Dynamic Modeling, Analysis of Tuberculosis Infection Among Diabetic Patients and Parameters Estimation Using Physics Informed Neural Networks
摘要
In this work, we present a compartmental dynamic model of tuberculosis infection among diabetic population of a certain demography and apply neural network algorithm to estimate parameters, forecast disease spread efficiently. The model is built on the fact that in some countries, in particular South Asian countries, the prevalence of diabetics is very high along with the high tuberculosis incidence, creating a joint epidemic. Hence, our model analyzes the tuberculosis transmission among diabetic population in that region. We perform a mathematical analysis of the model and discuss the existence and uniqueness of the solution. We also show the endemic equilibrium point and disease free equilibrium point of the proposed model. We establish the nonnegativity and boundedness of the solution. We discuss the stability analysis of the endemic equilibrium point. The reproduction number has also been derived. Next we apply a modified physics informed neural networks (PINNs) based on a deep neural network architecture, to forecast the disease transmission pattern and estimate the key model parameters. The essence of this PINNs algorithm is that it can utilize the differential equation and efficiently estimate the parameters even with a small dataset. We show that our modified PINNs can forecast the tuberculosis transmission pattern competently and estimate the key model parameters effectively. Sensitivity analysis has been performed validating accuracy and robustness of our model.