Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda

Isaac Kwasi Adu; Fredrick Asenso Wireko; Samuel Akwasi Adarkwa; Gerald Ohene Agyekum

doi:10.53391/mmnsa.1514196

EN

Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda

Abstract

In this article, we seek to formulate a robust mathematical model to study the Ebola disease through fractal-fractional operators. The study thus incorporates the transmission rate in the treatment centers and the relapse rate, since the Ebola virus persists or mostly hides in the immunologically protected sites of survivors. The Ebola virus disease (EVD) is one of the infectious diseases that has recorded a high death rate in countries where it is endemic, and Uganda is not an exception. The world at large has suffered from this deadly disease since 1976 when it was declared epidemic by the World Health Organization. The study employed fractal-fractional operators to identify the epidemiological patterns of EVD, especially in treatment centers and relapse. Memory loss and relapse are mostly observed in EVD survivors and this justifies the use of fractional operators to capture the true dynamics of the disease. Through dynamical analysis, the model is proven to be positive and bounded in the region. The model is further explicitly shown to have a solution that is unique and stable. The reproduction number was duly computed by using the next-generation matrix approach. By taking EVD epidemic cases in Uganda, the study fitted all parameters to real data. It has been shown through sensitivity index analysis that the transmission rate outside treatment centers and relapse have a significant effect on the endemic state of the disease, as they lead to an increase in the basic reproduction ratio.

Keywords

Ebola, EVD transmission, Caputo derivatives, numerical simulations, Hyers-Ulam stability

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Details

Primary Language

English

Subjects

Biological Mathematics, Complex Systems in Mathematics, Dynamical Systems in Applications

Journal Section

Research Article

Authors

Isaac Kwasi Adu ^*
0009-0001-8417-861X
Ghana

Fredrick Asenso Wireko
Ghana

Samuel Akwasi Adarkwa
Ghana

Gerald Ohene Agyekum
Ghana

Publication Date

September 30, 2024

Submission Date

July 11, 2024

Acceptance Date

September 14, 2024

Published in Issue

Year 2024 Volume: 4 Number: 3

DOI

https://doi.org/10.53391/mmnsa.1514196

IZ

https://izlik.org/JA84JH96CZ

APA

Adu, I. K., Wireko, F. A., Adarkwa, S. A., & Agyekum, G. O. (2024). Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda. Mathematical Modelling and Numerical Simulation With Applications, 4(3), 296-334. https://doi.org/10.53391/mmnsa.1514196

AMA

1.Adu IK, Wireko FA, Adarkwa SA, Agyekum GO. Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda. MMNSA. 2024;4(3):296-334. doi:10.53391/mmnsa.1514196

Chicago

Adu, Isaac Kwasi, Fredrick Asenso Wireko, Samuel Akwasi Adarkwa, and Gerald Ohene Agyekum. 2024. “Mathematical Analysis of Ebola Considering Transmission at Treatment Centres and Survivor Relapse Using Fractal-Fractional Caputo Derivatives in Uganda”. Mathematical Modelling and Numerical Simulation With Applications 4 (3): 296-334. https://doi.org/10.53391/mmnsa.1514196.

EndNote

Adu IK, Wireko FA, Adarkwa SA, Agyekum GO (September 1, 2024) Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda. Mathematical Modelling and Numerical Simulation with Applications 4 3 296–334.

IEEE

[1]I. K. Adu, F. A. Wireko, S. A. Adarkwa, and G. O. Agyekum, “Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda”, MMNSA, vol. 4, no. 3, pp. 296–334, Sept. 2024, doi: 10.53391/mmnsa.1514196.

ISNAD

Adu, Isaac Kwasi - Wireko, Fredrick Asenso - Adarkwa, Samuel Akwasi - Agyekum, Gerald Ohene. “Mathematical Analysis of Ebola Considering Transmission at Treatment Centres and Survivor Relapse Using Fractal-Fractional Caputo Derivatives in Uganda”. Mathematical Modelling and Numerical Simulation with Applications 4/3 (September 1, 2024): 296-334. https://doi.org/10.53391/mmnsa.1514196.

JAMA

1.Adu IK, Wireko FA, Adarkwa SA, Agyekum GO. Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda. MMNSA. 2024;4:296–334.

MLA

Adu, Isaac Kwasi, et al. “Mathematical Analysis of Ebola Considering Transmission at Treatment Centres and Survivor Relapse Using Fractal-Fractional Caputo Derivatives in Uganda”. Mathematical Modelling and Numerical Simulation With Applications, vol. 4, no. 3, Sept. 2024, pp. 296-34, doi:10.53391/mmnsa.1514196.

Vancouver

1.Isaac Kwasi Adu, Fredrick Asenso Wireko, Samuel Akwasi Adarkwa, Gerald Ohene Agyekum. Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda. MMNSA. 2024 Sep. 1;4(3):296-334. doi:10.53391/mmnsa.1514196