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A combination of differential equations and convolution in understanding the spread of an epidemic

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Abstract

Nonlinear dynamical method of projecting the transmission of an epidemic is accurate if the input parameters and initial value variables are reliable. Here, such a model is proposed for predicting an epidemic. A method to supplement two variables and two parameters for this proposed model is demonstrated through a robust statistical approach. The method described here worked well in case of three continuous distributions. Model predictions could be lower estimates due to under-reporting of disease cases. Anad hoc procedure with a technical note is provided in the appendix

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References

  • Anderson R M 1988 The epidemiology of HIV infection: variable incubation plus infectious periods and heterogeneity in sexual activity.J. R. Stat. Soc. A151: 66–98

    Article  Google Scholar 

  • Anderson R M, May R M 1991Infectious diseases of humans: Dynamics and control (London: Oxford University Press)

    Google Scholar 

  • Bain L J, Thoman D R 1968 Some tests of hypotheses concerning the three-parameter Weibull distribution.J. Am. Stat. Assoc. 63: 853–860

    Article  MathSciNet  Google Scholar 

  • Bowman K O, Shenton L R 2001 Weibull distributions when the shape parameter is defined.Comput. Stat. Data Anal. 36: 299–310

    Article  MATH  MathSciNet  Google Scholar 

  • Brookmeyer R, Gail M H 1988 A method for obtaining short-term projections and lower bounds on the size of the AIDS epidemic.J. Am. Stat. Assoc. 83: 301–308

    Article  MATH  Google Scholar 

  • Chen Z 1997 Statistical inference about the shape parameter of the Weibull distribution.Stat. Prob. Lett. 36: 85–90

    Article  MATH  Google Scholar 

  • Gray R Het al 2001 Probability of HIV-1 transmission per coital act in monogamous, heterosexual HIV-1-discordant couples in Rakai, Uganda.Lancet 357: 1149–1153.

    Article  Google Scholar 

  • Kakehashi M 1998 A mathematical analysis of the spread of HIV/AIDS in Japan IMA.J Math. Appl. Med. 15:299–311

    MATH  Google Scholar 

  • Kakehashi M 1999 A mathematical analysis of the spread of HIV/AIDS in Japan IMA.J.Math. Appl. Med, 16: 111–112

    Google Scholar 

  • Kakehashi M 2000 Validity of simple pair formation model for HIV spread with realistic parameter setting.Math. Pop. Stud, 8: 279–292

    Article  MATH  MathSciNet  Google Scholar 

  • Kakehashi M, Rao A S R S 2004 Mathematical and statistical approaches to risk management for the prevention of HIV/AIDS and other infectious diseases.J. Med, Safety (in press)

  • Malik H J, Abraham B 1973 Multivariate logistic distributions.Ann. Stat. 1: 588–590

    MATH  MathSciNet  Google Scholar 

  • Murray J D 1989Mathematical biology (Berlin: Springer-Verlag)

    MATH  Google Scholar 

  • Rao A S R S 2001 A methodology to estimate incubation distribution of AIDS in delayed surveillance and censored data.Int. Stat. Conf. on Environment and Pollution (Tokyo: The Biometric Society of Japan) pp 163–167

    Google Scholar 

  • Rao A S R S 2003a Mathematical modelling of AIDS epidemic in India.Curr. Sci. 84: 1191–1197

    Google Scholar 

  • Rao A S R S 2003b Can we obtain realistic HIV/AIDS estimates for Inida?J Biosci, 28, 4: 367–369

    Article  Google Scholar 

  • Rao A S R S 2004 Limiting theorems on ‘Case’ reporting.Appl. Math. Lett. (in press)

  • Rao A S R S and Kakehashi M 2002 Incubation time distribution in back-calculation applied to HIV/AIDS in India.Indian J. Pure Appl. Math, (submitted)

  • Rao C N and Srivenkataramana T 2001 Projection of HIV infections in India: An alternative to backcalculation.Curr. Sci. 81: 1302–1307

    Google Scholar 

  • Rao A S R S, Basu S, Basu A, Ghosh J K 2002 Parametric models for incubation distribution in presence of left and right censoring.Indian J. Pure Appl. Math, (submitted)

  • Tarter M E 1966 Exact moments and product moments of the order statistics from the truncated logistic distribution.J. Am. Stat. Assoc. 61: 514–525

    Article  MATH  MathSciNet  Google Scholar 

  • United Nations 2002 The UNAIDS Reference Group on Estimates, Modelling and Projections. Improved methods and assumptions for estimation of the HIV/AIDS epidemic and its impact: Recommendations of the UNAIDS Reference Group on Estimates, Modelling and Projections.AIDS 16(9):W1–14

    Article  Google Scholar 

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Authors and Affiliations

  1. Centre for Ecological Sciences, Indian Institute of Science, 560 012, Bangalore, India

    Arm S. R. Srinivasa Rao

  2. Institute of Health Sciences, Faculty of Medicine, Hiroshima University, 734 8551, Hiroshima, Japan

    Masayuki Kakehashi

Authors
  1. Arm S. R. Srinivasa Rao
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  2. Masayuki Kakehashi
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Rao, A.S.R.S., Kakehashi, M. A combination of differential equations and convolution in understanding the spread of an epidemic. Sadhana 29, 305–313 (2004). https://doi.org/10.1007/BF02703780

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  • DOI: https://doi.org/10.1007/BF02703780

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