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Mathematical Analysis of Quarantine on the Dynamical Transmission of Diphtheria Disease

Journal Name:

  • International Journal of Science and Engineering Investigations

Publication Year:

  • 2017

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
Five (5) Compartmental model of (S, E, Q, I, R) were presented to have better understanding on the effect of quarantine of exposed individuals in the dynamical spread of Diphtheria disease in the population. The stability of the model was analyzed for the existence of disease free and endemic equilibrium points. Basic Reproduction Number (R0) was obtained using next generation matrix method (NGM), and it is shown that the disease free equilibrium point is locally asymptotically stable whenever the basic reproduction number is less than unity i.e. (R0˂1) and unstable whenever the basic reproduction number is greater than unity (R0˃1).The basic reproduction number which is the number of new infected individual generated by a single infectious individual is a very important tool that helps in determining whether the disease persists and become endemic or dies out in the society. The model was solved numerically using the mathematical software (MAPLE) and the results were presented graphically. It was discovered that the higher the quarantine rate of exposed individual the lower the reproduction number and less is the infected individuals. Therefore, effort should be put in place in intensifying the quarantine rate of the disease so as to have the basic reproduction number not greater than unity, in order to prevent the endemic situation.
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  • 5
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17
  • English

REFERENCES

References: 

[1] Australian Quarantine a shared responsibility: The Government response, Australian Government. Department of Primary Industries and Energy. Retrieved 20 May 2016.
[2] Bachran C, Sutherland M, Bachran D, Fuchs H (2007). Quantification of diphtheria toxin-mediated ADP-ribosylation in a solid-phase assay. Clin. Chem., 53(9): 1676-1683.
[3] Brooks GF, Carroll CK, Butel JS, Morse AS (2007). Jawetz, Melnick & Adelberg’s Medical Microbiology, edited by G.F. Brooks, 24 edition: pp. 154 -217.
[4] Cárdenas R, Prieto G, Vargas J, Martinez A 1972. Corynebacterium diphtheriae. Características de cepas aisladas recientemente en Maracaibo - Venezuela. Kasmera 4: 185-198.
[5] Centers for Disease Control and Prevention: http://www.cdc.gov/quarantine/
[6] Formiga LCD 1985. New possibilities for the laboratory diagnosis of diphtheria. Brazi J Med Biol Res 18: 401-402.
[7] Formiga LCD, Mattos-Guaraldi AL 1993. Diphtheria: current status and laboratory procedures for diagnosis. Rev Bras Patol Clin 29: 93-96.
[8] Galazka AM 2000. The changing epidemiology of diphtheria in the vaccine era. J Infect Dis 181: 2-9.
[9] Galazka AM, Robertson SE 1995. Diphtheria: changing patterns in the developing world and the industrialized world. Eur J Epidemiol 11: 107-117.
[10] Halioua B, Patey O, Casciani D, Emond JP, Dublanchet A, Malkin JE, Lafaix C 1992. Cutaneous diphtheria in a patient with HIV infection. Ann Dermatol Venereol 18: 874-877.
[11] Hogg GG, Strachan JE, Huayi L, Beaton SA, Robinson PM, Taylor K 1996. Non-toxigenic Corynebacterium diphtheriae var. gravis: evidence for an invasive clone in a SouthWestern Australian community. Med J Aust 164: 72-75.
[12] Kneen R, Phan NG, Solomon T, Tran TM, Nguyen TT, Tran BL, Wain J, Day NP, Tran TH, Parry CM, White NJ 1998. Penicillin vs erythromycin in the treatment of diphtheria. Clin Infect Dis 27: 845-850.
[13] MacQueen S 1997. Diphtheria: a changing pattern. Nursing Times 93: 57-62.
[14] Singh J, Harit AK, Jain DC, Panda RC, Tewari KN, Bhatia R 1999. Diphtheria is declining but continues to kill many children: analysis of data from a sentinel center in Delhi. Epidemiol Infect 123: 209-215.
[15] Todar K (2008). Diphtheria. University of Wisconsin-Madison Department of Bacteriology, pp. 1-8.
[16] Wilson AP 1995. The return of Corynebacterium diphtheriae: the rise of nontoxigenic strains. J Hosp Infect 30: 306-312.
[17] Yan, X., & Zou, Y. (2008). Optimal and sub-optimal quarantine and isolation control in SARS epidemics. Mathematical and Computer Modelling, 47(12), 235–245.

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