Abstract
In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international spread of the infectious diseases. The relationship between epidemiology, mathematical modeling and computational tools lets us to build and test theories on the development and fighting with a disease. This study is motivated by the study of epidemiological models applied to infectious diseases in an optimal control perspective. We use the numerical methods to display the solutions of the optimal control problems to find the effect of vaccination on these models. Finally, global sensitivity analysis LHS Monte Carlo method using Partial Rank Correlation Coefficient (PRCC) has been performed to investigate the key parameters in model equations. This present work will advance the understanding about the spread of infectious diseases and lead to novel conceptual understanding for spread of them.
Highlights
Due to the fast spread of pandemic diseases, mathematical modeling in the field of epidemiology has attracted many scientists in different areas
Infectious diseases can be defined as diseases that can be transmitted from human to human, from human to animal, or from animal to animal
The mathematical modeling of infectious disease spread has been studied for many years and recently it has been widely discussed due to the spread of the COVID-19 pandemic
Summary
Due to the fast spread of pandemic diseases, mathematical modeling in the field of epidemiology has attracted many scientists in different areas. Many mathematical models have been developed to describe the transmission of communicable diseases [1] [2] [3]. These mathematical models describe the mechanisms of infectious diseases and they are helpful to analyze the effect of public health interventions to control the spreading of diseases. We describe biological systems by converting them into mathematical and theoretical framework with biological parameters and using computer code to solve the model system computationally to predict the future of infectious diseases, one needs to study the behavior of each individual which plays a key role to understand the behavior epidemiology of infectious diseases [4]
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