A Simple SIR Mathematical Model of Malaria Transmission with the Efficacy of the Vaccine

Ghoul, Rafia; He, Jing; Sana, Djaidja; As-Shareef, Ebrahim

doi:10.1145/3290818.3290826

Cited by 1 publication

(2 citation statements)

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“…This part is devoted to obtain the equilibrium points of steady states and stability analysis of systems ( 12)- (14). To that end, we set…”

Section: Mathematical Analysismentioning

confidence: 99%

“…Beretta et al studied mathematically the mortality in children and adults caused by malaria [13]. Rafia et al observed the consequences of vaccination on the dynamics of malaria [14]. In 2017, Traoré et al presented a model to estimate the variation in the intensity of malaria epidemic by considering the seasonal effects and frequent bite rate of mosquitoes [15].…”

Section: Introductionmentioning

confidence: 99%

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Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Ahmed

Macías‐Díaz

Raza³

et al. 2021

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Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R0<1. A similar result is obtained for the endemic equilibrium when R0>1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge–Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note.

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“…This part is devoted to obtain the equilibrium points of steady states and stability analysis of systems ( 12)- (14). To that end, we set…”

Section: Mathematical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Ahmed

Macías‐Díaz

Raza³

et al. 2021

Axioms

View full text Add to dashboard Cite

show abstract

A Simple SIR Mathematical Model of Malaria Transmission with the Efficacy of the Vaccine

Cited by 1 publication

References 3 publications

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

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