Analysis of COVID-19 mathematical model for predicting the impact of control measures in Rwanda

Mpinganzima, Lydie; Ntaganda, Jean Marie; Banzi, Wellars; Muhirwa, Jean Pierre; Nannyonga, Betty; Niyobuhungiro, Japhet; Rutaganda, Eric

doi:10.1016/j.imu.2023.101195

Cited by 2 publications

(1 citation statement)

References 14 publications

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“…For more generalization, the Caputo fractional order derivative model has been developed to fully describe COVID-19. Nazir et al [11] studied the fractional model using a modified Euler method and Mpinganzima et al [12,13] numerically investigated the prediction model in Rwanda for the impact of control measures. Abioye et al [14] analyzed the mathematical model for malaria and COVID-19 using a two-step Lagrange interpolation polynomial approximate method.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Investigation of the Infection Dynamics of COVID-19 Using the Fractional Differential Quadrature Method

Mohamed,

Mabrouk,

Rashed

2023

Computation

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In recent times, the global community has been faced with the unprecedented challenge of the coronavirus disease (COVID-19) pandemic, which has had a profound and enduring impact on both global health and the global economy. The utilization of mathematical modeling has become an essential instrument in the characterization and understanding of the dynamics associated with infectious illnesses. In this study, the utilization of the differential quadrature method (DQM) was employed in order to anticipate the characterization of the dynamics of COVID-19 through a fractional mathematical model. Uniform and non-uniform polynomial differential quadrature methods (PDQMs) and a discrete singular convolution method (DSCDQM) were employed in the examination of the dynamics of COVID-19 in vulnerable, exposed, deceased, asymptomatic, and recovered persons. An analysis was conducted to compare the methodologies used in this study, as well as the modified Euler method, in order to highlight the superior efficiency of the DQM approach in terms of code-execution times. The results demonstrated that the fractional order significantly influenced the outcomes. As the fractional order tended towards unity, the anticipated numbers of vulnerable, exposed, deceased, asymptomatic, and recovered individuals increased. During the initial week of the inquiry, there was a substantial rise in the number of individuals who contracted COVID-19, which was primarily attributed to the disease’s high transmission rate. As a result, there was an increase in the number of individuals who recovered, in tandem with the rise in the number of infected individuals. These results highlight the importance of the fractional order in influencing the dynamics of COVID-19. The utilization of the DQM approach, characterized by its proficient code-execution durations, provided significant insights into the dynamics of COVID-19 among diverse population cohorts and enhanced our comprehension of the evolution of the pandemic. The proposed method was efficient in dealing with ordinary differential equations (ODEs), partial differential equations (PDEs), and fractional differential equations (FDEs), in either linear or nonlinear forms. In addition, the stability of the DQM and its validity were verified during the present study. Moreover, the error analysis showed that DQM has better error percentages in many applications than other relevant techniques.

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Section: Introductionmentioning

confidence: 99%

Mathematical Investigation of the Infection Dynamics of COVID-19 Using the Fractional Differential Quadrature Method

Mohamed,

Mabrouk,

Rashed

2023

Computation

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Dynamical analysis of a novel fractional order SIDARTHE epidemic model of COVID-19 with the Caputo–Fabrizio(CF) derivative

Zhao,

Li,

Kang

et al. 2024

Adv Cont Discr Mod

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Fabrizio and Caputo suggested an extraordinary definition of fractional derivative, which has been used in many fields. The SIDARTHE infectious disease model with regard to COVID-19 is studied by the new notion in this paper. Making use of the Banach fixed point theorem, the existence and uniqueness of the model’s solution are demonstrated. Then, an efficient method is utilized to deduce the iterative scheme. Finally, some numerical simulations of the model under various fractional orders and parameters are shown. From the computed result, we can see that it not only supports the theoretical demonstration, but also has an intensive insight into the characteristics of the model.

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Analysis of COVID-19 mathematical model for predicting the impact of control measures in Rwanda

Cited by 2 publications

References 14 publications

Mathematical Investigation of the Infection Dynamics of COVID-19 Using the Fractional Differential Quadrature Method

Mathematical Investigation of the Infection Dynamics of COVID-19 Using the Fractional Differential Quadrature Method

Dynamical analysis of a novel fractional order SIDARTHE epidemic model of COVID-19 with the Caputo–Fabrizio(CF) derivative

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