Advanced analysis in epidemiological modeling: detection of waves

Abdon Atangana; Seda İğret Araz; Abdon Atangana; Seda İğret Araz

doi:10.3934/math.2022992

AIMS Mathematics

2022, Volume 7, Issue 10: 18010-18030. doi: 10.3934/math.2022992

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Advanced analysis in epidemiological modeling: detection of waves

Abdon Atangana ^{1,2
,
,},
Seda İğret Araz ^1,3

1.
Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
3.
Faculty of Education, Siirt University, Siirt 56100, Turkey

Received: 16 February 2022 Revised: 23 June 2022 Accepted: 18 July 2022 Published: 08 August 2022
MSC : 26A33, 65C40, 92D30

Mathematical concepts have been used in the last decades to predict the behavior of the spread of infectious diseases. Among them, the reproductive number concept has been used in several published papers to study the stability of the mathematical model used to predict the spread patterns. Some conditions were suggested to conclude if there would be either stability or instability. An analysis was also meant to determine conditions under which infectious classes will increase or die out. Some authors pointed out limitations of the reproductive number, as they presented its inability to help predict the spread patterns. The concept of strength number and analysis of second derivatives of the mathematical models were suggested as additional tools to help detect waves. This paper aims to apply these additional analyses in a simple model to predict the future.
- strength number,
- second derivative analysis,
- waves,
- piecewise modeling
Citation: Abdon Atangana, Seda İğret Araz. Advanced analysis in epidemiological modeling: detection of waves[J]. AIMS Mathematics, 2022, 7(10): 18010-18030. doi: 10.3934/math.2022992

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Abstract

Mathematical concepts have been used in the last decades to predict the behavior of the spread of infectious diseases. Among them, the reproductive number concept has been used in several published papers to study the stability of the mathematical model used to predict the spread patterns. Some conditions were suggested to conclude if there would be either stability or instability. An analysis was also meant to determine conditions under which infectious classes will increase or die out. Some authors pointed out limitations of the reproductive number, as they presented its inability to help predict the spread patterns. The concept of strength number and analysis of second derivatives of the mathematical models were suggested as additional tools to help detect waves. This paper aims to apply these additional analyses in a simple model to predict the future.

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