optimal control

On March 2, 2020, the Moroccan Ministry of Health announced the first case of COVID-19 in the city of Casablanca for a Moroccan tourist who came from Italy.  The SARS-COV-2 virus has spread throughout the Kingdom of Morocco.  In this paper, we study the spatiotemporal transmission of the COVID-19 virus in the Kingdom of Morocco.  By supporting a SI$_{\rm W}$IHR partial differential equation for the spread of the COVID-19 pandemic in Morocco as a case study.  Our main goal is to characterize the optimum order of controlling the spread of the COVID-19 pandemic by adopting

In this work, we analyze a viral hepatitis C model.  This epidemic remains a major problem for global public health, in all communities, despite the efforts made.  The model is analyzed using the stability theory of systems of nonlinear differential equations.  Based on the results of the analysis, the proposed model has two equilibrium points: a disease-free equilibrium point $E_0$ and an endemic equilibrium point $E^{*}$.  We investigate the existence of equilibrium point of the model.  Furthermore, based on the indirect Lyapunov method, we study the local stability o

A mathematical model of infectious disease contagion that accounts for population stratification based on immunity criteria is proposed.  Our goal is to demonstrate the effectiveness of this idea in preventing different epidemics and to lessen the significant financial and human costs these diseases cause.  We determined the fundamental reproduction rate, and with the help of this rate, we were able to examine the stability of the free equilibrium point and then proposed two control measures.  The Pontryagin's maximum principle is used to describe the optimal controls,

In this paper, we propose a new model of spatio-temporal dynamics concerning the tritrophic reaction-diffusion system by introducing Phytoplankton and Zooplankton.  We recall that the phytoplankton and zooplankton species are the basis of the marine food chain.  There is prey in each marine tritrophic system.  The main objective of this work is to control this species's biomass to ensure the system's sustainability.  To achieve this, we determine an optimal control that minimizes the biomass of super predators.