### Mathematical Biosciences and Engineering

2019, Issue 4: 2219-2232. doi: 10.3934/mbe.2019109
Research article Special Issues

# Calculation of final size for vector-transmitted epidemic model

• Received: 30 December 2018 Accepted: 20 February 2019 Published: 15 March 2019
• Calculation of final size of an epidemic model offers a useful estimation for the impact of an epidemic. Despite its usefulness, the majority of practical applications focuses on the classical Kermack McKendrick model for final size calculation. Estimation of final size for different types of epidemics such as vector-transmitted infection is a forthcoming target. In this paper, we derive an explicit form of a final size equation for a vector-transmitted epidemic model. Numerical calculation of a final size equation revealed the existence of a threshold curve which separates a region into two distinct bistable sub-regions if infection induced death is present. In other words, an epidemic outcome can be qualitatively different depending on the initial state of an epidemic.

Citation: Yu Tsubouchi, Yasuhiro Takeuchi, Shinji Nakaoka. Calculation of final size for vector-transmitted epidemic model[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2219-2232. doi: 10.3934/mbe.2019109

### Related Papers:

• Calculation of final size of an epidemic model offers a useful estimation for the impact of an epidemic. Despite its usefulness, the majority of practical applications focuses on the classical Kermack McKendrick model for final size calculation. Estimation of final size for different types of epidemics such as vector-transmitted infection is a forthcoming target. In this paper, we derive an explicit form of a final size equation for a vector-transmitted epidemic model. Numerical calculation of a final size equation revealed the existence of a threshold curve which separates a region into two distinct bistable sub-regions if infection induced death is present. In other words, an epidemic outcome can be qualitatively different depending on the initial state of an epidemic.

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• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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