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Calculation of final size for vector-transmitted epidemic model

1 College of Science and Engineering, Aoyama Gakuin University, Sagamihara 252-5258, Japan
2 Faculty of Advanced Life Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan
3 JST PRESTO, Kawaguchi-shi, Saitama 332-0012, Japan

Special Issues: Mathematical Modeling to Solve the Problems in Life Sciences

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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Keywords vector-transmitted infection; epidemic model; final size equation; basic reproduction number; quasi steady state approximation

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

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