```
# Set seed for reproducibility
set.seed(123)
# Number of time steps (e.g., months)
n_steps <- 12
# Initial number of infected individuals
initial_infected <- 10
# Parameters for malaria transmission dynamics
transmission_rate <- 0.2 # Rate of malaria transmission
recovery_rate <- 0.1 # Rate of recovery from malaria
# Initialize vectors to store data
time <- 1:n_steps
infected <- numeric(n_steps)
# Initialize the number of infected individuals
infected[1] <- initial_infected
# Simulate malaria transmission dynamics
for (i in 2:n_steps) {
# Calculate the number of new infections
new_infections <- rbinom(1, infected[i - 1], transmission_rate)
# Calculate the number of recoveries
recoveries <- rbinom(1, infected[i - 1], recovery_rate)
# Update the number of infected individuals
infected[i] <- infected[i - 1] + new_infections - recoveries
# Ensure that the number of infected individuals is non-negative
if (infected[i] < 0) {
infected[i] <- 0
}
}
# Plot the simulated malaria data
plot(time, infected,
type = "l",
xlab = "Time",
ylab = "Number of Infected Individuals",
main = "Simulated Malaria Data"
)
```

# 16 The Case of Malaria

Learning Objectives

- What is Malaria
- How does it spread
- Map Malaria outbreaks

In this chapter, we explore the dynamics of Malaria transmission in more detail. We examine the results of various model’s applications that simulate the spread of the virus.

## 16.1 Epidemiology

**Malaria** is a mosquito-borne infectious disease that affects humans and other animals. It is caused by parasitic protozoans belonging to the Plasmodium type. The disease is **transmitted through the bites of Anopheles mosquitoes**. The symptoms of malaria typically include fever, fatigue, vomiting, and headaches. If left untreated, malaria can be fatal. Malaria is a major public health concern in many tropical and subtropical regions, particularly in Africa.

Malaria transmission dynamics are influenced by various factors, including the prevalence of infected individuals, the density of mosquito vectors, and environmental conditions. The transmission of malaria occurs when an infected mosquito bites a human host, injecting the Plasmodium parasites into the bloodstream. The parasites then multiply within the host’s red blood cells, leading to the characteristic symptoms of malaria. The parasites can be transmitted back to mosquitoes when they feed on infected individuals, completing the transmission cycle.

## 16.2 Mapping Malaria Outbreaks

Mapping Malaria outbreaks can help identify high-risk areas and guide public health interventions. Geographic Information Systems (GIS) can be used to visualise the spatial distribution of Malaria cases and identify patterns of transmission. By analysing the distribution of Malaria cases in relation to environmental factors such as temperature, humidity, and vegetation cover, researchers can gain insights into the factors driving Malaria transmission and develop targeted control strategies.

## 16.3 Example: Simulating Malaria Transmission Dynamics

In this example, we will simulate Malaria transmission dynamics using a simple mathematical model. We will generate synthetic data representing the number of infected individuals over time and use machine learning to predict future trends. We will demonstrate the process of data preparation, feature engineering, model selection, training, evaluation, and iterative improvement.

Synthetic data are used in this example to illustrate the modelling and prediction process. In practice, real-world data on Malaria cases, environmental factors, and other relevant variables would be used to develop more accurate models.

### 16.3.1 Modelling with caret

- Data Preparation

Convert ‘time’ column to Date format

```
malaria_data <- data.frame(time = time, infected_cases = infected)
# malaria_data$time <- as.Date(malaria_data$time)
```

- Feature Engineering

Create lagged variables if needed

- Model Selection

Define the machine learning model (e.g., Random Forest)

```
model <- train(
infected_cases ~ lagged_cases, # Specify the formula
data = malaria_data, # Specify the data
# Specify the machine learning algorithm (Random Forest)
method = "rf",
# Cross-validation for hyperparameter tuning
trControl = trainControl(method = "cv"),
# Hyperparameter grid for tuning
tuneGrid = expand.grid(mtry = c(2, 3, 4))
)
```

- Model Training (Parameter Calibration)

The ‘train’ function automatically performs parameter calibration (hyperparameter tuning)

- Evaluation

Predict future trends using the trained model

`predictions <- predict(model, newdata = malaria_data)`

Evaluate the model’s performance (e.g., using RMSE)

- Iterative Improvement

Refine your model by adjusting parameters, feature engineering, etc.

- Adjusting Parameters, and fine-tune the model by adjusting parameters such as ‘mtry’ in Random Forest. For example, try different values of ‘mtry’ and see how it affects model performance. Define tuning grid for mtry:

```
tuneGrid <- expand.grid(mtry = seq(1, ncol(malaria_data) - 1))
model <- train(
infected_cases ~ lagged_cases,
data = malaria_data,
method = "rf",
trControl = trainControl(method = "cv"),
tuneGrid = tuneGrid # Adjust the range of 'mtry'
)
```

- Feature Engineering by exploring additional features that may improve model performance. For example, create lagged variables for other relevant features or transform existing features to capture non-linear relationships. Add a new feature (e.g., log-transformed feature) and re-train the model:

```
malaria_data$feature <- log(malaria_data$infected_cases)
malaria_data$lagged_feature <- lag(malaria_data$feature, 1)
malaria_data <- na.omit(malaria_data)
# Re-train the model with the new feature
model <- train(
# Include the new feature
infected_cases ~ lagged_cases + lagged_feature,
data = malaria_data,
method = "rf",
trControl = trainControl(method = "cv"),
tuneGrid = expand.grid(mtry = c(2, 3, 4))
)
```

- Evaluate Model Performance, after making adjustments, evaluate the model’s performance again.