# Modeling the 2013 Zika Outbreak in French Polynesia: Intervention Strategies
## Methodology
### Mosquito Ecology
#### 3.1.1 Variation with Temperature  
The dependence of the population dynamics of _Aedes Agypti_ mosquitoes on temperature is taken into account by varying the maturation and mortality rates with temperature ([PERSON], 2018). The rates are computed by regressing values of rates at different temperatures, available in ([PERSON], 2018; [PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2018). The historical temperature data for 2013-2014 in Tahiti were collected from ([PERSON], 2018). All of the 23 islands are assumed to have the same daily temperatures during the outbreak period due to lack of available data and similar weather conditions across the islands ([PERSON], 2018). After regressing the available data, it was observed that the maturation rates for Pupae, Eggs, and Larvae, and the mortality rate for Eggs showed the most variation with temperature. The oviposition rate and the number of eggs laid per oviposition were not regressed because of lack of data. The other rates did not vary significantly with temperature so were assumed to be independent of temperature. The regression functions and the ranges for temperature independent rates are shown in Table 1. The rates were regressed with temperature to find the best fit curve, and the curve that had the minimum sum squared of residuals and hence an adjusted R-squared value closer to one was selected for calculating the rates at varying temperature. The data points and the corresponding graphs are shown in Figure 2.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameter** & **Symbol** & **Type** & **Value** \\ \hline Number of eggs laid per oviposition & \(b\) & Ranged & random (50–300) [20] \\ Oviposition Rate & \(P_{A_{a}}\) & Ranged & random (3.0–4.0) [20] \\ Egg Mortality Rate & \(\mu_{E}\) & Regression & \(-0.00080967^{3}+0.06967T^{2}-1.963T+18.37\) \\ Egg Maturation Rate & \(\mu_{E}\) & Regression & \(-0.00035747^{2}+0.03335t-0.3827\) \\ Density Independent Larvae Mortality Rate & \(\mu_{L_{1}}\) & Ranged & random (0.32–0.80) [20] \\ Density Dependent Larvae Mortality Rate & \(\mu_{L_{2}}\) & Constant & 0.05 [20] \\ Larva Maturation Rate & \(\mu_{L}\) & Regression & \(-0.00010327^{2}+0.0076177^{2}-0.1744T+1.326\) \\ Pupa Mortality Rate & \(\mu_{P}\) & Ranged & random (0.33–1.0) [20] \\ Pupa Maturation Rate & \(\mu_{P}\) & Regression & \(-0.00010837^{4}+0.01104T^{3}-0.4147T^{2}+6.834T-41.54\) \\ Adult Mortality Rate (Hosting stage) & \(\mu_{A_{b}}\) & Ranged & random (0.322–0.598) [20] \\ Adult Maturation Rate (Hosting stage) & \(\mu_{A_{b}}\) & Ranged & random (0.322–0.598) [20] \\ Adult Maturation Rate (Resting stage) & \(\mu_{A_{b}}\) & Ranged & random (0.30–0.56) [20] \\ Adult Mortality Rate (Resting stage) & \(\mu_{A_{b}}\) & Ranged & random (0.0034–0.01) citemosquitomodel \\ Adult Mortality Rate (Oviposition stage) & \(\mu_{A_{b}}\) & Ranged & random (0.41–0.56) [20] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mosquito ecology parameters, all rates are counts per day and \(T\) is the daily temperature in \({}^{\circ}\)Celsius.  
Figure 2: The variation of maturation and mortality rates with temperature. The dotted line represents the best curve that fit the data points. The purple dots represent the data points.