Muhammad Tashfeen¹, Fazal Dayan¹, Muhammad Aziz ur Rehman¹, Thabet Abdeljawad^2,3,4,5,*, Aiman Mukheimer²

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.3, pp. 2527-2554, 2024, DOI:10.32604/cmes.2024.056269 - 31 October 2024

Abstract Foot-and-mouth disease (FMD) is a viral disease that affects cloven-hoofed animals including cattle, pigs, and sheep, hence causing export bans among others, causing high economic losses due to reduced productivity. The global effect of FMD is most felt where livestock rearing forms an important source of income. It is therefore important to understand the modes of transmission of FMD to control its spread and prevent its occurrence. This work intends to address these dynamics by including the efficacy of active migrant animals transporting the disease from one area to another in a fuzzy mathematical modeling… More >

Muhammad Tashfeen¹, Fazal Dayan¹, Muhammad Aziz Ur Rehman¹, Thabet Abdeljawad^2,3,4,5,*, Aiman Mukheimer²

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.2, pp. 1419-1446, 2024, DOI:10.32604/cmes.2024.053242 - 27 September 2024

Abstract This study analyzes the transmission of typhoid fever caused by Salmonella typhi using a mathematical model that highlights the significance of delay in its effectiveness. Time delays can affect the nature of patterns and slow down the emergence of patterns in infected population density. The analyzed model is expanded with the equilibrium analysis, reproduction number, and stability analysis. This study aims to establish and explore the non-standard finite difference (NSFD) scheme for the typhoid fever virus transmission model with a time delay. In addition, the forward Euler method and Runge-Kutta method of order 4 (RK-4)… More >

Umar Shafique^1,*, Mohamed Mahyoub Al-Shamiri², Ali Raza³, Emad Fadhal^4,*, Muhammad Rafiq^5,6, Nauman Ahmed^5,7

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 311-329, 2024, DOI:10.32604/cmes.2024.052383 - 20 August 2024

Abstract Based on the World Health Organization (WHO), Meningitis is a severe infection of the meninges, the membranes covering the brain and spinal cord. It is a devastating disease and remains a significant public health challenge. This study investigates a bacterial meningitis model through deterministic and stochastic versions. Four-compartment population dynamics explain the concept, particularly the susceptible population, carrier, infected, and recovered. The model predicts the nonnegative equilibrium points and reproduction number, i.e., the Meningitis-Free Equilibrium (MFE), and Meningitis-Existing Equilibrium (MEE). For the stochastic version of the existing deterministic model, the two methodologies studied are transition… More >

Gamze Yıldırım^1,2, Şuayip Yüzbaşı^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 281-310, 2024, DOI:10.32604/cmes.2024.052181 - 20 August 2024

Abstract In this study, a numerical method based on the Pell-Lucas polynomials (PLPs) is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment. The HIV/AIDS mathematical model with a treatment compartment is divided into five classes, namely, susceptible patients (S), HIV-positive individuals (I), individuals with full-blown AIDS but not receiving ARV treatment (A), individuals being treated (T), and individuals who have changed their sexual habits sufficiently (R). According to the method, by utilizing the PLPs and the collocation points, we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into… More >

Saima Rashid^1,2,*, Fahd Jarad^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 2289-2327, 2024, DOI:10.32604/cmes.2023.028773 - 11 March 2024

Abstract Because of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic More >

Muhammad Shoaib Arif^1,2,*, Kamaleldin Abodayeh¹, Yasir Nawaz²

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1405-1425, 2024, DOI:10.32604/cmes.2023.028946 - 17 November 2023

Abstract This work aimed to construct an epidemic model with fuzzy parameters. Since the classical epidemic model does not elaborate on the successful interaction of susceptible and infective people, the constructed fuzzy epidemic model discusses the more detailed versions of the interactions between infective and susceptible people. The next-generation matrix approach is employed to find the reproduction number of a deterministic model. The sensitivity analysis and local stability analysis of the system are also provided. For solving the fuzzy epidemic model, a numerical scheme is constructed which consists of three time levels. The numerical scheme has More >

Ahmed H. Msmali¹, Fazal Dayan^2,*, Muhammad Rafiq³, Nauman Ahmed⁴, Abdullah Ali H. Ahmadini¹, Hassan A. Hamali⁵

CMC-Computers, Materials & Continua, Vol.77, No.2, pp. 2251-2269, 2023, DOI:10.32604/cmc.2023.040266 - 29 November 2023

Abstract In this article, a Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is considered. The equilibrium analysis and reproduction number are studied. The conventional models have made assumptions of homogeneity in disease transmission that contradict the actual reality. However, it is crucial to consider the heterogeneity of the transmission rate when modeling disease dynamics. Describing the heterogeneity of disease transmission mathematically can be achieved by incorporating fuzzy theory. A numerical scheme nonstandard, finite difference (NSFD) approach is developed for the studied model and the results of numerical simulations are presented. Simulations of the constructed scheme are presented. The positivity,… More >

Yu-Ming Chu¹, Sobia Sultana², Saima Rashid^3,*, Mohammed Shaaf Alharthi⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2427-2464, 2023, DOI:10.32604/cmes.2023.028771 - 03 August 2023

Abstract Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous. Two examples are the spread of Spanish flu and COVID-19. The aim of this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators. Firstly, the strength number of the deterministic case is carried out. Then, for the stochastic model, we show that there is a critical number that can predict virus persistence and infection eradication. Because of the peculiarity of More >

Maha Noorwali¹, Mohammed Shehu Shagari^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1937-1956, 2023, DOI:10.32604/cmes.2023.028239 - 26 June 2023

Abstract The real world is filled with uncertainty, vagueness, and imprecision. The concepts we meet in everyday life are vague rather than precise. In real-world situations, if a model requires that conclusions drawn from it have some bearings on reality, then two major problems immediately arise, viz. real situations are not usually crisp and deterministic; complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously, process and understand. Conventional mathematical tools which require all inferences to be exact, are not always efficient to handle imprecisions in a wide variety of… More >

Ali Raza¹, Dumitru Baleanu^2,3,4, Zafar Ullah Khan⁵, Muhammad Mohsin^6,*, Nauman Ahmed⁷, Muhammad Rafiq⁸, Pervez Anwar⁹

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 257-275, 2023, DOI:10.32604/cmes.2023.023231 - 05 January 2023

Abstract Most developing countries such as Afghanistan, Pakistan, India, Bangladesh, and many more are still fighting against poliovirus. According to the World Health Organization, approximately eighteen million people have been infected with poliovirus in the last two decades. In Asia, still, some countries are suffering from the virus. The stochastic behavior of the poliovirus through the transition probabilities and non-parametric perturbation with fundamental properties are studied. Some basic properties of the deterministic model are studied, equilibria, local stability around the stead states, and reproduction number. Euler Maruyama, stochastic Euler, and stochastic Runge-Kutta study the behavior of More >