Muhammad Altaf Khan^1,*, Mahmoud H. DarAssi², Irfan Ahmad³, Noha Mohammad Seyam⁴, Ebraheem Alzahrani⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.2, pp. 1365-1394, 2024, DOI:10.32604/cmes.2024.053681 - 27 September 2024

Abstract 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) is locally asymptotically stable (LAS) when . Further, we show the global asymptotical stability (GAS) of the endemic equilibrium (EE) for and for . The existence of bifurcation analysis in the More >

Andrew Omame^1,2,*, Mujahid Abbas^3,6, Dumitru Baleanu^4,5,6

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.3, pp. 2973-3012, 2024, DOI:10.32604/cmes.2023.029681 - 15 December 2023

Abstract A patient co-infected with COVID-19 and viral hepatitis B can be at more risk of severe complications than the one infected with a single infection. This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19. The model is fitted to real COVID-19 data from Pakistan. The proposed model incorporates logistic growth and saturated incidence functions. Rigorous analyses using the tools of stochastic calculus, are performed to study appropriate conditions for the existence of unique global solutions, stationary distribution in the More >

Amer Ibrahim Al-Omari¹, Ibrahim M. Almanjahie^2,3,*

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 1503-1522, 2021, DOI:10.32604/cmc.2021.015047 - 05 February 2021

Abstract This article proposes two new Ranked Set Sampling (RSS) designs for estimating the population parameters: Simple Z Ranked Set Sampling (SZRSS) and Generalized Z Ranked Set Sampling (GZRSS). These designs provide unbiased estimators for the mean of symmetric distributions. It is shown that for non-uniform symmetric distributions, the estimators of the mean under the suggested designs are more efficient than those obtained by RSS, Simple Random Sampling (SRS), extreme RSS and truncation based RSS designs. Also, the proposed RSS schemes outperform other RSS schemes and provide more efficient estimates than their competitors under imperfect rankings. More >

Muhammad Altaf Khan^1,*, Khanadan Khan², Mohammad A. Safi³, Mahmoud H. DarAssi⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 777-795, 2020, DOI:10.32604/cmes.2020.08208 - 01 May 2020

Abstract The present paper investigates the theoretical analysis of the tuberculosis (TB) model in the discrete-time case. The model is parameterized by the TB infection cases in the Pakistani province of Khyber Pakhtunkhwa between 2002 and 2017. The model is parameterized and the basic reproduction number is obtained and it is found R₀ ¼ 1:5853. The stability analysis for the model is presented and it is shown that the discrete-time tuberculosis model is stable at the disease-free equilibrium whenever R₀ < 1 and further we establish the results for the endemic equilibria and prove that the model More >