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

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

Model-derived epidemiological and entomological parameter estimates for 2012.

<p>(<i>A</i>) Example of estimated values for 2012 (solid, red) together with the weekly minimum temperatures for 2012 (solid, blue) and long-term average of minimum temperatures (2001–2011, dashed green). The dashed red line marks the epidemic threshold . (<i>B</i>) Example of estimated number of mosquitoes per human (solid, black), incubation period (solid, cyan) and adult life-span (solid, orange) for 2012.</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

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

Constant parameters.

<p>Constant parameters.</p

Effects of host mobility on spatial coherence.

<p>(<b><i>A</i></b>) 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><i>B</i></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 <i>r</i> 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.</p

Tourism and temperature data for the island of Madeira.

<p>(<i>A</i>) Mean of minimum (green), average (blue) and maximum (red) temperatures per day between 2002 and 2012. Coloured areas are the standard deviation. (<i>B</i>) Number of airline passengers entering Madeira per year (dashed, black) and local investment in tourism per year (solid, grey). (<i>C</i>) Relative weight (bubbles) of each country in the total number of passengers arriving at Madeira per year (columns). Data compiled from the 30 most frequent cities of origin for airline passengers per year. Portuguese cities were excluded - Oporto, Lisbon, Porto Santo (Madeira) and Ponta Delgada (Azores). (<i>D</i>) Map representation of (C), including Portugal. Colours match the weight of each country with the 4 highest highlighted in green.</p

Model-derived epidemic potential for the island of Madeira.

<p>(<i>A</i>) Temperatures for the year of 2012 (red, solid line) and average temperatures for the past 10 years (2001–2011; blue, solid line). The points mark the mean outbreak size (number of cases) for 100 stochastic introductions at different timepoints using temperature data from 2012 (red) and the average over the past 10 years (blue). (<i>B</i>) Derived real-time (red, solid line) for 2012, with an annual mean of (dashed line). (<i>C</i>) Derived real-time (blue, solid line) for the past 10 year, with an annual mean of (dashed line). (<i>B,C</i>) Grey shaded areas are the frequency of simulations (in 100) achieving either more than 3 (light grey) or 1000 (dark grey) cases.</p

Climate and dengue outbreak data for the island of Madeira.

<p>Mean of minimum temperatures per week (solid, green), precipitation (solid, cyan) and dengue reported cases per week (dotted, black) for August-2012 to March-2013.</p