Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach

Rathgama Guruge Uma Indeewari Meththananda; Naleen Chaminda Ganegoda; Shyam Sanjeewa Nishantha Perera

doi:doi:10.11648/j.mma.20190401.12

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Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach

Rathgama Guruge Uma Indeewari Meththananda, Naleen Chaminda Ganegoda, Shyam Sanjeewa Nishantha Perera

Published in Mathematical Modelling and Applications (Volume 4, Issue 1)

Received: 30 March 2019 Accepted: 14 May 2019 Published: 4 June 2019

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Abstract

Many mathematical models developed through differential equations to describe the age dependent infectiousness of diseases, face the complexity of modelling heterogenic behavior of transmission. There, many of the cases assume the host to stay in the same risk class regardless of the age of the hosts. The proposed model mimics the infectiousness according to the age-scale of an individual via integral equation approach. This model indicates the applicability of Fredholm type integral equations with degenerated kernel. Introducing biological, behavioral and environmental influences provokes to address the accumulating nature of different factors in modelling the risk of getting infected. The risk of getting infected is modeled by the inability of responding with acquired immunity and the accumulated risk given from the other individuals in each age group via the mobility patterns. Within this approach environmental stimulus are modeled via periodic functions in order to describe the stochastic behavior of the spreading capabilities. In this study, the behavioral analysis evaluates the maximum risk of getting infectious in the considered parsimonious approach. And the sensitivity analysis describes the contribution of the mobility risk and stochastic nature on the overall risk. Further the model guides to formulate hypotheses and data collection strategies to measure the risk of a disease.

Published in	Mathematical Modelling and Applications (Volume 4, Issue 1)
DOI	10.11648/j.mma.20190401.12
Page(s)	10-14
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), 2019. Published by Science Publishing Group

Keywords

Age Dependent, Degenerated Kernel, Infectiousness, Integral Equations

References

[1]	N. Grassly, and C. Fraser, “Mathematical models of infectious disease transmission,” Nature Reviews Microbiology, vol. 6, no. 6, pp. 477–487, 2008.
[2]	Dodd, P., Looker, C., Plumb, I., Bond, V., Schaap, A., Shanaube, K., Muyoyeta, M., Vynnycky, E., Godfrey-Faussett, P., Corbett, E., Beyers, N., Ayles, H. and White, R. (2015). Age- and Sex-Specific Social Contact Patterns and Incidence of Mycobacterium tuberculosis Infection. American Journal of Epidemiology, p. kwv160.
[3]	Read, J., Lessler, J., Riley, S., Wang, S., Tan, L., Kwok, K., Guan, Y., Jiang, C. and Cummings, D. (2014). Social mixing patterns in rural and urban areas of southern China. Proceedings of the Royal Society B: Biological Sciences, 281 (1785), pp. 20140268-20140268.
[4]	Pitzer, V. and Lipsitch, M. (2009). Exploring the relationship between incidence and the average age of infection during seasonal epidemics. Journal of Theoretical Biology, 260 (2), pp. 175-185.
[5]	Chan, E. Michael, S. Pani, R. Norman, D. Bundy, P. Vanamail, K. Ramaiah, P. Das, and A. Srividya, “Epifil: a dynamic model of infection and disease in lymphatic filariasis,” The American Journal of Tropical Medicine and Hygiene, vol. 59, no. 4, pp. 606–614, 1998.
[6]	M. Gambhir, and E. Michael, “Complex Ecological Dynamics and Eradicability of the Vector Borne Macroparasitic Disease,” Lymphatic Filariasis. PLoS ONE, vol. 3, no. 8, pp. 100–110, 2008.
[7]	E. Shim, Z. Feng, M. Martcheva and C. Castillo-Chavez, “An age-structured epidemic model of rotavirus with vaccination,” Journal of Mathematical Biology, vol. 53, no. 4, pp. 719–746, 2006.
[8]	R. Norman, M. Chan, A. Srividya, S. Pani, K. Ramaiah, P. Vanamail, E. Michael, P. Das and D. Bundy, “EPIFIL: The development of an age-structured model for describing the transmission dynamics and control of lymphatic filariasis,” Epidemiology and Infection, vol. 124, no. 3, pp. 529–541, 2000.
[9]	J. Murray, An Introduction to Mathematical Biology. New York: Springer, 2001.
[10]	Matt Keeling and Pej Rohani, Modelling Infectious Diseases. New Jersey: Princeton University Press, 2008.
[11]	M. Li and X. Liu, “An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate,” Abstract and Applied Analysis, pp. 1-7, 2014.
[12]	A. Jerri, Introduction to integral equations with applications. New York: Dekker, 1985.
[13]	W. A. Stolk, “Lymphatic Filariasis: Transmission, Treatment and Elimination.” (Ph.D. Thesis), Erasmus University Rotterdam, Netherlands, 2005.

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Rathgama Guruge Uma Indeewari Meththananda, Naleen Chaminda Ganegoda, Shyam Sanjeewa Nishantha Perera. (2019). Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach. Mathematical Modelling and Applications, 4(1), 10-14. https://doi.org/10.11648/j.mma.20190401.12

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ACS Style

Rathgama Guruge Uma Indeewari Meththananda; Naleen Chaminda Ganegoda; Shyam Sanjeewa Nishantha Perera. Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach. Math. Model. Appl. 2019, 4(1), 10-14. doi: 10.11648/j.mma.20190401.12

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AMA Style

Rathgama Guruge Uma Indeewari Meththananda, Naleen Chaminda Ganegoda, Shyam Sanjeewa Nishantha Perera. Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach. Math Model Appl. 2019;4(1):10-14. doi: 10.11648/j.mma.20190401.12

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@article{10.11648/j.mma.20190401.12,
  author = {Rathgama Guruge Uma Indeewari Meththananda and Naleen Chaminda Ganegoda and Shyam Sanjeewa Nishantha Perera},
  title = {Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach},
  journal = {Mathematical Modelling and Applications},
  volume = {4},
  number = {1},
  pages = {10-14},
  doi = {10.11648/j.mma.20190401.12},
  url = {https://doi.org/10.11648/j.mma.20190401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20190401.12},
  abstract = {Many mathematical models developed through differential equations to describe the age dependent infectiousness of diseases, face the complexity of modelling heterogenic behavior of transmission. There, many of the cases assume the host to stay in the same risk class regardless of the age of the hosts. The proposed model mimics the infectiousness according to the age-scale of an individual via integral equation approach. This model indicates the applicability of Fredholm type integral equations with degenerated kernel. Introducing biological, behavioral and environmental influences provokes to address the accumulating nature of different factors in modelling the risk of getting infected. The risk of getting infected is modeled by the inability of responding with acquired immunity and the accumulated risk given from the other individuals in each age group via the mobility patterns. Within this approach environmental stimulus are modeled via periodic functions in order to describe the stochastic behavior of the spreading capabilities. In this study, the behavioral analysis evaluates the maximum risk of getting infectious in the considered parsimonious approach. And the sensitivity analysis describes the contribution of the mobility risk and stochastic nature on the overall risk. Further the model guides to formulate hypotheses and data collection strategies to measure the risk of a disease.},
 year = {2019}
}

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TY  - JOUR
T1  - Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach
AU  - Rathgama Guruge Uma Indeewari Meththananda
AU  - Naleen Chaminda Ganegoda
AU  - Shyam Sanjeewa Nishantha Perera
Y1  - 2019/06/04
PY  - 2019
N1  - https://doi.org/10.11648/j.mma.20190401.12
DO  - 10.11648/j.mma.20190401.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 10
EP  - 14
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20190401.12
AB  - Many mathematical models developed through differential equations to describe the age dependent infectiousness of diseases, face the complexity of modelling heterogenic behavior of transmission. There, many of the cases assume the host to stay in the same risk class regardless of the age of the hosts. The proposed model mimics the infectiousness according to the age-scale of an individual via integral equation approach. This model indicates the applicability of Fredholm type integral equations with degenerated kernel. Introducing biological, behavioral and environmental influences provokes to address the accumulating nature of different factors in modelling the risk of getting infected. The risk of getting infected is modeled by the inability of responding with acquired immunity and the accumulated risk given from the other individuals in each age group via the mobility patterns. Within this approach environmental stimulus are modeled via periodic functions in order to describe the stochastic behavior of the spreading capabilities. In this study, the behavioral analysis evaluates the maximum risk of getting infectious in the considered parsimonious approach. And the sensitivity analysis describes the contribution of the mobility risk and stochastic nature on the overall risk. Further the model guides to formulate hypotheses and data collection strategies to measure the risk of a disease.
VL  - 4
IS  - 1
ER  -

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Author Information

Rathgama Guruge Uma Indeewari Meththananda

Department of Spatial Sciences, General Sir John Kotelawala Defence University, Sooriyawewa, Sri Lanka
Naleen Chaminda Ganegoda

Department of Mathematics, University of Sri Jayewardenepura, Nugegoda, Sri Lanka
Shyam Sanjeewa Nishantha Perera

Research & Development Centre for Mathematical Modeling, Department of Mathematics, University of Colombo, Colombo, Sri Lanka

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APA Style

Rathgama Guruge Uma Indeewari Meththananda, Naleen Chaminda Ganegoda, Shyam Sanjeewa Nishantha Perera. (2019). Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach. Mathematical Modelling and Applications, 4(1), 10-14. https://doi.org/10.11648/j.mma.20190401.12

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ACS Style

Rathgama Guruge Uma Indeewari Meththananda; Naleen Chaminda Ganegoda; Shyam Sanjeewa Nishantha Perera. Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach. Math. Model. Appl. 2019, 4(1), 10-14. doi: 10.11648/j.mma.20190401.12

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AMA Style

Rathgama Guruge Uma Indeewari Meththananda, Naleen Chaminda Ganegoda, Shyam Sanjeewa Nishantha Perera. Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach. Math Model Appl. 2019;4(1):10-14. doi: 10.11648/j.mma.20190401.12

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@article{10.11648/j.mma.20190401.12,
  author = {Rathgama Guruge Uma Indeewari Meththananda and Naleen Chaminda Ganegoda and Shyam Sanjeewa Nishantha Perera},
  title = {Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach},
  journal = {Mathematical Modelling and Applications},
  volume = {4},
  number = {1},
  pages = {10-14},
  doi = {10.11648/j.mma.20190401.12},
  url = {https://doi.org/10.11648/j.mma.20190401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20190401.12},
  abstract = {Many mathematical models developed through differential equations to describe the age dependent infectiousness of diseases, face the complexity of modelling heterogenic behavior of transmission. There, many of the cases assume the host to stay in the same risk class regardless of the age of the hosts. The proposed model mimics the infectiousness according to the age-scale of an individual via integral equation approach. This model indicates the applicability of Fredholm type integral equations with degenerated kernel. Introducing biological, behavioral and environmental influences provokes to address the accumulating nature of different factors in modelling the risk of getting infected. The risk of getting infected is modeled by the inability of responding with acquired immunity and the accumulated risk given from the other individuals in each age group via the mobility patterns. Within this approach environmental stimulus are modeled via periodic functions in order to describe the stochastic behavior of the spreading capabilities. In this study, the behavioral analysis evaluates the maximum risk of getting infectious in the considered parsimonious approach. And the sensitivity analysis describes the contribution of the mobility risk and stochastic nature on the overall risk. Further the model guides to formulate hypotheses and data collection strategies to measure the risk of a disease.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Modeling the Age-Dependent Infectiousness of Diseases: An Integral Equation Approach
AU  - Rathgama Guruge Uma Indeewari Meththananda
AU  - Naleen Chaminda Ganegoda
AU  - Shyam Sanjeewa Nishantha Perera
Y1  - 2019/06/04
PY  - 2019
N1  - https://doi.org/10.11648/j.mma.20190401.12
DO  - 10.11648/j.mma.20190401.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 10
EP  - 14
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20190401.12
AB  - Many mathematical models developed through differential equations to describe the age dependent infectiousness of diseases, face the complexity of modelling heterogenic behavior of transmission. There, many of the cases assume the host to stay in the same risk class regardless of the age of the hosts. The proposed model mimics the infectiousness according to the age-scale of an individual via integral equation approach. This model indicates the applicability of Fredholm type integral equations with degenerated kernel. Introducing biological, behavioral and environmental influences provokes to address the accumulating nature of different factors in modelling the risk of getting infected. The risk of getting infected is modeled by the inability of responding with acquired immunity and the accumulated risk given from the other individuals in each age group via the mobility patterns. Within this approach environmental stimulus are modeled via periodic functions in order to describe the stochastic behavior of the spreading capabilities. In this study, the behavioral analysis evaluates the maximum risk of getting infectious in the considered parsimonious approach. And the sensitivity analysis describes the contribution of the mobility risk and stochastic nature on the overall risk. Further the model guides to formulate hypotheses and data collection strategies to measure the risk of a disease.
VL  - 4
IS  - 1
ER  -

Copy | Download