The process of forecasting mosquito activity is complex but grounded in scientific research and real-world data. Our service builds upon established models, incorporating real-time data along with environmental, economic, and geographic factors to provide accurate and reliable forecasts. Let's walk through the steps of our forecasting process with an example.

Convergence of Random Forest Algorithm

Data Collection: We gather various types of data that influence mosquito populations:

- Environmental data: temperature, humidity, rainfall, wind patterns

- Geographic data: landscape features, water bodies, vegetation

- Economic data: urban development, population density

Real-Time Monitoring:

Our system continuously collects current data from weather stations, satellite imagery, and other sources to ensure up-to-date information.

Mathematical Modeling:

We use advanced algorithms that consider how different factors interact to affect mosquito breeding and activity.

Historical Analysis:

Our model incorporates past mosquito population trends and their correlation with various factors.

Prediction Generation:

By processing all this data, our system generates daily forecasts of mosquito activity levels.

Regional GDP: Regional GDP data was sourced from economic databases to understand the impact of socio-economic conditions on mosquito activity.

Standing Water Sources: Standing water sources were identified using satellite imagery and geographical databases. These sources were classified by type and size to quantify potential mosquito breeding sites.

Data Preprocessing: The collected data was normalized, cleaned, and preprocessed to ensure consistency and accuracy. Feature engineering was applied to create new features, such as the humidity index and average rainfall over the past week.

Temperature Model: We use a sinusoidal function to account for seasonal variations:

$T(t) = T_{\text{mean}} + A_T \cdot \sin\left(\frac{2\pi(t - \phi_T)}{365}\right)$

GDP Model: We use a modified exponential growth function with cyclical components:

$GDP(t) = GDP_0 \cdot e^{rt} \cdot (1 + A_{\sin} \cdot \sin(\frac{2\pi t}{T_{\text{cycle}}}) + A_{\cos} \cdot \cos(\frac{2\pi t}{T_{\text{cycle}}}))$

Where $GDP_0$ is the initial GDP value (¥6.8 trillion for Kyoto as of 2022)

Historical Outbreak Impact: Modeled using a decay function with seasonal variations:

$H(t) = \sum_{i=1}^n H_i \cdot e^{-\delta(t-t_i)} \cdot (1 + \varepsilon \cdot \sin(\frac{2\pi(t-t_i)}{365}))$

Where $H_i$ is the severity of outbreak $i$, and $t_i$ is the time of outbreak $i$

The final mosquito activity forecast grade is calculated as:

$F = w_E(α_T G_T + α_H G_H + α_R G_R) + w_G(β_E G_E + β_W G_W) + w_C(γ_{GDP} G_{GDP} + γ_P G_P) + w_D(δ_H G_H + δ_V G_V)$

Where w are weights for each factor category, and G are individual factor grades

Our model incorporates Kyoto's unique features:

- GDP influence, including significant tourism impact

- Historical Japanese Encephalitis and Dengue fever outbreaks in the region

- Focus on key vector species: Culex tritaeniorhynchus and Aedes albopictus

- Geographic features: Higashiyama and Kitayama mountain ranges, Kamo and Katsura rivers

To further refine our predictions and dynamically adapt to changing conditions, we employ a Random Forest algorithm for post-processing and weight adjustment.

Random Forest Model:

We use an ensemble of decision trees to capture non-linear relationships and interactions between features.

Each tree in the forest is trained on a bootstrap sample of the data, with a random subset of features considered at each split.

Feature Importance:

We calculate feature importance to identify the most influential factors in our model:

$I_j = \frac{1}{N_T} \sum_{T} \sum_{t \in T: v(s_t)=j} p(t) (\Delta i(s_t)^2)$

Where $I_j$ is the importance of feature j, $N_T$ is the number of trees, $p(t)$ is the proportion of samples reaching node t, and $Δi(s_t)^2$ is the decrease in impurity.

Weight Adaptation:

We adjust the weights in our composite grading system based on the feature importance:

$w_k^{new} = w_k^{old} + \eta \cdot (I_k - \bar{I})$

Where $w_k^{new}$ is the updated weight for factor k, $η$ is the learning rate, $I_k$ is the importance of factor k, and $\bar{I}$ is the mean importance across all factors.

This adaptive approach allows our model to continuously improve its accuracy by learning from new data and adjusting the relative importance of different factors based on their observed impact on mosquito activity.