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

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 or death, no immigration or… 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

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 the proposed system are investigated.… 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

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 reliable technique. The designed… 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

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 for a reliable analysis of… 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

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 >

Muhammad Shoaib Arif^1,*, Ali Raza^1,2, Kamaleldin Abodayeh³, Muhammad Rafiq⁴, Mairaj Bibi⁵, Amna Nazeer⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 477-491, 2020, DOI:10.32604/cmes.2020.011121

Abstract The essential features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. The aim of our paper, to achieve the comparison analysis of the stochastic susceptible, infected recovered epidemic model. The stochastic modelling is a realistic way to study the dynamics of compartmental modelling as compared to deterministic modelling. The effect of reproduction number has also observed in the stochastic susceptible, infected recovered epidemic model. For comparison analysis, we developed some explicit stochastic techniques, but they are the time-dependent techniques. The implicitly driven… More >

Wasfi Shatanawi^{1, 2, 3}, Muhammad Shoaib Arif^{4, *}, Ali Raza⁴, Muhammad Rafiq⁵, Mairaj Bibi⁶, Javeria Nawaz Abbasi⁶

CMC-Computers, Materials & Continua, Vol.64, No.2, pp. 797-811, 2020, DOI:10.32604/cmc.2020.010759

Abstract The structure-preserving features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. Unfortunately, the existing stochastic approaches in literature do not restore aforesaid structure-preserving features, particularly for the stochastic models. Therefore, these gaps should be occupied up in literature, by constructing the structure-preserving features preserving numerical approach. This writing aims to describe the structure-preserving dynamics of the stochastic model. We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling. The usual explicit… More >