Developing cholera outbreak forecasting through qualitative dynamics: Insights into Malawi case study

TL;DR

This study develops a mechanistic SIBR model to capture cholera transmission, including an environmental reservoir, and calibrates it to Malawi data using DRAM MCMC to study $R_0$ and bifurcations (forward and Hopf). It then constructs epidemic-informed ML models, EI-ARIMA and EI-ARNN, by embedding the infection dynamics into time-series forecasts, and demonstrates superior short-term forecasting performance against traditional baselines. The approach provides interpretable, policy-relevant forecasts and a replicable framework for integrating mechanistic insights with data-driven methods in infectious disease forecasting. While data limitations exist, the results support broader application of epidemic-informed forecasting to guide public health interventions.

Abstract

Cholera, an acute diarrheal disease, is a serious concern in developing and underdeveloped areas. A qualitative understanding of cholera epidemics aims to foresee transmission patterns based on reported data and mechanistic models. The mechanistic model is a crucial tool for capturing the dynamics of disease transmission and population spread. However, using real-time cholera cases is essential for forecasting the transmission trend. This prospective study seeks to furnish insights into transmission trends through qualitative dynamics followed by machine learning-based forecasting. The Monte Carlo Markov Chain approach is employed to calibrate the proposed mechanistic model. We identify critical parameters that illustrate the disease's dynamics using partial rank correlation coefficient-based sensitivity analysis. The basic reproduction number as a crucial threshold measures asymptotic dynamics. Furthermore, forward bifurcation directs the stability of the infection state, and Hopf bifurcation suggests that trends in transmission may become unpredictable as societal disinfection rates rise. Further, we develop epidemic-informed machine learning models by incorporating mechanistic cholera dynamics into autoregressive integrated moving averages and autoregressive neural networks. We forecast short-term future cholera cases in Malawi by implementing the proposed epidemic-informed machine learning models to support this. We assert that integrating temporal dynamics into the machine learning models can enhance the capabilities of cholera forecasting models. The execution of this mechanism can significantly influence future trends in cholera transmission. This evolving approach can also be beneficial for policymakers to interpret and respond to potential disease systems. Moreover, our methodology is replicable and adaptable, encouraging future research on disease dynamics.

Figures (12)

• Figure 1: Schematic portrayal of SIBR model. The flowchart demonstrates the interplay of individuals in the model: susceptible (S), infected (I), vibrio cholera bacteria (B), and recovered (R).
• Figure 2: The fitted SIBR model to new cases (weekly) with $95\%$ confidence interval. Cholera data is collected from Country https://cholera.health.gov.mw/surveillance for the time span from February $22^{nd}$, 2022 to July $10^{th}$, 2023. The 95% confidence interval for the fitted curve is also plotted here.
• Figure 3: Scatter plot showing 1D DRAM Chain. Here, the mean value is assigned as estimated parameter values from initial mean values, along with the upper and lower limits of the parameters and the length of chain 1000.
• Figure 4: Scatter plots depicting partial rank correlation of parameters to infected individuals ($I$). Here, a randomized sample size of 500 and a unit step size are considered with a significance level of $0.05$. Uniform and N(0,1) probability distributions are employed under the LHS approach. Here the corresponding PRCC value and P-value are $\alpha:(0.96742, 0)$, $\tau: (0.9997, 0)$, $\sigma_h:(0.0313, 0.4853)$, $\sigma_e:(0.0234, 0.6008)$, $\omega:(0.0124, 0.7822)$, $\phi_0:(0.0555, 0.2158)$, $\phi_1:(0.0381, 0.3952)$, $a:(0.8946, 0)$, $\gamma:(0.9123,0)$, $\xi:(0.0523, 0.2376)$, $\sigma_h:(0.0491, 0.2724)$, $\beta:(0.0019, 0.9647)$. Here, $\alpha$, $\tau$, $\gamma$ and $a$ are sensitive parameters for infected individuals ($I$).
• Figure 5: Bar diagram indicating PRCC-based sensitivity indices of parameters to basic reproduction number ($R_0$) with random sample size 500 and significance level 0.05. Here, $\alpha$, $\omega$, $\beta$, and $\delta$ have an inverse relationship with sensitivity, whereas $\pi$, $\phi_h$, and $\gamma$ exhibit a direct relationship with $R_0$.

Theorems & Definitions (11)

• Lemma 1
• Lemma 2
• Theorem 1
• Lemma 3
• Theorem 2
• Theorem 3
• Theorem 4
• proof
• proof
• proof