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

TL;DR

This paper develops a temperature- and altitude-dependent compartmental model for malaria, analyzes its stability, and employs neural networks and dynamic mode decomposition to predict disease dynamics and assess risk.

Contribution

It introduces a novel data-driven approach combining mathematical modeling, neural networks, and DMD to understand and predict malaria transmission dynamics.

Findings

Model stability analysis identifies conditions for disease persistence or eradication.

Neural networks accurately predict disease compartment trajectories from data.

DMD provides a quantitative measure of disease risk.

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.