Directly transmitted infections modeling considering an age-structured contact rate

Mathematical models dealing with childhood viral infections consider the spread of disease according to the law of mass action. This law states that there are random encounters (or contacts) among susceptible and infectious individuals. Therefore, mathematical descriptions of the transmission of infections are heavily dependent on the assumptions concerning the contact rate. In order to develop an age-structured contact rate model, a pattern of contacts among individuals in a community is developed by stochastic processes.

[1]  B T Grenfell,et al.  The estimation of age-related rates of infection from case notifications and serological data , 1985, Journal of Hygiene.

[2]  H. Yang,et al.  The loss of immunity in directly transmitted infections modeling: Effects on the epidemiological parameters , 1998, Bulletin of mathematical biology.

[3]  Hyun Mo Yang Modelling Vaccination Strategy Against Directly Transmitted Diseases Using a Series of Pulses , 1998 .

[4]  P. Fine,et al.  Measles in England and Wales--I: An analysis of factors underlying seasonal patterns. , 1982, International journal of epidemiology.

[5]  William H. Press,et al.  Numerical recipes : the art of scientific computing : FORTRAN version , 1989 .

[6]  D. Schenzle An age-structured model of pre- and post-vaccination measles transmission. , 1984, IMA journal of mathematics applied in medicine and biology.

[7]  D. Griffel Applied functional analysis , 1982 .

[8]  O. Bjørnstad,et al.  Chapter 17 , 2019 .

[9]  Effects of vaccination programmes on transmission rates of infections and related threshold conditions for control. , 1993, IMA journal of mathematics applied in medicine and biology.

[10]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[11]  R. Anderson,et al.  Rubella epidemiology in South East England , 1986, Journal of Hygiene.

[12]  P. Fine,et al.  Measles in England and Wales--II: The impact of the measles vaccination programme on the distribution of immunity in the population. , 1982, International journal of epidemiology.

[13]  M. Kendall,et al.  Kendall's Advanced Theory of Statistics: Volume 1 Distribution Theory , 1987 .

[14]  D. Tudor,et al.  An age-dependent epidemic model with application to measles , 1985 .

[15]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[16]  J. Yorke,et al.  Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates. , 1973, American journal of epidemiology.

[17]  R M May,et al.  Age-related changes in the rate of disease transmission: implications for the design of vaccination programmes , 1985, Journal of Hygiene.

[18]  D J Nokes,et al.  Rubella seroepidemiology in a non-immunized population of São Paulo State, Brazil , 1994, Epidemiology and Infection.

[19]  E Trucco,et al.  Mathematical models for cellular systems the Von Foerster equation. I. , 1965, The Bulletin of mathematical biophysics.

[20]  H. Inaba,et al.  Threshold and stability results for an age-structured epidemic model , 1990, Journal of mathematical biology.

[21]  C. Farrington Modelling forces of infection for measles, mumps and rubella. , 1990, Statistics in medicine.

[22]  H. Yang,et al.  Directly transmitted infections modeling considering an age-structured contact rate-epidemiological analysis , 1999 .

[23]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .

[24]  D Greenhalgh,et al.  Vaccination campaigns for common childhood diseases. , 1990, Mathematical biosciences.