Data-Driven approach for the unified influence of media function and information density on the transmission dynamics of SIRS epidemic model via: Disease informed neural networks

In this study, we formulated a model that unifies the influence of media functions and information intervention on the transmission dynamics of the epidemic model. The media is used to inform people about the outbreak of a disease in a given population. The mass media function affects the rate of disease transmission by improving public awareness and promoting protective actions through the media. Information density reflects how much knowledge about the epidemic exists in the population, which determines individual responses and resource allocation over time. In this paper, we incorporate the mass media function and information density into the SIRS epidemic model. Our model provides a better perspective on the synergistic interplay of disease transmission, media-induced behavior changes, and the spread of information within the population. To explore the dynamics of the new model, the boundedness, non-negativity, and equilibria are analyzed. The local and global stability analyses of the new model are explored at feasible equilibrium points. The sensitivity analysis of the basic reproduction number and the epidemic equilibrium point is analyzed using a novel numerical method. Bifurcation analysis, such as saddle node, transcritical, pitchfork, forward, and backward bifurcations, has been carried out to highlight the most prominent qualitative changes in the model dynamics. Subsequently, we extended an approach known as disease-informed neural networks (DINNs), which can be applied to efficiently project the spread of diseases and recovery. The application of physics-informed neural networks (PINNs) is formulated on the proposed model. We expound on how neural networks have the potential to learn the degree of spread of the epidemic in a society: prediction of evolution, exploring some sensitive parameters. To demonstrate the strength and usefulness of DINNs, some computational experiments will be performed, including Gaussian noise to synthetic data, and the results proved that DINNs is a robust approach to efficiently estimate the dynamics of the disease spread and project future behavior based on synthetically generated data.