Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies

Rotich Kiplimo Titus; Lagat Robert Cheruiyot; Choge Paul Kipkurgat

doi:doi:10.11648/j.mma.20200503.16

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Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies

Rotich Kiplimo Titus, Lagat Robert Cheruiyot, Choge Paul Kipkurgat

Published in Mathematical Modelling and Applications (Volume 5, Issue 3)

Received: 17 July 2020 Accepted: 29 July 2020 Published: 10 August 2020

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Abstract

Covid-19 is a highly prevalent contagious disease, with high fatalities. With the absence of a one bullet drug or vaccine, infected individual is highly likely to die within a short time. The transmission and progression of Covid-19 can be described using distinct stages, namely exposure and latency, infectiousness, and recovery with waning immunity or death. This implies that, mathematical model will place individuals into four compartments, that is, Susceptible (S), Exposed (E), Infective (I) and Recovered (R), representing a SEIR model. Due to its fast fatal capacity, changes in population due to births do not affect the disease dynamics, but for the purpose of monitoring deaths, a compartment for deaths (D) is incorporated. The analysis of intervention strategies necessitates modification of SEIR model to include Quarantine (Q), Isolation (I), and Homebased care (H) compartments. In this paper, Public health Education Campaign, Quarantine and testing, Isolation, Treatment, use of facemask and Social distance intervention strategies were analyzed. Numerical results indicated that the most responsive mitigation strategy is use of quality facemask and observance of social distance. At 90% adherence to this plan reduces the force of infection from β=0.0197 to β=0.0033. This will consequently reduce the basic reproductive ratio from R₀=14.0362 to R₀=2.3388, which prevents 99.37% of population from contracting the disease. However, it is shown that a combination of other intervention strategies have synergetic effect of bringing down reproductive ratio to less than one. Sensitivity analysis indicated that isolation and treatment of infected individuals in government facilities is the most effective method with elasticity of v=-6.4, but due to financial implications, the alternative homebased care need to be fortified. This means, for Covid-19 pandemic to die off, we require early identification of infected individuals through mass testing and immediate isolation. In order to optimize financial constraints associated with isolation, currently at α=11%, the threshold efficacy of other intervention strategies should be enhanced to; public health campaign є > 50%, complacency ξ < 30%, facemask quality c > 89%, social distance r > 2m, and mass testing τ > 0.27. With these interventions, it is estimated that the reproductive ratio, reduces to less than one after 225 days from the first occurrence of Covid-19, and the epidemic will then begin to decline gradually to insignificant levels.

Published in	Mathematical Modelling and Applications (Volume 5, Issue 3)
DOI	10.11648/j.mma.20200503.16
Page(s)	176-182
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), 2020. Published by Science Publishing Group

Keywords

Face mask Efficacy, Radial Social Distance, Reproductive Ratio, Complacency, Isolation, Homebased Care

References

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[4]	Keeling, M. J. and P. Rohani, Modeling infectious diseases in humans and animals. 2011: Princeton University Press.
[5]	Rodrigues, H. S., Optimal control and numerical optimization applied to epidemiological models. arXiv preprint arXiv: 1401.7390, 2014.
[6]	Sohrabi, C., et al., World Health Organization declares global emergency: A review of the 2019 novel coronavirus (COVID-19). International Journal of Surgery, 2020.
[7]	Tang, J. W., et al., Airflow dynamics of human jets: sneezing and breathing-potential sources of infectious aerosols. PLoS One, 2013. 8 (4): p. e59970.
[8]	Bowen, L. E., Does that face mask really protect you? Applied biosafety, 2010. 15 (2): p. 67-71.
[9]	Organization, W. H., Coronavirus disease 2019 (‎ COVID-19)‎: situation report, 93. 2020.
[10]	Kermack, W. O. and A. G. McKendrick, A contribution to the mathematical theory of epidemics, in Royal Soc. 1927: London (A). p. 700-721.
[11]	Van den Driessche, P. and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences, 2002. 180 (1-2): p. 29-48.
[12]	Podder, C. N., et al., Mathematical study of the impact of quarantine, isolation and vaccination in curtailing an epidemic. Journal of Biological Systems, 2007. 15 (02): p. 185-202.
[13]	Yan, X. and Y. Zou, Control of epidemics by quarantine and isolation strategies in highly mobile populations. International Journal of Information and Systems Sciences, 2009. 5 (3-4): p. 271-286.
[14]	Samsuzzoha, M., M. Singh, and D. Lucy, Uncertainty and sensitivity analysis of the basic reproduction number of a vaccinated epidemic model of influenza. Applied Mathematical Modelling, 2013. 37 (3): p. 903-915.
[15]	Blower, S. M. and H. Dowlatabadi, Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example. International Statistical Review/Revue Internationale de Statistique, 1994: p. 229-243.
[16]	Stoecklin, S. B., et al., First cases of coronavirus disease 2019 (COVID-19) in France: surveillance, investigations and control measures, January 2020. Eurosurveillance, 2020. 25 (6): p. 2000094.
[17]	Bai, Y., X. Nie, and C. Wen, Epidemic prediction of 2019-nCoV in Hubei province and comparison with SARS in Guangdong province. Available at SSRN 3531427, 2020.

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Rotich Kiplimo Titus, Lagat Robert Cheruiyot, Choge Paul Kipkurgat. (2020). Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies. Mathematical Modelling and Applications, 5(3), 176-182. https://doi.org/10.11648/j.mma.20200503.16

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ACS Style

Rotich Kiplimo Titus; Lagat Robert Cheruiyot; Choge Paul Kipkurgat. Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies. Math. Model. Appl. 2020, 5(3), 176-182. doi: 10.11648/j.mma.20200503.16

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AMA Style

Rotich Kiplimo Titus, Lagat Robert Cheruiyot, Choge Paul Kipkurgat. Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies. Math Model Appl. 2020;5(3):176-182. doi: 10.11648/j.mma.20200503.16

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@article{10.11648/j.mma.20200503.16,
  author = {Rotich Kiplimo Titus and Lagat Robert Cheruiyot and Choge Paul Kipkurgat},
  title = {Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {3},
  pages = {176-182},
  doi = {10.11648/j.mma.20200503.16},
  url = {https://doi.org/10.11648/j.mma.20200503.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200503.16},
  abstract = {Covid-19 is a highly prevalent contagious disease, with high fatalities. With the absence of a one bullet drug or vaccine, infected individual is highly likely to die within a short time. The transmission and progression of Covid-19 can be described using distinct stages, namely exposure and latency, infectiousness, and recovery with waning immunity or death. This implies that, mathematical model will place individuals into four compartments, that is, Susceptible (S), Exposed (E), Infective (I) and Recovered (R), representing a SEIR model. Due to its fast fatal capacity, changes in population due to births do not affect the disease dynamics, but for the purpose of monitoring deaths, a compartment for deaths (D) is incorporated. The analysis of intervention strategies necessitates modification of SEIR model to include Quarantine (Q), Isolation (I), and Homebased care (H) compartments. In this paper, Public health Education Campaign, Quarantine and testing, Isolation, Treatment, use of facemask and Social distance intervention strategies were analyzed. Numerical results indicated that the most responsive mitigation strategy is use of quality facemask and observance of social distance. At 90% adherence to this plan reduces the force of infection from β=0.0197 to β=0.0033. This will consequently reduce the basic reproductive ratio from R0=14.0362 to R0=2.3388, which prevents 99.37% of population from contracting the disease. However, it is shown that a combination of other intervention strategies have synergetic effect of bringing down reproductive ratio to less than one. Sensitivity analysis indicated that isolation and treatment of infected individuals in government facilities is the most effective method with elasticity of v=-6.4, but due to financial implications, the alternative homebased care need to be fortified. This means, for Covid-19 pandemic to die off, we require early identification of infected individuals through mass testing and immediate isolation. In order to optimize financial constraints associated with isolation, currently at α=11%, the threshold efficacy of other intervention strategies should be enhanced to; public health campaign є > 50%, complacency ξ  89%, social distance r > 2m, and mass testing τ > 0.27. With these interventions, it is estimated that the reproductive ratio, reduces to less than one after 225 days from the first occurrence of Covid-19, and the epidemic will then begin to decline gradually to insignificant levels.},
 year = {2020}
}

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TY  - JOUR
T1  - Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies
AU  - Rotich Kiplimo Titus
AU  - Lagat Robert Cheruiyot
AU  - Choge Paul Kipkurgat
Y1  - 2020/08/10
PY  - 2020
N1  - https://doi.org/10.11648/j.mma.20200503.16
DO  - 10.11648/j.mma.20200503.16
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
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PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.mma.20200503.16
AB  - Covid-19 is a highly prevalent contagious disease, with high fatalities. With the absence of a one bullet drug or vaccine, infected individual is highly likely to die within a short time. The transmission and progression of Covid-19 can be described using distinct stages, namely exposure and latency, infectiousness, and recovery with waning immunity or death. This implies that, mathematical model will place individuals into four compartments, that is, Susceptible (S), Exposed (E), Infective (I) and Recovered (R), representing a SEIR model. Due to its fast fatal capacity, changes in population due to births do not affect the disease dynamics, but for the purpose of monitoring deaths, a compartment for deaths (D) is incorporated. The analysis of intervention strategies necessitates modification of SEIR model to include Quarantine (Q), Isolation (I), and Homebased care (H) compartments. In this paper, Public health Education Campaign, Quarantine and testing, Isolation, Treatment, use of facemask and Social distance intervention strategies were analyzed. Numerical results indicated that the most responsive mitigation strategy is use of quality facemask and observance of social distance. At 90% adherence to this plan reduces the force of infection from β=0.0197 to β=0.0033. This will consequently reduce the basic reproductive ratio from R0=14.0362 to R0=2.3388, which prevents 99.37% of population from contracting the disease. However, it is shown that a combination of other intervention strategies have synergetic effect of bringing down reproductive ratio to less than one. Sensitivity analysis indicated that isolation and treatment of infected individuals in government facilities is the most effective method with elasticity of v=-6.4, but due to financial implications, the alternative homebased care need to be fortified. This means, for Covid-19 pandemic to die off, we require early identification of infected individuals through mass testing and immediate isolation. In order to optimize financial constraints associated with isolation, currently at α=11%, the threshold efficacy of other intervention strategies should be enhanced to; public health campaign є > 50%, complacency ξ  89%, social distance r > 2m, and mass testing τ > 0.27. With these interventions, it is estimated that the reproductive ratio, reduces to less than one after 225 days from the first occurrence of Covid-19, and the epidemic will then begin to decline gradually to insignificant levels.
VL  - 5
IS  - 3
ER  -

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Author Information

Rotich Kiplimo Titus

Department of Mathematics Physics and Computing, Moi University, Eldoret, Kenya
Lagat Robert Cheruiyot

Department of Mathematics and Actuarial Science, South Eastern Kenya University, Kitui, Kenya
Choge Paul Kipkurgat

Department of Mathematics Physics and Computing, Moi University, Eldoret, Kenya

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APA Style

Rotich Kiplimo Titus, Lagat Robert Cheruiyot, Choge Paul Kipkurgat. (2020). Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies. Mathematical Modelling and Applications, 5(3), 176-182. https://doi.org/10.11648/j.mma.20200503.16

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ACS Style

Rotich Kiplimo Titus; Lagat Robert Cheruiyot; Choge Paul Kipkurgat. Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies. Math. Model. Appl. 2020, 5(3), 176-182. doi: 10.11648/j.mma.20200503.16

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AMA Style

Rotich Kiplimo Titus, Lagat Robert Cheruiyot, Choge Paul Kipkurgat. Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies. Math Model Appl. 2020;5(3):176-182. doi: 10.11648/j.mma.20200503.16

Copy | Download

@article{10.11648/j.mma.20200503.16,
  author = {Rotich Kiplimo Titus and Lagat Robert Cheruiyot and Choge Paul Kipkurgat},
  title = {Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {3},
  pages = {176-182},
  doi = {10.11648/j.mma.20200503.16},
  url = {https://doi.org/10.11648/j.mma.20200503.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200503.16},
  abstract = {Covid-19 is a highly prevalent contagious disease, with high fatalities. With the absence of a one bullet drug or vaccine, infected individual is highly likely to die within a short time. The transmission and progression of Covid-19 can be described using distinct stages, namely exposure and latency, infectiousness, and recovery with waning immunity or death. This implies that, mathematical model will place individuals into four compartments, that is, Susceptible (S), Exposed (E), Infective (I) and Recovered (R), representing a SEIR model. Due to its fast fatal capacity, changes in population due to births do not affect the disease dynamics, but for the purpose of monitoring deaths, a compartment for deaths (D) is incorporated. The analysis of intervention strategies necessitates modification of SEIR model to include Quarantine (Q), Isolation (I), and Homebased care (H) compartments. In this paper, Public health Education Campaign, Quarantine and testing, Isolation, Treatment, use of facemask and Social distance intervention strategies were analyzed. Numerical results indicated that the most responsive mitigation strategy is use of quality facemask and observance of social distance. At 90% adherence to this plan reduces the force of infection from β=0.0197 to β=0.0033. This will consequently reduce the basic reproductive ratio from R0=14.0362 to R0=2.3388, which prevents 99.37% of population from contracting the disease. However, it is shown that a combination of other intervention strategies have synergetic effect of bringing down reproductive ratio to less than one. Sensitivity analysis indicated that isolation and treatment of infected individuals in government facilities is the most effective method with elasticity of v=-6.4, but due to financial implications, the alternative homebased care need to be fortified. This means, for Covid-19 pandemic to die off, we require early identification of infected individuals through mass testing and immediate isolation. In order to optimize financial constraints associated with isolation, currently at α=11%, the threshold efficacy of other intervention strategies should be enhanced to; public health campaign є > 50%, complacency ξ  89%, social distance r > 2m, and mass testing τ > 0.27. With these interventions, it is estimated that the reproductive ratio, reduces to less than one after 225 days from the first occurrence of Covid-19, and the epidemic will then begin to decline gradually to insignificant levels.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies
AU  - Rotich Kiplimo Titus
AU  - Lagat Robert Cheruiyot
AU  - Choge Paul Kipkurgat
Y1  - 2020/08/10
PY  - 2020
N1  - https://doi.org/10.11648/j.mma.20200503.16
DO  - 10.11648/j.mma.20200503.16
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 176
EP  - 182
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20200503.16
AB  - Covid-19 is a highly prevalent contagious disease, with high fatalities. With the absence of a one bullet drug or vaccine, infected individual is highly likely to die within a short time. The transmission and progression of Covid-19 can be described using distinct stages, namely exposure and latency, infectiousness, and recovery with waning immunity or death. This implies that, mathematical model will place individuals into four compartments, that is, Susceptible (S), Exposed (E), Infective (I) and Recovered (R), representing a SEIR model. Due to its fast fatal capacity, changes in population due to births do not affect the disease dynamics, but for the purpose of monitoring deaths, a compartment for deaths (D) is incorporated. The analysis of intervention strategies necessitates modification of SEIR model to include Quarantine (Q), Isolation (I), and Homebased care (H) compartments. In this paper, Public health Education Campaign, Quarantine and testing, Isolation, Treatment, use of facemask and Social distance intervention strategies were analyzed. Numerical results indicated that the most responsive mitigation strategy is use of quality facemask and observance of social distance. At 90% adherence to this plan reduces the force of infection from β=0.0197 to β=0.0033. This will consequently reduce the basic reproductive ratio from R0=14.0362 to R0=2.3388, which prevents 99.37% of population from contracting the disease. However, it is shown that a combination of other intervention strategies have synergetic effect of bringing down reproductive ratio to less than one. Sensitivity analysis indicated that isolation and treatment of infected individuals in government facilities is the most effective method with elasticity of v=-6.4, but due to financial implications, the alternative homebased care need to be fortified. This means, for Covid-19 pandemic to die off, we require early identification of infected individuals through mass testing and immediate isolation. In order to optimize financial constraints associated with isolation, currently at α=11%, the threshold efficacy of other intervention strategies should be enhanced to; public health campaign є > 50%, complacency ξ  89%, social distance r > 2m, and mass testing τ > 0.27. With these interventions, it is estimated that the reproductive ratio, reduces to less than one after 225 days from the first occurrence of Covid-19, and the epidemic will then begin to decline gradually to insignificant levels.
VL  - 5
IS  - 3
ER  -

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