A method to estimate the incidence of communicable diseases under seasonal fluctuations with application to cholera

被引:25
作者
Pourabbas, E [1 ]
d'Onofrio, A [1 ]
Rafanelli, M [1 ]
机构
[1] CNR, Ist Anal Sistemi & Informat, I-00185 Rome, Italy
关键词
SIRS mathematical model; seasonal variation of contact rate; Witch of Agnesi; cholera incidence; numerical computation;
D O I
10.1016/S0096-3003(99)00212-X
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper describes a method for estimating the seasonal variation of infection rate (or contact rate) and the trajectories of the number of susceptible, infectious and removed individuals in a deterministic SIRS model. The key idea of the proposed method is that the number of periodically varying infectives at time t can be represented as a sum of functions of the form b(1)/(1 + b(2)(t - kT - b(3))(2)), k =...,-1, 0, 1,..., where b(1), b(2) and b3 are parameters to be estimated from the incidence data, and Tis the period. Given the infective trajectory, the other trajectories and the contact rate can be estimated via the model definition. The method is illustrated using cholera incidence data from three developing countries. Finally, an analysis of the sensitivity of parameter estimation for validating the obtained results using numerical analysis techniques is made. (C) 2001 Elsevier Science Inc. All rights reserved.
引用
收藏
页码:161 / 174
页数:14
相关论文
共 16 条
[1]  
BAILEY N, 1982, POPULATION DYNAMICS
[2]  
BAILEY NT, 1975, MATH THEORY INFECT D
[3]   ESTIMATION FOR AN EPIDEMIC MODEL [J].
BECKER, N .
BIOMETRICS, 1976, 32 (04) :769-777
[4]   ON ESTIMATING THE CONTAGIOUSNESS OF A DISEASE TRANSMITTED FROM PERSON TO PERSON [J].
BECKER, N ;
ANGULO, J .
MATHEMATICAL BIOSCIENCES, 1981, 54 (1-2) :137-154
[5]  
CVIETANOVITZ B, 1978, B WHO S1, V56
[6]  
Dietz K, 1976, Proceedings of a Workshop on Mathematical Models in Medicine, P1
[7]   A DISCRETE METHOD FOR THE IDENTIFICATION OF PARAMETERS OF A DETERMINISTIC EPIDEMIC MODEL [J].
DILENA, G ;
SERIO, G .
MATHEMATICAL BIOSCIENCES, 1982, 60 (02) :161-175
[8]   Dynamical complexity in age-structured models of the transmission of the measles virus: Epidemiological implications at high levels of vaccine uptake [J].
Ferguson, NM ;
Nokes, DJ ;
Anderson, RM .
MATHEMATICAL BIOSCIENCES, 1996, 138 (02) :101-130
[9]  
GROSSMAN Z, 1977, ANAL APPROACH NONLIN
[10]  
HETHCOTE H W, 1976, Mathematical Biosciences, V28, P335, DOI 10.1016/0025-5564(76)90132-2