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Analysis of a mathematical model for malaria using data-driven approach

Adithya Rajnarayanan, Manoj Kumar, Abdessamad Tridane

TL;DR

The paper addresses malaria transmission dynamics under temperature and altitude influences using a two-species SIR-SI compartmental model. It combines analytical stability analysis with data-driven parameter estimation via ANN, RNN, and PINN, and uses Dynamic Mode Decomposition to quantify disease risk. The results show a disease-free equilibrium when $R_0<1$ and an endemic equilibrium when $R_0>1$, with PINNs delivering the most accurate trajectory predictions. The work offers a practical framework for forecasting and risk assessment, potentially guiding public health interventions with a physics-informed, data-driven approach.

Abstract

Malaria is one of the deadliest diseases in the world, every year millions of people become victims of this disease and many even lose their lives. Medical professionals and the government could take accurate measures to protect the people only when the disease dynamics are understood clearly. In this work, we propose a compartmental model to study the dynamics of malaria. We consider the transmission rate dependent on temperature and altitude. We performed the steady state analysis on the proposed model and checked the stability of the disease-free and endemic steady state. An artificial neural network (ANN) is applied to the formulated model to predict the trajectory of all five compartments following the mathematical analysis. Three different neural network architectures namely Artificial neural network (ANN), convolution neural network (CNN), and Recurrent neural network (RNN) are used to estimate these parameters from the trajectory of the data. To understand the severity of a disease, it is essential to calculate the risk associated with the disease. In this work, the risk is calculated using dynamic mode decomposition(DMD) from the trajectory of the infected people.

Analysis of a mathematical model for malaria using data-driven approach

TL;DR

The paper addresses malaria transmission dynamics under temperature and altitude influences using a two-species SIR-SI compartmental model. It combines analytical stability analysis with data-driven parameter estimation via ANN, RNN, and PINN, and uses Dynamic Mode Decomposition to quantify disease risk. The results show a disease-free equilibrium when and an endemic equilibrium when , with PINNs delivering the most accurate trajectory predictions. The work offers a practical framework for forecasting and risk assessment, potentially guiding public health interventions with a physics-informed, data-driven approach.

Abstract

Malaria is one of the deadliest diseases in the world, every year millions of people become victims of this disease and many even lose their lives. Medical professionals and the government could take accurate measures to protect the people only when the disease dynamics are understood clearly. In this work, we propose a compartmental model to study the dynamics of malaria. We consider the transmission rate dependent on temperature and altitude. We performed the steady state analysis on the proposed model and checked the stability of the disease-free and endemic steady state. An artificial neural network (ANN) is applied to the formulated model to predict the trajectory of all five compartments following the mathematical analysis. Three different neural network architectures namely Artificial neural network (ANN), convolution neural network (CNN), and Recurrent neural network (RNN) are used to estimate these parameters from the trajectory of the data. To understand the severity of a disease, it is essential to calculate the risk associated with the disease. In this work, the risk is calculated using dynamic mode decomposition(DMD) from the trajectory of the infected people.
Paper Structure (12 sections, 3 theorems, 18 equations, 32 figures, 5 tables)

This paper contains 12 sections, 3 theorems, 18 equations, 32 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Model formulation
  3. Disease-free steady state analysis
  4. Endemic steady state analysis
  5. Numerical validation of the stability theorems
  6. Temperature and altitude dependence of the transmission rate
  7. Parameter estimation
  8. Methodology
  9. Prediction of trajectories
  10. Finding the risk of a disease
  11. Concluding remarks
  12. Data availability statement

Key Result

Theorem 2.1

If $R_{0}<1$, the disease-free steady state is locally stable.

Figures (32)

  • Figure 1: In 2017, four countries from Africa accounted for 45% of all malaria cases worldwide.
  • Figure 2: Schematic diagram of SIR-SI system
  • Figure 3: When reproduction number is less than 1
  • Figure 4: Effect on human population when height is 75 m
  • Figure 5: Effect on mosquitoes population when height is 75 m
  • ...and 27 more figures

Theorems & Definitions (5)

  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Lemma 2.3