Modeling Heterogeneity in Direct Infectious Disease Transmission in a Compartmental Model

Lingcai Kong, Jinfeng Wang, Weiguo Han and Zhidong Cao
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Lingcai Kong: State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
Jinfeng Wang: State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
Weiguo Han: University Corporation for Atmospheric Research/Visiting Scientist Programs, 3090 Center Green Drive, Boulder, CO 80301, USA
Zhidong Cao: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Science, Beijing 100190, China

IJERPH, 2016, vol. 13, issue 3, 1-13

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, R 0 , 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.

Keywords: infectious diseases; mathematical models; homogeneous mixing; heterogeneity; negative binomial distribution (search for similar items in EconPapers)
JEL-codes: I I1 I3 Q Q5 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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