Computational Approximations for Real-World Application of Epidemic Model

Abstract

The real-world applications and analysis have a significant role in the scientific literature. For instance, mathematical modeling, computer graphics, camera, operating system, Java, disk encryption, web, streaming, and many more are the applications of real-world problems. In this case, we consider disease modeling and its computational treatment. Computational approximations have a significant role in different sciences such as behavioral, social, physical, and biological sciences. But the well-known techniques that are widely used in the literature have many problems. These methods are not consistent with the physical nature and even violate the actual behavior of the continuous model. The structural properties needed for such disciplines, as dynamical consistency, positivity, and boundedness, are the critical requirements of the models in these fields. We studied the transmission of Lassa fever dynamically and numerically. The model's positivity, boundedness, reproduction number, equilibria, and local stability are investigated in dynamical analysis. In numerical analysis, we developed some explicit and implicit methods. Unfortunately, explicit methods like Euler and Runge Kutta are time-dependent and violate the physical properties of the disease. Then, the proposed implicit method for the said model, the non-standard finite difference, is independent of the time step, dynamically consistent, positive, and bounded. In the end, a comparison of methods is presented.