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. 2017 Jul 19;11(7):e0005797.
doi: 10.1371/journal.pntd.0005797. eCollection 2017 Jul.

Temperature modulates dengue virus epidemic growth rates through its effects on reproduction numbers and generation intervals

Amir S Siraj  1 , Rachel J Oidtman  1 , John H Huber  2 , Moritz U G Kraemer  3   4   5 , Oliver J Brady  6   7 , Michael A Johansson  8   9 , T Alex Perkins  1
Affiliations

Temperature modulates dengue virus epidemic growth rates through its effects on reproduction numbers and generation intervals

Amir S Siraj et al. PLoS Negl Trop Dis. .

Abstract

Epidemic growth rate, r, provides a more complete description of the potential for epidemics than the more commonly studied basic reproduction number, R0, yet the former has never been described as a function of temperature for dengue virus or other pathogens with temperature-sensitive transmission. The need to understand the drivers of epidemics of these pathogens is acute, with arthropod-borne virus epidemics becoming increasingly problematic. We addressed this need by developing temperature-dependent descriptions of the two components of r-R0 and the generation interval-to obtain a temperature-dependent description of r. Our results show that the generation interval is highly sensitive to temperature, decreasing twofold between 25 and 35°C and suggesting that dengue virus epidemics may accelerate as temperatures increase, not only because of more infections per generation but also because of faster generations. Under the empirical temperature relationships that we considered, we found that r peaked at a temperature threshold that was robust to uncertainty in model parameters that do not depend on temperature. Although the precise value of this temperature threshold could be refined following future studies of empirical temperature relationships, the framework we present for identifying such temperature thresholds offers a new way to classify regions in which dengue virus epidemic intensity could either increase or decrease under future climate change.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Random variables associated with components of the transmission cycle (top) and their successive sums (bottom).
On the top, the intrinsic incubation (IIP), human-to-mosquito transmission period (HMTP), extrinsic incubation period (EIP), and mosquito-to-human transmission period (MHTP) are shown from left to right, with the latter two parameterized for a temperature of 30°C. On the bottom, random variables for the elapsed time between inoculation of the primary infection and each event in the transmission cycle is shown in successive order from left to right.
Fig 2
Fig 2
Relationships between temperature and entomological parameters (A) and epidemiological quantities (B-D). The thick solid (dashed) line in B shows the mean (median) generation interval at each temperature, and colors indicate the probability density of generation intervals at a given temperature (red to yellow = low to high). Contours show probability density values in intervals of 0.05. Colored surfaces in C and D show how temperature and mosquito emergence rate λ affect R0 and r (red to yellow = low to high), respectively. Black planes in C and D indicate the combinations of temperature and λ values for which R0 and r fall above or below threshold values (1 or 0, respectively). The thick black lines in C and D show the temperatures at which either R0 or r is maximized for a given value of λ. For comparison, the thin line in D indicates temperatures at which R0 is maximized.
Fig 3
Fig 3. Temperature at which r peaks across a range of mosquito emergence rates λ, obtained by solving for r with 1,000 simulations of R0 based on Monte Carlo resampling of its three temperature-dependent parameters μ(T), n(T), and a(T) and applying Eq (1).
The solid line is the median r at each λ value, and the shaded region shows the 95% confidence interval of r conditional on λ.
Fig 4
Fig 4. Relative contributions of the generation interval (blue) and the basic reproduction number R0 (orange) to temperature-driven changes in epidemic growth rate r.
Temperature changes are considered in 0.1°C increments and assume λ = 0.2. See S1 Fig for consideration of alternative λ value.
Fig 5
Fig 5. DENV epidemic growth rate, r, for high (red) and low (blue) mosquito densities based on our full model and other approximations.
The top panels show comparisons of the full model estimates (solid lines) with those based on temperature independent, exponentially distributed (A) and fixed-length (B) generation intervals (mean = 16 days [34]) (dashed lines). The bottom panels show comparisons of estimates of the full model (solid lines) with those based on exponentially distributed (C) and fixed-length (D) generation intervals (dashed lines), with their mean values at each temperature set to the corresponding mean from the full model.
Fig 6
Fig 6. Epidemic growth under an exponential model with values of the epidemic growth rate r ranging from 0.01 to 0.05 for a duration of 180 days.
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