1003308-g002" target="_blank">Figure 2A</a>.</p

Results from experimental data.

<p>Best-fit parameter estimates derived by simulated annealing (top row) and MCMC parameter distributions (bottom row) are shown for three sets of <i>P. falciparum var</i> gene transcription data previously analysed by Recker <i>et al. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0039335#pone.0039335-Recker2" target="_blank">[15]</a>. Each data set comprises a single time series of measurements from an initially clonal culture. The results are consistent with an SMS network structure although the MCMC output (right column) also indicates the likelihood of alternative pathways.</p

Model fitting to Madeira's dengue outbreak data.

<p>(<i>A,B</i>) Reported cases (incidence and cumulative) per week (dotted, black) and example of model fitting (solid, purple). Coloured area (purple) is the standard deviation of all accepted steps in the MCMC chain. The dashed vertical line represents the date of the first reported clinical cases. The red dashed line represents the epidemic progression ignoring the first week in November, when a new surveillance method was introduced. (<i>C</i>) Stationary distributions of the estimated timepoint of first case for 30 independent MCMC runs with random initial conditions and 1 million steps.</p

Constant parameters.

<p>Constant parameters.</p

Natural, Persistent Oscillations in a Spatial Multi-Strain Disease System with Application to Dengue

<div><p>Many infectious diseases are not maintained in a state of equilibrium but exhibit significant fluctuations in prevalence over time. For pathogens that consist of multiple antigenic types or strains, such as influenza, malaria or dengue, these fluctuations often take on the form of regular or irregular epidemic outbreaks in addition to oscillatory prevalence levels of the constituent strains. To explain the observed temporal dynamics and structuring in pathogen populations, epidemiological multi-strain models have commonly evoked strong immune interactions between strains as the predominant driver. Here, with specific reference to dengue, we show how spatially explicit, multi-strain systems can exhibit all of the described epidemiological dynamics even in the absence of immune competition. Instead, amplification of natural stochastic differences in disease transmission, can give rise to persistent oscillations comprising semi-regular epidemic outbreaks and sequential dominance of dengue's four serotypes. Not only can this mechanism explain observed differences in serotype and disease distributions between neighbouring geographical areas, it also has important implications for inferring the nature and epidemiological consequences of immune mediated competition in multi-strain pathogen systems.</p></div

Estimated parameters.

<p>Free parameters used by the MCMC approach to fit the data.</p

Effects of population structuring and host mobility.

<p>(<b><i>A</i></b>) 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><i>B</i></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 (<i>A</i>) and (<i>B</i>), 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 (<i>A</i>) and between 7 and 9 years in (<i>B</i>). 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 (<i>A</i>) and no host mobility in (<i>B</i>), with ratios above 1 representing an increase and below 1 a decrease. Dashed vertical and horizontal lines mark the parameter set of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003308#pcbi-1003308-g002" target="_blank">Figure 2</a>. Shown are the means and deviations for 25 stochastic simulations.</p

Effects of serotype immune interactions within structured populations.

<p>(<b><i>A</i></b>) 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><i>B</i></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 (<i>A</i>) and between 6 and 9 years in (<i>B</i>). 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 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003308#pcbi-1003308-g002" target="_blank">Figure 2</a>. Shown are the means and deviations for 25 stochastic simulations.</p

Temporal epidemiological patterns of dengue.

<p>(<b><i>A</i></b>) 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 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003308#pcbi-1003308-t001" target="_blank">Table 1</a> with . The overall qualitative behaviour in incidence and serotype oscillations are in good agreement with dengue characteristic epidemiologies. (<b><i>B</i></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.</p

Temperature-dependent parameters.

<p>Analytical solutions from other studies are used. See <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003083#s2" target="_blank">Methods</a> section.</p