Simulation of mechanisms of viral interference in influenza.

Biological interference among viral agents might have significant implications for disease prevention and therapy. Field data for influenza yield conflicting evidence concerning the independence of infection rates, or disease severity, for two co-circulating viruses. To examine the effects of several assumed modes of interference for influenza, simulations of a Monte Carlo micropopulation model of influenza epidemics have been performed. Model parameters were selected so that the simulated attack rates for each of two different viral strains matched actual field data. Rates of infection were compared for single agents and for two viruses with only behavioural interference. Other simulations included temporary immunity to the other virus for the duration of the infection, and/or reduced shedding of viral particles for dual infections. Simulated viral competition had little impact on epidemic severity, duration, or size distribution. Under the conditions studied, viral interference in natural populations would be difficult to infer from field observations of attack rates. Other simulations extended a partial immunity and/or reduced viral shedding during an infection with a second virus. These indicated that interference might be suggested by field data, but it could not be demonstrated conclusively. Still other simulations showed that for epidemics with much higher attack rates for both viruses, it would be relatively easy to demonstrate interference. However, in order to observe interference between influenza strains, it would be necessary to monitor on an almost daily basis, using a method of viral detection which would have to be both highly specific and also very sensitive.

Simulation studies of influenza epidemics: assessment of parameter estimation and sensitivity.

The influenza simulation model of Elveback et al is used to evaluate the accuracy of the maximum likelihood procedure of Longini et al for estimating the secondary attack rate in households. The sample population from the Tecumseh Respiratory Illness Study is mapped into the simulation model and simulations are carried out over a range of parameter values and conditions, some of which were derived from influenza seasons in Tecumseh and from the Seattle Flu Study for the years 1975-1980. The estimation procedure is found to be quite robust for parameter values preset within appropriate limits for influenza. However, a significant difference is found between the preset and estimated household contact parameter for epidemics of medium and high intensity when the preset value is zero. Incremental increases in the household contact parameter are shown to produce marked increases in the overall infection attack rate demonstrating that household spread is an important link in maintaining infection in other mixing groups such as schools, preschool groups and neighbourhood clusters of households.

Software systems to control sensitivity studies of Monte Carlo simulation models.

Studies of the sensitivity of Monte Carlo models to changes in the values of their features involve repetitive simulations. Subsequent displays and analyses express variation in simulated outcomes as a function of change in location in multidimensional feature space and provide feedback via inputs for future simulations. A software system has been designed to control execution of the interacting programs required, reducing the need for human intervention. Assumptions about the goals and operation of the system as a whole are isolated within a program which executes component packages using interprogram control and communication mechanisms. The latter allow component programs to operate independently of the sources of data or the execution environment: they may be used separately, or in software systems, such as for sensitivity analysis of a Monte Carlo epidemic model. The methodology contributes to modularity at the level of executable programs and to the plausibility and efficiency of sensitivity studies.

Order of response surfaces for representation of a Monte Carlo epidemic model.

Response hypersurfaces for two selected outcomes and for 6 model features were generated for Latin Hypercube (LH) samples of the parameter space of a discrete, micro-population, Monte Carlo model of an epidemic of an infectious disease agent. SAS stepwise, multivariate regression routines were used to generate response hypersurfaces of first, second and third order in the model features for each outcome. These are used as illustrative examples to examine the appropriateness of the order of the polynomial describing the response hypersurface. The response hypersurfaces are very dependent on the model outcomes and also on the selected ranges of the model features. Results indicate that there is little reason to prefer any particular order for the response hypersurfaces. Further, it is suggested that apparent interaction terms found when using quadratic and cubic response hypersurfaces may represent artifacts of the choice of a particular order for the response hypersurface. Nonetheless, the comparison of the 3 orders of response hypersurfaces can, under some circumstances, reveal basic characteristics of the sensitivity of the outcome to the model features.

Latin hypercube sampling and the sensitivity analysis of a Monte Carlo epidemic model.

Discrete, algorithmic simulation and Monte Carlo methodologies are currently used in population biology, connectionist cognitive modeling, and physics. However, little is typically known about the sensitivity of such models to changes in the values of the model features. Traditional methods of sensitivity analysis for systems of differential equations do not apply. Sometimes, one or two parameters are modified at a time in an ad hoc fashion in an attempt to assess sensitivity. To include more model features and their interactions in a sensitivity study, while limiting computer utilization, various sampling methods have been suggested. In this article, a sensitivity study based on a Latin hypercube (LH) sampling design is compared with a similar study using a full factorial (FF), fixed-point sample. A discrete, Monte Carlo model of epidemics of influenzavirus infections in a human community is used for illustrative purposes. Although the FF scheme used over 14 times as many samples as the LH sampling one, both provided comparable predictive ability and comparable information about simulation sensitivity to model features.