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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2018 / Volume: 47 Issue: 6

Numerical solution and stability analysis of a nonlinear vaccination model with historical effects

Davood Rostamy
Ehsan Mottaghi
Sayfa
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Yayın Tarihi
2018-12-12
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Our results show that historical effects play an important role on the disease spreading.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we extend the classical vaccination epidemic model from a deterministic framework to a model with historical effects by formulating it as a system of fractional-order differential equations (FDEs).
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Temel Bulgular & Veri:The basic reproduction number $R_0$ of the resulting fractional model is computed and it is shown that if $R_0$ is less than one, the disease-free equilibrium is locally asymptotically stable.
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Sonuç & Katkı:Our results show that historical effects play an important role on the disease spreading.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:epidemic model · fractional-order differential equations · equilibrium points

Abstract

In this paper, we extend the classical vaccination epidemic model from a deterministic framework to a model with historical effects by formulating it as a system of fractional-order differential equations (FDEs). The basic reproduction number $R_0$ of the resulting fractional model is computed and it is shown that if $R_0$ is less than one, the disease-free equilibrium is locally asymptotically stable. Particularly, we analytically calculate a certain threshold-value for $R_0$ and present the existence conditions of endemic equilibrium. By using stability analysis, we prove stability and $\alpha$-stability of the endemic equilibrium points. The proposed model is applied on \emph{Pertussis} disease and the fractional nonlinear system of the model is solved by applying multi-step generalized differential transform method (MSGDTM). Our results show that historical effects play an important role on the disease spreading.

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Bu Makaleye Atıf Yap

Rostamy, D., Mottaghi, E. (2018). Numerical solution and stability analysis of a nonlinear vaccination model with historical effects. Hacettepe Journal of Mathematics and Statistics, Volume: 47 Issue: 6. https://ajindex.com/articles/1402859

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