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Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies
Mathematical Modelling and Applications
Volume 5, Issue 3, September 2020, Pages: 176-182
Received: Jul. 17, 2020; Accepted: Jul. 29, 2020; Published: Aug. 10, 2020
Authors
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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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.
Keywords
Face mask Efficacy, Radial Social Distance, Reproductive Ratio, Complacency, Isolation, Homebased Care
Rotich Kiplimo Titus, Lagat Robert Cheruiyot, Choge Paul Kipkurgat, Mathematical Modeling of Covid-19 Disease Dynamics and Analysis of Intervention Strategies, Mathematical Modelling and Applications. Vol. 5, No. 3, 2020, pp. 176-182. doi: 10.11648/j.mma.20200503.16
References
[1]
Millán-Oñate, J., et al., A new emerging zoonotic virus of concern: the 2019 novel Coronavirus (COVID-19). Infectio, 2020. 24 (3).
[2]
Read, M. C., Severe respiratory disease associated with a novel coronavirus, 19 February 2013 (ECDC, RRA, edited). 2020.
[3]
Weiss, S. R. and S. Navas-Martin, Coronavirus pathogenesis and the emerging pathogen severe acute respiratory syndrome coronavirus. Microbiol. Mol. Biol. Rev., 2005. 69 (4): p. 635-664.
[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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