contagious virus

Analysis and optimal control problem for a fractional mathematical model of tuberculosis with smoking consideration

This article studies a mathematical model of the fractional order of tuberculosis (TB).  It describes the dynamics of the spread of tuberculosis among smokers.  The purpose of this research is to protect vulnerable people against the virus.  According to the survey results, the required model has an equilibrium point: the disease-free equilibrium point $E_f$.  We also analyze the local stability of this equilibrium point of the model, using the basic reproduction number $\mathcal{R}_{0}$ calculated according to the new generation method.  In our model, we include three

A discrete mathematical model SIRS with the evolution of regions to attack infectious diseases

This paper presents a new SIRS mathematical model describing the evolution of an infectious disease, assuming that the spatial supports of this infection are also evolutionary and obey a compartmental model.  We propose four control strategies to manage the spread of the disease among individuals and regions.  The Pontryagin maximum principle is employed to characterize the optimal controls, and the optimality system is solved using an iterative approach.  Finally, numerical simulations are conducted to validate the theoretical analysis using MATLAB.