title: Modeling Heterogeneity in Direct Infectious Disease Transmission in a Compartmental Model.
abstract: Mathematical models have been used to understand the transmission dynamics of infectious diseases and to assess the impact of intervention strategies. Traditional mathematical models usually assume a homogeneous mixing in the population, which is rarely the case in reality. Here, we construct a new transmission function by using as the probability density function a negative binomial distribution, and we develop a compartmental model using it to model the heterogeneity of contact rates in the population. We explore the transmission dynamics of the developed model using numerical simulations with different parameter settings, which characterize different levels of heterogeneity. The results show that when the reproductive number, R₀, is larger than one, a low level of heterogeneity results in dynamics similar to those predicted by the homogeneous mixing model. As the level of heterogeneity increases, the dynamics become more different. As a test case, we calibrated the model with the case incidence data for severe acute respiratory syndrome (SARS) in Beijing in 2003, and the estimated parameters demonstrated the effectiveness of the control measures taken during that period.
authors.affiliation: State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China. konglc@lreis.ac.cn.|University of the Chinese Academy of Sciences, Beijing 100049, China. konglc@lreis.ac.cn.|Key Laboratory of Surveillance and Early-Warning on Infectious Disease, Chinese Center for Disease Control and Prevention, Beijing 102206, China. konglc@lreis.ac.cn.
authors.forename: Lingcai
authors.initials: L
authors.lastname: Kong
authors.affiliation: State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China. wangjf@lreis.ac.cn.|Key Laboratory of Surveillance and Early-Warning on Infectious Disease, Chinese Center for Disease Control and Prevention, Beijing 102206, China. wangjf@lreis.ac.cn.|Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China. wangjf@lreis.ac.cn.
authors.forename: Jinfeng
authors.initials: J
authors.lastname: Wang
authors.affiliation: University Corporation for Atmospheric Research/Visiting Scientist Programs, 3090 Center Green Drive, Boulder, CO 80301, USA. hanwg.bj@gmail.com.
authors.forename: Weiguo
authors.initials: W
authors.lastname: Han
authors.affiliation: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Science, Beijing 100190, China. zhidong.cao@ia.ac.cn.
authors.forename: Zhidong
authors.initials: Z
authors.lastname: Cao
mesh_terms: D000068476:Beijing / Q000453:epidemiology; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D004812:Epidemiologic Methods; D018740:Genetic Heterogeneity; D006801:Humans; D015994:Incidence; D008954:Models, Biological; D008962:Models, Theoretical
keywords: heterogeneity; homogeneous mixing; infectious diseases; mathematical models; negative binomial distribution