Calculation of final size for vector-transmitted epidemic model

Yu Tsubouchi; Yasuhiro Takeuchi; Shinji Nakaoka; Yu Tsubouchi; Yasuhiro Takeuchi; Shinji Nakaoka

doi:10.3934/mbe.2019109

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2219-2232. doi: 10.3934/mbe.2019109

Previous Article Next Article

Research article Special Issues

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

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.
- 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[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2219-2232. doi: 10.3934/mbe.2019109

Related Papers:

Abstract

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.

References

[1]	E. Avila-Vales and B. Buonomo, Analysis of a mosquito-borne disease transmission model with vector stages and nonlinear forces of infection, Ric. di Matem., 64 (2015), 377.
[2]	J. Chen, J. C. Beier and R. S. Cantrell, et al., Modeling the importation and local transmission of vector-borne diseases in florida: The case of zika outbreak in 2016, J. Theor. Biol., 455 (2018), 342–356.
[3]	D. Clancy and A. B. Piunovskiy, An explicit optimal isolation policy for a deterministic epidemic model, Appl. Math. Comput., 163 (2005), 1109–1121.
[4]	J. E. Kim, Y. Choi and C. H. Lee, Effects of climate change on plasmodium vivax malaria transmission dynamics: A mathematical modeling approach, Appl. Math. Comput., 347 (2019), 616–630,
[5]	C. N. Ngonghala, S. Y. D. Valle, R. Zhao and J. Mohammed-Awel, Quantifying the impact of decay in bed-net efficacy on malaria transmission, J. Theor. Biol., 363 (2014), 247 – 261,
[6]	S. Pandey, S. Nanda, A. Vutha and R. Naresh, Modeling the impact of biolarvicides on malaria transmission., J. Theor. Biol., 454 (2018), 396–409.
[7]	S. Side and M. Md. Noorani, A sir model for spread of dengue fever disease (simulation for south sulawesi, indonesia and selangor, malaysia), W. J. Model. Sim., 9 (2013), 96–105.
[8]	K. P. Wijaya and D. Aldila, Learning the seasonality of disease incidences from empirical data, arXiv preprint arXiv:1710.05464.
[9]	L. Allen, An Introduction to Mathematical Biology, Pearson/Prentice Hall, 2007.
[10]	L. Allen, F. Brauer and P. van den Driessche, et al., Mathematical Epidemiology, Lecture Notes in Mathematics, Springer Berlin Heidelberg, 2008.
[11]	O. Diekmann, H. Heesterbeek and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics:, Princeton University Press, 2013.
[12]	M. Iannelli and A. Pugliese, An introduction to mathematical population dynamics : along the trail of Volterra and Lotka, no. 79 in Collana unitext, Springer, 2014.
[13]	N. Nakada, M. Nagata and Y. Dong, et al., Dynamics of tumor immune escape via adaptive change, Nonl. Theor. Appl., 9 (2018), 295–304.

Reader Comments

Your name:*

Email:*
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)