Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever

Huei-Li Lin; Kuang-Hui Lin; Yu-Chiau Shyu; Feng-Bin Wang

doi:doi:10.11648/j.acm.20231202.11

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Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever

Huei-Li Lin, Kuang-Hui Lin, Yu-Chiau Shyu, Feng-Bin Wang

Published in Applied and Computational Mathematics (Volume 12, Issue 2)

Received: 13 March 2023 Accepted: 3 April 2023 Published: 11 April 2023

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Abstract

Typhoid fever is a disease caused by the bacteria Salmonella Typhi through the ingestion of contaminated food or water, and it is still serious in developing countries. The infection routes include both human-to-human transmission and environment-to-human transmission. It was observed that higher incidence of typhoid fever occur during the rainy season and people living near water bodies may have a higher rate of typhoid infection. On the other hand, asymptomatically infected individuals also play a central role in the transmission of typhoid since they are not experiencing any symptoms but they are able to shed S. Typhi into the environment for years. Thus, a well-described model of the Typhoid transmission should include the asymptomatical compartment and the factors of spatial homogeneity and seasonality. This motivates us to develop a periodic two-patch system to investigate the spatial and seasonal effects on the transmission of Typhoid fever, in which the bacteria in the environment is included, and the population of human is divided into five classes, namely, susceptible individuals, infected individuals, carrier individuals, individuals under treatment and recovered individuals. We first introduce the basic reproduction number for the model, then we show that the extinction/persistence of Typhoid can be determined by R₀. Our numerical results indicate that an outbreak of Typhoid fever in a two-patch environment could be eliminated if migration between patches is prohibited. Finally, we also numerically observe that the infection risks of Typhoid may be underestimated if seasonal effects are ignored.

Published in	Applied and Computational Mathematics (Volume 12, Issue 2)
DOI	10.11648/j.acm.20231202.11
Page(s)	26-41
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2023. Published by Science Publishing Group

Keywords

Typhoid Fever, Spatial Homogeneity, Seasonal Effects, Basic Reproduction Number, Threshold Dynamics

References

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APA Style

Huei-Li Lin, Kuang-Hui Lin, Yu-Chiau Shyu, Feng-Bin Wang. (2023). Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever. Applied and Computational Mathematics, 12(2), 26-41. https://doi.org/10.11648/j.acm.20231202.11

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ACS Style

Huei-Li Lin; Kuang-Hui Lin; Yu-Chiau Shyu; Feng-Bin Wang. Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever. Appl. Comput. Math. 2023, 12(2), 26-41. doi: 10.11648/j.acm.20231202.11

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AMA Style

Huei-Li Lin, Kuang-Hui Lin, Yu-Chiau Shyu, Feng-Bin Wang. Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever. Appl Comput Math. 2023;12(2):26-41. doi: 10.11648/j.acm.20231202.11

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@article{10.11648/j.acm.20231202.11,
  author = {Huei-Li Lin and Kuang-Hui Lin and Yu-Chiau Shyu and Feng-Bin Wang},
  title = {Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever},
  journal = {Applied and Computational Mathematics},
  volume = {12},
  number = {2},
  pages = {26-41},
  doi = {10.11648/j.acm.20231202.11},
  url = {https://doi.org/10.11648/j.acm.20231202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20231202.11},
  abstract = {Typhoid fever is a disease caused by the bacteria Salmonella Typhi through the ingestion of contaminated food or water, and it is still serious in developing countries. The infection routes include both human-to-human transmission and environment-to-human transmission. It was observed that higher incidence of typhoid fever occur during the rainy season and people living near water bodies may have a higher rate of typhoid infection. On the other hand, asymptomatically infected individuals also play a central role in the transmission of typhoid since they are not experiencing any symptoms but they are able to shed S. Typhi into the environment for years. Thus, a well-described model of the Typhoid transmission should include the asymptomatical compartment and the factors of spatial homogeneity and seasonality. This motivates us to develop a periodic two-patch system to investigate the spatial and seasonal effects on the transmission of Typhoid fever, in which the bacteria in the environment is included, and the population of human is divided into five classes, namely, susceptible individuals, infected individuals, carrier individuals, individuals under treatment and recovered individuals. We first introduce the basic reproduction number for the model, then we show that the extinction/persistence of Typhoid can be determined by R0. Our numerical results indicate that an outbreak of Typhoid fever in a two-patch environment could be eliminated if migration between patches is prohibited. Finally, we also numerically observe that the infection risks of Typhoid may be underestimated if seasonal effects are ignored.},
 year = {2023}
}

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TY  - JOUR
T1  - Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever
AU  - Huei-Li Lin
AU  - Kuang-Hui Lin
AU  - Yu-Chiau Shyu
AU  - Feng-Bin Wang
Y1  - 2023/04/11
PY  - 2023
N1  - https://doi.org/10.11648/j.acm.20231202.11
DO  - 10.11648/j.acm.20231202.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 26
EP  - 41
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20231202.11
AB  - Typhoid fever is a disease caused by the bacteria Salmonella Typhi through the ingestion of contaminated food or water, and it is still serious in developing countries. The infection routes include both human-to-human transmission and environment-to-human transmission. It was observed that higher incidence of typhoid fever occur during the rainy season and people living near water bodies may have a higher rate of typhoid infection. On the other hand, asymptomatically infected individuals also play a central role in the transmission of typhoid since they are not experiencing any symptoms but they are able to shed S. Typhi into the environment for years. Thus, a well-described model of the Typhoid transmission should include the asymptomatical compartment and the factors of spatial homogeneity and seasonality. This motivates us to develop a periodic two-patch system to investigate the spatial and seasonal effects on the transmission of Typhoid fever, in which the bacteria in the environment is included, and the population of human is divided into five classes, namely, susceptible individuals, infected individuals, carrier individuals, individuals under treatment and recovered individuals. We first introduce the basic reproduction number for the model, then we show that the extinction/persistence of Typhoid can be determined by R0. Our numerical results indicate that an outbreak of Typhoid fever in a two-patch environment could be eliminated if migration between patches is prohibited. Finally, we also numerically observe that the infection risks of Typhoid may be underestimated if seasonal effects are ignored.
VL  - 12
IS  - 2
ER  -

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Author Information

Huei-Li Lin

Department of Natural Science in the Center for General Education, Chang Gung University, Taoyuan, Taiwan
Kuang-Hui Lin

Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
Yu-Chiau Shyu

Community Medicine Research Center, Chang Gung Memorial Hospital, Keelung Branch, Keelung, Taiwan
Feng-Bin Wang

Department of Natural Science in the Center for General Education, Chang Gung University, Taoyuan, Taiwan

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APA Style

Huei-Li Lin, Kuang-Hui Lin, Yu-Chiau Shyu, Feng-Bin Wang. (2023). Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever. Applied and Computational Mathematics, 12(2), 26-41. https://doi.org/10.11648/j.acm.20231202.11

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ACS Style

Huei-Li Lin; Kuang-Hui Lin; Yu-Chiau Shyu; Feng-Bin Wang. Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever. Appl. Comput. Math. 2023, 12(2), 26-41. doi: 10.11648/j.acm.20231202.11

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AMA Style

Huei-Li Lin, Kuang-Hui Lin, Yu-Chiau Shyu, Feng-Bin Wang. Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever. Appl Comput Math. 2023;12(2):26-41. doi: 10.11648/j.acm.20231202.11

Copy | Download

@article{10.11648/j.acm.20231202.11,
  author = {Huei-Li Lin and Kuang-Hui Lin and Yu-Chiau Shyu and Feng-Bin Wang},
  title = {Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever},
  journal = {Applied and Computational Mathematics},
  volume = {12},
  number = {2},
  pages = {26-41},
  doi = {10.11648/j.acm.20231202.11},
  url = {https://doi.org/10.11648/j.acm.20231202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20231202.11},
  abstract = {Typhoid fever is a disease caused by the bacteria Salmonella Typhi through the ingestion of contaminated food or water, and it is still serious in developing countries. The infection routes include both human-to-human transmission and environment-to-human transmission. It was observed that higher incidence of typhoid fever occur during the rainy season and people living near water bodies may have a higher rate of typhoid infection. On the other hand, asymptomatically infected individuals also play a central role in the transmission of typhoid since they are not experiencing any symptoms but they are able to shed S. Typhi into the environment for years. Thus, a well-described model of the Typhoid transmission should include the asymptomatical compartment and the factors of spatial homogeneity and seasonality. This motivates us to develop a periodic two-patch system to investigate the spatial and seasonal effects on the transmission of Typhoid fever, in which the bacteria in the environment is included, and the population of human is divided into five classes, namely, susceptible individuals, infected individuals, carrier individuals, individuals under treatment and recovered individuals. We first introduce the basic reproduction number for the model, then we show that the extinction/persistence of Typhoid can be determined by R0. Our numerical results indicate that an outbreak of Typhoid fever in a two-patch environment could be eliminated if migration between patches is prohibited. Finally, we also numerically observe that the infection risks of Typhoid may be underestimated if seasonal effects are ignored.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever
AU  - Huei-Li Lin
AU  - Kuang-Hui Lin
AU  - Yu-Chiau Shyu
AU  - Feng-Bin Wang
Y1  - 2023/04/11
PY  - 2023
N1  - https://doi.org/10.11648/j.acm.20231202.11
DO  - 10.11648/j.acm.20231202.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 26
EP  - 41
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20231202.11
AB  - Typhoid fever is a disease caused by the bacteria Salmonella Typhi through the ingestion of contaminated food or water, and it is still serious in developing countries. The infection routes include both human-to-human transmission and environment-to-human transmission. It was observed that higher incidence of typhoid fever occur during the rainy season and people living near water bodies may have a higher rate of typhoid infection. On the other hand, asymptomatically infected individuals also play a central role in the transmission of typhoid since they are not experiencing any symptoms but they are able to shed S. Typhi into the environment for years. Thus, a well-described model of the Typhoid transmission should include the asymptomatical compartment and the factors of spatial homogeneity and seasonality. This motivates us to develop a periodic two-patch system to investigate the spatial and seasonal effects on the transmission of Typhoid fever, in which the bacteria in the environment is included, and the population of human is divided into five classes, namely, susceptible individuals, infected individuals, carrier individuals, individuals under treatment and recovered individuals. We first introduce the basic reproduction number for the model, then we show that the extinction/persistence of Typhoid can be determined by R0. Our numerical results indicate that an outbreak of Typhoid fever in a two-patch environment could be eliminated if migration between patches is prohibited. Finally, we also numerically observe that the infection risks of Typhoid may be underestimated if seasonal effects are ignored.
VL  - 12
IS  - 2
ER  -

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