PURPOSE: Transmission system models make restrictive assumptions that might distort the conclusions of model analyses. We propose methods to progressively relax the following assumptions of classical deterministic compartmental models: 1) that the population has an effectively infinite size 2) that contact is instantaneous with no duration, 3) that mixing in this large population is instantaneously thorough after contact. METHODS: Analyses of contact patterns between high and low risk groups on gonorrhea transmission were performed. Initial models were similar to those analyzed by Hethcote and Yorke with compartments corresponding to sets of individuals. The instantaneous contact assumption in these models was relaxed by using continuous deterministic pairing models in the style of models presented by Dietz and Hadelar. That model makes restrictive assumptions about concurrent contacts, population sizes, and instantaneously random mixing. To relax these assumptions, we simulated our GERMS model of discrete individuals forming pairings and transmitting infection in continuous time. RESULTS: Relaxing the instantaneous contact assumption demonstrated a progressively decreased effect of mixing between high and low risk groups as the duration of contact was increased. The GERMS model simulations were shown to effectively reproduce pairing model behavior given the same restrictive assumptions as the pairing model. Further GERMS model analysis then demonstrated that concurrency assumptions alter the effects of contact rates between risk groups in ways that are dependent upon contact parameters. Finally GERMS models were used to structure mixing into four local areas. This affected the dynamics of reaching equilibrium but not the equilibrium value. CONCLUSIONS: Assessing the effects of assumptions in continuous compartmental models of transmission systems is feasible and important.
PURPOSE: Transmission system models make restrictive assumptions that might distort the conclusions of model analyses. We propose methods to progressively relax the following assumptions of classical deterministic compartmental models: 1) that the population has an effectively infinite size 2) that contact is instantaneous with no duration, 3) that mixing in this large population is instantaneously thorough after contact. METHODS: Analyses of contact patterns between high and low risk groups on gonorrhea transmission were performed. Initial models were similar to those analyzed by Hethcote and Yorke with compartments corresponding to sets of individuals. The instantaneous contact assumption in these models was relaxed by using continuous deterministic pairing models in the style of models presented by Dietz and Hadelar. That model makes restrictive assumptions about concurrent contacts, population sizes, and instantaneously random mixing. To relax these assumptions, we simulated our GERMS model of discrete individuals forming pairings and transmitting infection in continuous time. RESULTS: Relaxing the instantaneous contact assumption demonstrated a progressively decreased effect of mixing between high and low risk groups as the duration of contact was increased. The GERMS model simulations were shown to effectively reproduce pairing model behavior given the same restrictive assumptions as the pairing model. Further GERMS model analysis then demonstrated that concurrency assumptions alter the effects of contact rates between risk groups in ways that are dependent upon contact parameters. Finally GERMS models were used to structure mixing into four local areas. This affected the dynamics of reaching equilibrium but not the equilibrium value. CONCLUSIONS: Assessing the effects of assumptions in continuous compartmental models of transmission systems is feasible and important.
Authors: Jawaid W Rasul; Robert G Rommel; Geoffrey M Jacquez; Ben G Fitzpatrick; Azmy S Ackleh; Neal Simonsen; Richard A Scribner Journal: J Stud Alcohol Drugs Date: 2011-01 Impact factor: 2.582