Ali Raza^1,2,*, Dumitru Baleanu^3,4, Muhammad Rafiq⁵, Syed Zaheer Abbas⁶, Abubakar Siddique⁶, Umer Javed⁸, Mehvish Naz⁷, Arooj Fatima⁶, Tayyba Munawar⁶, Hira Batool⁶, Zaighum Nazir⁶

CMC-Computers, Materials & Continua, Vol.71, No.2, pp. 3621-3634, 2022, DOI:10.32604/cmc.2022.023286 - 07 December 2021

Abstract Cancer is a common term for many diseases that can affect any part of the body. In 2020, ten million people will die due to cancer. A worldwide leading cause of death is cancer by the World Health Organization (WHO) report. Interaction of cancer cells, viral therapy, and immune response are identified in this model. Mathematical and computational modeling is an effective tool to predict the dynamics of cancer virotherapy. The cell population is categorized into three parts like uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). The modeling of More >

Kamaledin Abodayeh¹, Ali Raza^2,3,*, Muhammad Rafiq⁴, Muhammad Shoaib Arif⁵, Muhammad Naveed⁵, Zunir Zeb³, Syed Zaheer Abbas³, Kiran Shahzadi³, Sana Sarwar³, Qasim Naveed³, Badar Ul Zaman³, Muhammad Mohsin⁶

CMC-Computers, Materials & Continua, Vol.70, No.3, pp. 6073-6088, 2022, DOI:10.32604/cmc.2022.020732 - 11 October 2021

Abstract Pneumonia is a highly transmissible disease in children. According to the World Health Organization (WHO), the most affected regions include south Asia and sub-Saharan Africa. Worldwide, 15% of pediatric deaths can be attributed to pneumonia. Computing techniques have a significant role in science, engineering, and many other fields. In this study, we focused on the efficiency of numerical techniques via computer programs. We studied the dynamics of the pneumonia-like infections of epidemic models using numerical techniques. We discuss two types of analysis: dynamical and numerical. The dynamical analysis included positivity, boundedness, local stability, reproduction number, More >

Muhammad Naveed^1,*, Dumitru Baleanu^2,3, Ali Raza⁴, Muhammad Rafiq⁵, Atif Hassan Soori¹

CMC-Computers, Materials & Continua, Vol.70, No.2, pp. 3415-3431, 2022, DOI:10.32604/cmc.2022.020112 - 27 September 2021

Abstract Through the study, the nonlinear delayed modelling has vital significance in the different field of allied sciences like computational biology, computational chemistry, computational physics, computational economics and many more. Polio is a contagious viral illness that in its most severe form causes nerve injury leading to paralysis, difficulty breathing and sometimes death. In recent years, developing regions like Asia, Africa and sub-continents facing a dreadful situation of poliovirus. That is the reason we focus on the treatment of the polio epidemic model with different delay strategies in this article. Polio delayed epidemic model is categorized More >

Ali Raza¹, Muhammad Rafiq², Dalal Alrowaili³, Nauman Ahmed⁴, Ilyas Khan^5,*, Kottakkaran Sooppy Nisar⁶, Muhammad Mohsin⁷

CMC-Computers, Materials & Continua, Vol.70, No.1, pp. 1649-1666, 2022, DOI:10.32604/cmc.2022.019148 - 07 September 2021

Abstract Nonlinear modelling has a significant role in different disciplines of sciences such as behavioral, social, physical and biological sciences. The structural properties are also needed for such types of disciplines, as dynamical consistency, positivity and boundedness are the major requirements of the models in these fields. One more thing, this type of nonlinear model has no explicit solutions. For the sake of comparison its computation will be done by using different computational techniques. Regrettably, the aforementioned structural properties have not been restored in the existing computational techniques in literature. Therefore, the construction of structural preserving… More >

Muhammad Farman¹, Ali Akgül^2,*, Aqeel Ahmad¹, Dumitru Baleanu^3,4,5, Muhammad Umer Saleem⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 753-769, 2021, DOI:10.32604/cmes.2021.014882 - 19 April 2021

Abstract COVID-19 acts as a serious challenge to the whole world. Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease. We analyze the diseases free and endemic equilibrium point including stability of the model. The certain threshold value of the basic reproduction number R₀ is found to observe whether population is in disease free state or endemic state. Moreover, the epidemic peak has been obtained and we expect a considerable number of cases. Finally, some numerical More >

Prasantha Bharathi Dhandapani¹, Dumitru Baleanu^2,3,4,*, Jayakumar Thippan¹, Vinoth Sivakumar¹

Computer Systems Science and Engineering, Vol.37, No.3, pp. 331-346, 2021, DOI:10.32604/csse.2021.015619 - 08 March 2021

Abstract In this research, we propose a new change in classical epidemic models by including the change in the rate of death in the overall population. The existing models like Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) include the death rate as one of the parameters to estimate the change in susceptible, infected and recovered populations. Actually, because of the deficiencies in immunity, even the ordinary flu could cause death. If people’s disease resistance is strong, then serious diseases may not result in mortalities. The classical model always assumes a closed system where there is no new birth… More >

Naveed Shahid^1,2, Dumitru Baleanu^3,4,5, Nauman Ahmed^1,2, Tahira Sumbal Shaikh⁶, Ali Raza^7,*, Muhammad Sajid Iqbal¹, Muhammad Rafiq⁸, Muhammad Aziz-ur Rehman²

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 1713-1728, 2021, DOI:10.32604/cmc.2021.014191 - 05 February 2021

Abstract The novel coronavirus disease, coined as COVID-19, is a murderous and infectious disease initiated from Wuhan, China. This killer disease has taken a large number of lives around the world and its dynamics could not be controlled so far. In this article, the spatio-temporal compartmental epidemic model of the novel disease with advection and diffusion process is projected and analyzed. To counteract these types of diseases or restrict their spread, mankind depends upon mathematical modeling and medicine to reduce, alleviate, and anticipate the behavior of disease dynamics. The existence and uniqueness of the solution for… More >

Umbreen Fatima¹, Dumitru Baleanu^2,3,4, Nauman Ahmed^5,8, Shumaila Azam⁵, Ali Raza^6,*, Muhammad Rafiq⁷, Muhammad Aziz-ur Rehman⁸

CMC-Computers, Materials & Continua, Vol.66, No.3, pp. 3183-3194, 2021, DOI:10.32604/cmc.2021.012666 - 28 December 2020

Abstract Reaction–diffusion systems are mathematical models which link to several physical phenomena. The most common is the change in space and time of the meditation of one or more materials. Reaction–diffusion modeling is a substantial role in the modeling of computer propagation like infectious diseases. We investigated the transmission dynamics of the computer virus in which connected to each other through network globally. The current study devoted to the structure-preserving analysis of the computer propagation model. This manuscript is devoted to finding the numerical investigation of the reaction–diffusion computer virus epidemic model with the help of a More >

Ali Raza¹, Muhammad Rafiq², Nauman Ahmed³, Ilyas Khan^{4, *}, Kottakkaran Sooppy Nisar⁵, Zafar Iqbal³

CMC-Computers, Materials & Continua, Vol.65, No.1, pp. 263-278, 2020, DOI:10.32604/cmc.2020.011289 - 23 July 2020

Abstract In this manuscript, we consider a stochastic smoking epidemic model from behavioural sciences. Also, we develop a structure preserving numerical method to describe the dynamics of stochastic smoking epidemic model in a human population. The structural properties of a physical system include positivity, boundedness and dynamical consistency. These properties play a vital role in non-linear dynamics. The solution for nonlinear stochastic models necessitates the conservation of these properties. Unfortunately, the aforementioned properties of the model have not been restored in the existing stochastic methods. Therefore, it is essential to construct a structure preserving numerical method More >

Muhammad Naveed^{1, *}, Dumitru Baleanu^{2, 3, 4}, Muhammad Rafiq⁵, Ali Raza⁶, Atif Hassan Soori¹, Nauman Ahmed⁷

CMC-Computers, Materials & Continua, Vol.65, No.1, pp. 225-241, 2020, DOI:10.32604/cmc.2020.011534 - 23 July 2020

Abstract Mathematical delay modelling has a significant role in the different disciplines such as behavioural, social, physical, biological engineering, and bio-mathematical sciences. The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus (COVID-19). Due to the unavailability of vaccines for the coronavirus worldwide, delay factors such as social distance, quarantine, travel restrictions, extended holidays, hospitalization, and isolation have contributed to controlling the coronavirus epidemic. We have analysed the reproduction number and its sensitivity to parameters. If, More >