Evaluating targeted interventions via meta-population models with multi-level mixing.
Among the several means by which heterogeneity can be modeled, Levins' (1969) meta-population approach preserves the most analytical tractability, a virtue to the extent that generality is desirable. When model populations are stratified, contacts among their respective sub-populations must be described. Using a simple meta-population model, Feng et al. (2015) showed that mixing among sub-populations, as well as heterogeneity in characteristics affecting sub-population reproduction numbers, must be considered when evaluating public health interventions to prevent or control infectious disease outbreaks. They employed the convex combination of preferential within- and proportional among-group contacts first described by Nold (1980) and subsequently generalized by Jacquez et al. (1988). As the utility of meta-population modeling depends on more realistic mixing functions, the authors added preferential contacts between parents and children and among co-workers (Glasser et al., 2012). Here they further generalize this function by including preferential contacts between grandparents and grandchildren, but omit workplace contacts. They also describe a general multi-level mixing scheme, provide three two-level examples, and apply two of them. In their first application, the authors describe age- and gender-specific patterns in face-to-face conversations (Mossong et al., 2008), proxies for contacts by which respiratory pathogens might be transmitted, that are consistent with everyday experience. This suggests that meta-population models with inter-generational mixing could be employed to evaluate prolonged school-closures, a proposed pandemic mitigation measure that could expose grandparents, and other elderly surrogate caregivers for working parents, to infectious children. In their second application, the authors use a meta-population SEIR model stratified by 7 age groups and 50 states plus the District of Columbia, to compare actual with optimal vaccination during the 2009-2010 influenza pandemic in the United States. They also show that vaccination efforts could have been adjusted month-to-month during the fall of 2009 to ensure maximum impact. Such applications inspire confidence in the reliability of meta-population modeling in support of public health policymaking.
Department of Mathematics, Purdue University, West Lafayette, IN, United States.
Zhilan
Z
Feng
National Center for HIV/AIDS, Viral Hepatitis, STD, and TB Prevention, CDC, Atlanta, GA, United States.
Andrew N
AN
Hill
National Center for Immunization and Respiratory Diseases, CDC, Atlanta, GA, United States.
Aaron T
AT
Curns
National Center for Immunization and Respiratory Diseases, CDC, Atlanta, GA, United States . Electronic address: jglasser@cdc.gov.
John W
JW
Glasser
D003140:Communicable Disease Control / Q000379:methods*; D006801:Humans; D007251:Influenza, Human / Q000517:prevention & control* / Q000635:transmission; D008962:Models, Theoretical; D055361:Multilevel Analysis
Designing or evaluating public health interventions; Meta-population modeling; Mixing functions
Lancet Infect Dis. 2016 May;16(5):599-605
26852723
Math Biosci. 2002 Nov-Dec;180:29-48
12387915
Lancet Infect Dis. 2012 Sep;12(9):696-702
22738894
Nat Rev Immunol. 2008 Sep;8(9):737-44
18728636
IMA J Math Appl Med Biol. 1991;8(1):1-29
1875096
Proc Biol Sci. 2014 Apr 30;281(1785):20140268
24789897
Am J Epidemiol. 2008 Apr 1;167(7):775-85
18230677
Epidemics. 2015 Mar;10:63-7
25843386
PLoS One. 2012;7(10):e48187
23118949
PLoS Med. 2008 Mar 25;5(3):e74
18366252
Math Biosci. 2012 Jan;235(1):1-7
22037144
Am J Epidemiol. 2008 Nov 1;168(9):1082-90
18801889
Nature. 2005 Nov 17;438(7066):355-9
16292310
J Theor Biol. 2015 Dec 7;386:177-87
26375548