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 Rafiq¹, Ali Ahmadian^{2, *}, Ali Raza³, Dumitru Baleanu⁴, Muhammad Sarwar Ahsan¹, Mohammad Hasan Abdul Sathar⁵

CMC-Computers, Materials & Continua, Vol.65, No.1, pp. 33-51, 2020, DOI:10.32604/cmc.2020.010893

Abstract Nonlinear stochastic modeling has significant role in the all discipline of sciences. The essential control measuring features of modeling are positivity, boundedness and dynamical consistency. Unfortunately, the existing stochastic methods in literature do not restore aforesaid control measuring features, particularly for the stochastic models. Therefore, these gaps should be occupied up in literature, by constructing the control measuring features numerical method. We shall present a numerical control measures for stochastic malaria model in this manuscript. The results of the stochastic model are discussed in contrast of its equivalent deterministic model. If the basic reproduction number is less than one, then… 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 >

Kamaleldin Abodayeh¹, Ali Raza^{2, *}, Muhammad Shoaib Arif², Muhammad Rafiq³, Mairaj Bibi⁴, Muhammad Mohsin⁵

CMC-Computers, Materials & Continua, Vol.62, No.3, pp. 1125-1142, 2020, DOI:10.32604/cmc.2020.08885

Abstract This paper aims to perform a comparison of deterministic and stochastic models. The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model. Also, the deterministic solution is itself mean of the stochastic solution of the model. For numerical analysis, first, we developed some explicit stochastic methods, but unfortunately, they do not remain consistent in certain situations. Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model. The proposed method is independent of the choice of parameters and behaves well in all scenarios. So, some… More >