The COVID-19 Model with Partially Recovered Carriers

Novel coronavirus (COVID-19) has been spreading and wreaking havoc globally, despite massive efforts by the government and World Health Organization (WHO). Consideration of partially recovered carriers is hypothesized to play a leading role in the persistence of the disease and its introduction to new areas. A model for transmission of COVID-19 by symptomless partially recovered carriers is proposed and analysed. It is shown that key parameters can be identified such that below a threshold level, built on these parameters, the epidemic tends towards extinction, while above another threshold, it tends towards a nontrivial epidemic state. Moreover, optimal control analysis of the model, using Pontryagin’s maximum principle, is performed. The optimal controls are characterized in terms of the optimality system and solved numerically for several scenarios. Numerical simulations and sensitivity analysis of the basic reproduction number, R c , indicate that the disease is mainly driven by parameters involving the partially recovered carriers rather than symptomatic ones. Moreover, optimal control analysis of the model, using Pontryagin’s maximum principle, is performed. The optimal controls were characterized in terms of the optimality system and solved numerically for several scenarios. Numerical simulations were explored to illustrate our theoretical findings, scenarios were built, and the model predicted that social distancing and treatment of the symptomatic will slow down the epidemic curve and reduce mortality of COVID-19 given that there is an average adherence to social distancing and effective treatment are administered.

Analysis of seir model with a single control for COVID-19

A SEIR mathematical model with a single control vaccination is formulated. Properties of Pontryagin's maximum principle is verified and found the optimal levels of controls. Optimal values of S, E, I, R were derived by equlibrium analysis. Numerical simulations were carried out to exhibit the Susceptible, Exposed, Infectious and Recovery class with and without vaccination.

A Within-host Tuberculosis Model Using Optimal Control

In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of tuberculosis. We considered an in-host tuberculosis model that described the interaction between Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal control is applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula is obtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results. The results suggest that control or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large. In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of tuberculosis.We considered an in-host tuberculosis model that described the interaction between macrophages Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal controlis applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula isobtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results.The results suggest thatcontrol or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large.

Optimal paper web weight control system based on the Pontryagin’s maximum principle

The paper describes the stages of paper production, considers the structure of a paper-making machine. Questions related to the proof and use of the Pontryagin’s maximum principle in the theory of optimal control are considered. Optimal paper web weight control system based on the Pontryagin’s maximum principle is presented. Adaptive learning methods for modeling nonlinear systems represent some of the latest advances in adaptive algorithms and machine learning techniques designed to model and identify nonlinear systems. Real-world problems always involve a certain degree of non-linearity, which makes linear models a suboptimal choice. This article may be of interest to research engineers and practitioners in the study and application of control systems using adaptive regulators. This book serves as an essential resource for researchers, graduate students and doctoral students working in the field of machine learning, signal processing, adaptive filtering, nonlinear control, system identification, cooperative systems, and computational intelligence. This book may also be of interest to the industry market and practitioners working with a wide range of nonlinear systems.