Measles, a highly contagious airborne disease, remains endemic in many developing countries with low vaccination coverage. In this paper, we present a deterministic mathematical compartmental model to analyze the dynamics of measles. We establish global stability conditions for both disease-free and endemic equilibria using the Lyapunov functional stability method. By using arbitrary parameters, we find that the proposed model exhibits forward bifurcation. To simulate the solution of the model for the forward problem, we perform numerical integration using MATLAB software. Moreover, we calibrate the model with real data from Ethiopia and estimate the parameters along with a 95 percent confidence interval (CI) by formulating an inverse problem. It is noteworthy that our model fits well with the actual data from Ethiopia. The estimated basic reproduction number ( ) is determined to be , demonstrating the endemic status of the disease. Additionally, our local sensitivity analysis indicates that reducing the transmission rate and increasing vaccination coverage can effectively minimize .
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| http://dx.doi.org/10.1016/j.heliyon.2024.e33594 | DOI Listing |
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Article Synopsis
- Measles is a complex infectious disease that poses significant public health challenges, and traditional models often fail to effectively capture its intricate dynamics during outbreaks.
- This study introduces a high-dimensional neural network model (SFNN) that demonstrates better forecasting accuracy compared to a classical mechanistic model (TSIR) when analyzing measles data from England and Wales between 1944-1965.
- The findings suggest that combining mechanistic and machine learning approaches, like using TSIR to enhance Physics-Informed-Neural-Networks (PINN), can further improve predictions and understand underlying disease dynamics without rigid assumptions.
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