Search

A mathematical model is designed to investigate Tuberculosis (TB) disease under the vaccination, treatment, and environmental impact with real cases. First, we introduce the model formulation in non-integer order derivative and then, extend the model into fractional order derivative. The fractional system's existence, uniqueness, and other relevant properties are shown. Then, we study the stability analysis of the equilibrium points. The disease-free equilibrium (DFE) 0 is locally asymptotically stable (LAS) when ℛ v < 1. Further, we show the global asymptotical stability (GAS) of the endemic equilibrium (EE) ∗ for ℛ v > 1 and 0 for ℛ v ≤ 1. The existence of bifurcation analysis in the model is investigated, and it is shown the system possesses the forward bifurcation phenomenon. Sensitivity analysis has been performed to determine the sensitive parameters that impact ℛ v. We consider the real TB statistics from Khyber Pakhtunkhwa in Pakistan and parameterized the model. The computed basic reproduction number obtained using the real cases is ℛ 0 ≈ 3.6615. Various numerical results regarding disease elimination of the sensitive parameters are shown graphically. [ABSTRACT FROM AUTHOR]

We construct a model to investigate HIV/AIDS dynamics in real cases and study its mathematical analysis. The study examines the qualitative outcomes and confirms the local and global asymptotic stability of both the endemic equilibrium and the disease-free equilibrium. The model's criteria for exhibiting both local and global asymptotically stable behavior are examined. We compute the endemic equilibria and obtain the existence of a unique positive endemic equilibrium. The data is fitted to the model using the idea of nonlinear least-squares fitting. Accurate parameter values are achieved by fitting the data to the model using a 95% confidence interval. The basic reproduction number is computed using parameters that have been fitted or estimated. Sensitivity analysis is performed to discover the influential parameters that impact the reproduction number and the eradication of the disease. The results show that implementing preventive measures can reduce HIV/AIDS cases. [ABSTRACT FROM AUTHOR]

In this work, we consider an adaptive control method, which is simpler and generalized to obtain some conditions on the parameters for hyperchaotic models determined by using a Lyapunov direct method. Further, an adaptive controller for synchronization is designed by using Lyapunov functions by which the deriving system and the response system can realize adaptive modified function projective synchronization up to scaling matrix. Numerical simulation of each system is discussed in detail with graphical results. The graphical results are presented in detail in order to validate the theoretical results. These results in this article generalize and improve the corresponding results of the recent works. [ABSTRACT FROM AUTHOR]