The transmission of meningococcal infection: a mathematical study

Abstract The most common type of bacterial meningitis in the developed countries is caused by Neisseria meningitidis bacteria, which cause meningococcal meningitis. Case fatality rate can be between 3% and 10% in developed countries and as high as 20% in African countries. During epidemics in sub-Saharan countries, the so-called meningitis belt, the case fatality rate can peak to 70% or higher. Some people who have bacterial meningitis experience some form of after effects: epilepsy, damaged eyesight, hearing loss, brain damage. There is no immunity after infection. Approximately on average 10% of the population at any time carry the germs for days, weeks, or months. Carriers can infect other individuals by close contacts, even though they do not become ill themselves. An age-structured mathematical model is formulated that enables the understanding of the dynamics of the infection transmission. The model is used to study the conditions for the stability of the disease-free steady state (which imply extinction of the disease) and the existence of an endemic state (which leads to persistence of the disease in the population). The results of the model are applied to identify the contribution of the carriers to the transmission of the disease. Final epidemiological conclusions are given.

[1]  Carlos Castillo-Chavez,et al.  How May Infection-Age-Dependent Infectivity Affect the Dynamics of HIV/AIDS? , 1993, SIAM J. Appl. Math..

[2]  Horst R. Thieme,et al.  Global behavior of an age-structured epidemic model , 1991 .

[3]  A. J. Hall.  Infectious diseases of humans: R. M. Anderson & R. M. May. Oxford etc.: Oxford University Press, 1991. viii + 757 pp. Price £50. ISBN 0-19-854599-1 , 1992 .

[4]  Norman T. J. Bailey,et al.  The Mathematical Theory of Infectious Diseases , 1975 .

[5]  M. van Boven,et al.  Waning immunity and sub-clinical infection in an epidemic model: implications for pertussis in The Netherlands. , 2000, Mathematical biosciences.

[6]  J. Hale.  Asymptotic Behavior of Dissipative Systems , 1988 .

[7]  G. Webb.  An operator-theoretic formulation of asynchronous exponential growth , 1987 .

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

[9]  Y Cha,et al.  Existence and uniqueness of endemic states for the age-structured S-I-R epidemic model. , 1998, Mathematical biosciences.

[10]  S. Busenberg,et al.  A general solution of the problem of mixing of subpopulations and its application to risk- and age-structured epidemic models for the spread of AIDS. , 1991, IMA journal of mathematics applied in medicine and biology.

[11]  M. Iannelli,et al.  Analytical and numerical results for the age-structured S-I-S epidemic model with mixed inter-intracohort transmission , 1992 .

[12]  M. Byrne,et al.  Meningococcal disease in childhood--a regional study in Ireland. , 1994, The Journal of infection.

[13]  C. Castillo-Chavez,et al.  Global stability of an age-structure model for TB and its applications to optimal vaccination strategies. , 1998, Mathematical biosciences.

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

[15]  Olof J. Staffans,et al.  Volterra Integral and Functional Equations , 1990 .

[16]  Jack K. Hale,et al.  Persistence in infinite-dimensional systems , 1989 .

[17]  K. Cartwright,et al.  Mathematical modelling of infection and disease due to Neisseria meningitidis and Neisseria lactamica. , 2000, International journal of epidemiology.