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PubMed2005

Population pharmacokinetic investigation of phenobarbital by mixed effect modelling using routine clinical pharmacokinetic data in Japanese neonates and infants.

The population pharmacokinetics of phenobarbital was evaluated using 69 serum concentration measurements obtained from the routine phenobarbital monitoring of 35 neonates and infants. The data were analysed using the nonlinear mixed effects model. A one-compartment open pharmacokinetic model with first-order elimination was used. Covariates screened were current bodyweight (TBW), gestational age, postnatal age (PNA), postconceptional age and gender. The final pharmacokinetic parameters were CL/F (mL/h) = 3.41.TBW (kg) + 1.64. PNA (weeks), Vd/F(L) = 1.09.TBW.(kg) [corrected] and F = 0.406 for oral administration and F = 1 for suppository. Application of the findings in this study to patient care may permit selection of an appropriate initial maintenance dosage to achieve target phenobarbital concentrations, thus enabling the clinician to achieve the desired therapeutic effect in neonates and infants.

Administration, Rectal↗

PubMed1999

Reduced gap strains induce changes in bone regeneration during distraction.

A bilateral New Zealand white rabbit model of distraction osteogenesis (DO) was used to investigate the relationship between strain environment and bone regeneration during limb lengthening. In seven (n = 7) rabbits, a stiffener was applied to the fixator on one side to reduce strains within the gap tissue after lengthening was completed. Animals were euthanized six days later and their distraction zones were harvested and analyzed for changes in new bone volume and architecture. Nonlinear finite element analyses (FEA) were performed to predict changes in the gap strain environment. FEA results predicted a nearly uniform sevenfold decrease in average strain measures within the distraction zone. No change in total average new bone volume and significant decreases in both bone volume fraction (BV/TV) and trabecular thickness (Tb.Th) were observed in tibiae in which gap strains were reduced experimentally, compared to contralateral controls. These results suggest that fixator stiffening influenced the architecture but not the amount of newly formed bone. This animal model of distraction might be used to study the mechanisms by which strain fields affect events in bone repair and regeneration, such as cell proliferation, precursor tissue differentiation, and altered growth factor and nutrient delivery to tissues.

Animals↗

PubMed1988

Norfloxacin binds to human fecal material.

Earlier studies have reported very high (120 to 2,700 mg/kg) concentrations of norfloxacin in feces after therapeutic doses. MICs for fecal microorganisms are with few exceptions far below these levels. Nevertheless, clinical investigations show that the main part of the aerobic gram-positive and the anaerobic microflora remains unaffected after norfloxacin administration. In this study, the binding of [14C]norfloxacin to fecal material was analyzed. The binding of a group of nonlabeled quinolones to feces and the interactions between Enterococcus faecium, Bacteroides fragilis, and norfloxacin were also investigated. The results showed that norfloxacin has the ability to bind to feces. The specific binding was reversible, saturated after 90 min of incubation at 37 degrees C, and increased linearly with fecal concentration. Scatchard plots and nonlinear regression computer analyses revealed two different binding classes. The primary specific binding had a dissociation constant (KD) of 1.0 microM and a maximal binding capacity (Bmax) of 0.12 mumol/g of feces. The KD and Bmax of the secondary, more unspecific binding were 450 microM and 11.8 mumol/g of feces, respectively. The binding of unlabeled ciprofloxacin, enoxacin, ofloxacin, pefloxacin, and norfloxacin to feces was comparable to that of [14C]norfloxacin. The results of norfloxacin binding to suspensions of B. fragilis suggested that the main part of the binding is to the bacterial fraction of feces. In the presence of 8.0 g (dry weight) of B. fragilis per liter, the MBC of norfloxacin for E. faecium increased from 8 to 256 micrograms/ml. The finding of the present study indicated that binding of norfloxacin to feces may explain the paradox of high fecal concentrations of norfloxacin versus the actual effect on the normal gastrointestinal microflora.

Adult↗

PubMed2000

Age at first alcohol use: a risk factor for the development of alcohol disorders.

OBJECTIVE: This study aimed to describe the natural course of DSM-III-R alcohol disorders as a function of age at first alcohol use and to investigate the influence of early use as a risk factor for progression to the development of alcohol disorders, exclusive of the effect of confounding influences. METHOD: Data were obtained from a community sample (N=5,856) of lifetime drinkers participating in the 1990-1991 Mental Health Supplement of the Ontario Health Survey. RESULTS: Survival analyses revealed a rapid progression to alcohol-related harm among those who reported having their first drink at ages 11-14. After 10 years, 13.5% of the subjects who began to drink at ages 11 and 12 met the criteria for a diagnosis of alcohol abuse, and 15.9% had a diagnosis of dependence. Rates for subjects who began to drink at ages 13 and 14 were 13.7% and 9.0%, respectively. In contrast, rates for those who started drinking at ages 19 and older were 2.0% and 1.0%. Unexpectedly, a delay in progression to harm was observed for the youngest drinkers (ages 10 and under). Hazard regression analyses revealed a nonlinear effect of age at first alcohol use, marked by an elevated risk of developing disorders among subjects first using alcohol at ages 11-14. CONCLUSIONS: First use of alcohol at ages 11-14 greatly heightens the risk of progression to the development of alcohol disorders and therefore is a reasonable target for intervention strategies that seek to delay first use as a means of averting problems later in life.

Adolescent↗

PubMed1996

Chronic infusion of nitric oxide in experimental pulmonary hypertension: pulmonary pressure-flow analysis.

Inhaled-nitric oxide (NO) is a selective pulmonary vasodilator in short-term clinical studies. Use of NO inhalation in chronic pulmonary hypertension is complicated by potential problems with ambulatory NO delivery. We hypothesized that long-term infusion of NO solution into the central venous circulation, which did not suffer from this drawback, might reduce chronic pulmonary hypertension. Saturated NO solution was infused in chronically hypoxic rats by implantable minipumps at a rate which was effective in reducing acute hypoxic vasoconstriction in isolated, Krebs' albumin perfused lungs (2.5 microL.h-1). Pulmonary haemo dynamics and the pressure-flow relationship were studied after 4 weeks of infusion. NO was still present in the minipumps at the end of the infusion period. Despite causing methaemoglobinaemia, NO infusion did not significantly attenuate pulmonary arterial pressure, pulmonary vascular resistance, right ventricular hypertrophy, or the parameters of the pulmonary vascular pressure-flow relationship. Pressure-flow curves, analysed with the nonlinear, distensible vessel model, indicated increased near-zero pressure resistance (Ro) in chronic hypoxia. The tendency of chronic NO infusion to reduce Ro did not reach statistical significance. Long-term infusion of nitric oxide solution is technically feasible but does not effectively reverse chronic pulmonary hypertension. The failure of infused NO to reduce pulmonary hypertension is explained by the fact that the inactivation of NO by haemoglobin is much faster than anticipated.

Animals↗

PubMedDate not supplied

Prediction of height velocity of prepubertal children with growth hormone deficiency in the first year of treatment with recombinant human growth hormone.

AIM: Several methods have been developed to predict the outcome of growth hormone (GH) therapy in children with growth hormone deficiency (GHD). METHODS: Over 50 factors for each of 92 prepubertal patients with GHD (26 patients with total and 45 patients with partial GHD, 21 patients with neurosecretory dysfunction) were collected and included in multiple regression analyses and other nonlinear models to predict height velocity (HV) (cm/yr) in the first year of treatment. Afterwards the model was validated by two other cohorts of patients from other universities, which followed the same treatment regime as our clinic. RESULTS: Twelve parameters had a significant correlation to HV (p<0.05) and a coefficient of determination >20%. Two parameters (In BA, In GHmax) showed a coefficient of determination >60% for children with GHD in multiple regression analysis. The validation of the mathematical model against another data set showed different results. GH was measured by the same method, but BA was scored at the first clinic as in our clinic by only one doctor and in the other university by several radiologists. The accuracy of prediction in the first clinic was significantly higher than in the other university. CONCLUSION: This model demonstrates that exact scoring of BA and precise measurement of GHmax in the stimulation test is necessary, and if carried out carefully leads to useful prediction values for determining height velocity.

Body Height↗

PubMed2004

Bacterial energetics, stoichiometry, and kinetic modeling of 2,4-dinitrotoluene biodegradation in a batch respirometer.

A stoichiometric equation and kinetic model were developed and validated using experimental data from batch respirometer studies on the biodegradation of 2,4-dinitrotoluene (DNT). The stoichiometric equation integrates bacterial energetics and is revised from that in a previous study by including the mass balance of phosphorus (P) in the biomass. Stoichiometric results on O2 consumption, CO2 evolution, and nitrite evolution are in good agreement with respirometer data. However, the optimal P requirement is significantly higher than the stoichiometrically derived P, implying potentially limited bioavailability of P and the need for buffering capacity in the media to mitigate the adverse pH effect for optimal growth of DNT-degrading bacteria. An array of models was evaluated to fit the O2/CO2 data acquired experimentally and the DNT depletion data calculated from derived stoichiometric coefficients and cell yield. The deterministic, integrated Monod model provides the goodness of fit to the test data on DNT depletion, and the Monod model parameters (Ks, X0, mumax, and Y) were estimated by nonlinear regression. Further analyses with an equilibrium model (MINTEQ) indicate the interrelated nature of medium chemical compositions in controlling the rate and extent of DNT biodegradation. Results from the present batch respirometer study help to unravel some key factors in controlling DNT biodegradation in complex remediation systems, in particular the interactions between acidogenic DNT bacteria and various parameters, including pH and P, the latter of which could serve as a nutrient, a buffer, and a controlling factor on the bioavailable fractions of minerals (Ca, Fe, Zn, and Mo) in the medium.

Aerobiosis↗

PubMed2001

Quantitative pharmacogenetics of nortriptyline: a novel approach.

OBJECTIVE: To quantitatively model nortriptyline clearance as a function of the cytochrome P450 (CYP) 2D6 genotype and to estimate the contribution of genotype to the interindividual variability in steady-state plasma concentration and metabolic clearance. DESIGN: Modelling study using data from two previously published studies. PARTICIPANTS: 20 healthy volunteers receiving single oral doses of nortriptyline and 20 patients with depression on steady-state oral treatment. METHODS: A total of 275 nortriptyline plasma concentrations were analysed by standard nonlinear regression and nonlinear mixed effect models. The pharmacokinetic model was a 1-compartment model with first order absorption and elimination. All participants had previously been genotyped with respect to the CYP2D6 polymorphism. RESULTS: A model in which the intrinsic clearance is a linear function of the number of functional CYP2D6 genes and hepatic blood flow is fixed to 60 L/h gave the closest fit of the pharmacokinetic model to the data. Stable estimates were obtained for population pharmacokinetic parameters and interindividual variances. Assuming 100% absorption, the model allows systemic clearance and bioavailability to be estimated. Bioavailability was found to vary between 0.17 and 0.71, depending on the genotype. Using the frequency distribution of CYP2D6 genotype with the above results we estimate that, in compliant Swedish individuals on nortriptyline monotherapy, the number of functional CYP2D6 genes could explain 21% of the total interindividual variance in oral clearance of nortriptyline and 34% of that in steady-state plasma concentrations. CONCLUSION: Nonlinear mixed-effects modelling can be used to quantify the influence of the number of functional CYP2D6 genes on the metabolic clearance and plasma concentration of drugs metabolised by this enzyme. Gene dose has a significant impact on drug pharmacokinetics and prior knowledge of it may aid in predicting plasma concentration of the drug and thus tailoring patient-specific dosage regimens.

Adolescent↗

PubMed2006

Patient characteristics influencing ciclosporin pharmacokinetics and accurate Bayesian estimation of ciclosporin exposure in heart, lung and kidney transplant patients.

BACKGROUND AND OBJECTIVES: Population pharmacokinetic studies of ciclosporin microemulsion are needed to identify the individual factors influencing ciclosporin pharmacokinetic variability in transplant patients and to design efficient tools for the accurate estimation of ciclosporin overall exposure (area under the plasma concentration-time curve from 0 to 12 hours [AUC12]). In the present retrospective study, a large database of heart, lung (with or without cystic fibrosis) and kidney (both adult and paediatric) transplant patients receiving ciclosporin microemulsion was analysed with the aims of (i) building a population pharmacokinetic model and finding the main covariates linked with ciclosporin microemulsion pharmacokinetic parameters; and (ii) developing a maximum a posteriori probability Bayesian estimator (MAP-BE) to estimate ciclosporin microemulsion pharmacokinetic parameters using a limited-sampling strategy. METHODS: 3,072 concentration data from 147 patients (i.e. 309 full pharmacokinetic profiles) were analysed using the nonlinear mixed-effects model program NONMEM. The influence of numerous covariates was tested, and the final model was validated by data splitting. For Bayesian estimation, the best limited-sampling strategy was determined based on the D-optimality criterion, and validation performed in an independent group of 60 patients. RESULTS: The pharmacokinetics of ciclosporin microemulsion were accurately described by a two-compartment model with Erlang distribution for the absorption process. The type of graft and post-transplantation period were identified as significant sources of variability of the absorption parameter. Both apparent volume of the central compartment after oral administration (V1/F) and apparent oral clearance (CL/F) increased with bodyweight. The best limited-sampling strategy for Bayesian estimation was 0 hour, 1 hour and 3 hour post-dose, providing accurate estimation of ciclosporin microemulsion AUC12 in all patients of the test group, with a mean bias of 2.0 +/- 10.5% (range: -19.1% to -21.4% and 95% CI -0.6, +4.7). CONCLUSION: Population pharmacokinetic analysis of ciclosporin microemulsion in allograft transplants resulted in the design of a new pharmacokinetic model for ciclosporin microemulsion, identification of significant covariates and the design of an accurate MAP-BE based on three blood concentrations and these covariates.

Adolescent↗

PubMed2000

Cost implications for the use of inhaled anti-inflammatory medications in the treatment of asthma.

OBJECTIVE: To compare the expected costs of treating patients with asthma with versus without inhaled anti-inflammatory medications, adjusting for other factors that also influence medical care expenditures. DESIGN: Nonlinear exponential regression analyses were used to estimate relationships between medical care expenditures and treatment with inhaled corticosteroids, sodium cromoglycate (cromolyn) or nedocromil. The regressions adjusted for differences in patients' demographics, location, plan type and severity of illness. SETTING: Large, self-insured, corporate-sponsored medical plans represented in MarketScan database. PATIENTS AND PARTICIPANTS: 7466 continuously enrolled patients with asthma. INTERVENTIONS: Treatment with inhaled corticosteroids, sodium cromoglycate or nedocromil. MAIN OUTCOME MEASURES: (i) Total inpatient, outpatient and pharmaceutical expenditures; and (ii) asthma-related expenditures in the 1996 calendar year. RESULTS: If all patients had been treated with inhaled anti-inflammatory drugs, total expenditures would be expected to be about $US944.82 per patient lower, on average, than would be the case if no patients received these drugs. Asthma-related expenditures would be about $US498.74 per patient higher, on average, if all patients were treated with these drugs. CONCLUSIONS: Using inhaled anti-inflammatory agents would be associated with higher asthma-related expenditures but lower total expenditures. Treatment with inhaled anti-inflammatory drugs may represent an investment in better care that pays off with better health and lower total medical care expenditures.

Administration, Inhalation↗

PubMed2000

Effect of supplements on growth and forage intake by stocker steers grazing wheat pasture.

This experiment was conducted with stocker steers to determine the effects of supplementary fiber and grain on ruminal acid concentrations and OM intake following abrupt dietary change to lush, primary-growth wheat (Triticum aestivum) pasture and to measure the effects of those supplements on weight gain at different levels of herbage mass (HM). Each of four irrigated wheat pastures (2.4, 3.6, 4.9, and 6.1 ha) was stocked with nine Angus crossbred steers (mean = 189 kg). In each pasture, three steers were individually fed a daily supplement of 11.3 g of cottonseed hulls (CSH)/kg BW(.75), three steers were fed a supplement mixture of 11.3 g CSH/kg BW(.75) and 8.5 g corn grain/kg BW(.75), and three steers remained as controls. Body weight and HM changes were measured at 28-d intervals throughout the experiment. Ruminal samples for VFA determination were collected twice during the 1st wk on pasture. Organic matter intake calculations were based on fecal output and OM digestibility estimates made during the 2nd wk on pasture. Fecal outputs were estimated from nonlinear least squares analyses using a two-compartment rumen model of excretion patterns of Yb following a single oral dose. Digestibility of OM was estimated using indigestible NDF in feed and feces as an internal marker. Dietary supplements had no detectable effect on ruminal VFA characteristics. The magnitude of changes in ruminal acetate:propionate ratios between d 3 and 7 on pasture was significantly and negatively related to ADG during the first 28-d growth measurement period. Body condition scores taken on d 0 also had a significant, negative relationship to ADG. Average fecal output was greater for steers fed supplements (36 g/kg BW(.75)) than for control steers (30 g/kg BW(.75)) (P < .03). The supplements also significantly reduced estimates of total diet OM digestibility. However, supplements had no measurable effect on BW changes. Herbage mass up to 1,000 kg/ha had a significant and positive effect on ADG, which was 1.44 kg during Period 1, when HM was apparently not limiting in any pasture. The deduced threshold level of the influence of HM on ADG was 850 kg/ha. Under the conditions of this experiment, the effects of supplemental fiber and(or) grain on fecal output and OM digestibility were detected. However, in the amounts fed, these supplements had no detectable effect on ADG at any level of HM.

Animal Feed↗

PubMed1999

Perception of artificial stereoscopic stimuli from an incorrect viewing point.

The present study investigates the distortions in the perception of artificial stereoscopic displays seen from an inappropriate distance and/or orientation. Stereoscopic displays represent 3-D information correctly, provided they are seen from the correct station point. The viewing point may differ from the correct station point in its distance or in its orientation to the screen. These differences lead to distortions that can be predicted mathematically. However, the perceptual function may be different from the predictions, since people may possibly compensate for the distortions. To test the degree of this compensation, participants saw anaglyphic stereoscopic stimuli that showed angles in the horizontal plane, and their perception of the configuration was tested for various orientations and distances. The estimates were compared with the values predicted from the mathematical functions, and participants' virtual positions were reconstructed via nonlinear regressions. The analyses revealed a moderate compensation for viewing orientations and a systematically overestimation of the viewing distances. These results indicate that people compensate partially for distortions in stereopsis, given that the relevant information is available.

Adult↗

PubMed1996

Dynamic modeling of epidemiologic patterns of schistosomiasis morbidity.

This paper uses preliminary mathematical models to examine how the dynamic relationship between schistosomiasis infection and disease is altered by chemotherapy. Two types of morbidity are examined: an acute form that is proportional to current infection intensity and that resolves after treatment, and a chronic form that represents accumulated experience of infection and that does not resolve after treatment, or resolves according to some delay function. The analyses indicate that nonlinearities in the age and frequency distributions of infection intensity have a marked impact on the patterns of morbidity. They also suggest that treatment close to the age of maximum infection intensity (i.e., children of schoolage) is most effective in controlling morbidity in the community as a whole. These models are preliminary, and their further development to include more realistic assumptions in relation to field data is discussed.

Acute Disease↗

PubMed1994

Changes in ventilatory function in grain processing and animal feed workers in relation to exposure to organic dust.

OBJECTIVES: The effects of organic dust exposure on the configuration of the maximum expiratory flow volume (MEFV) curve was examined multivariately. METHODS: Data from 390 male workers in the animal feed industry in The Netherlands were analyzed. A multivariate technique called nonlinear canonical correlation analyses was used to study the relationship between a set of organic dust exposure variables and a set of ventilatory function variables. RESULTS: The results indicate an almost independent effect of the overall mean organic dust exposure and the number of years of organic dust exposure on ventilatory function. Increasing mean organic dust exposure was associated with a decrease in both forced expiratory volume in 1 s (FEV1.0) and forced vital capacity (FVC) and decreased flows at high lung volumes only. Increasing number of years of dust exposure was associated with a decrease in FEV1.0 and a decrease in flow at all lung volumes, while the FVC seemed relatively constant. These two distinct patterns of reduction in ventilatory function may represent two different pathological processes. Whereas workers with prolonged exposure showed reduced values for all of the MEFV curve variables, except the FVC, those with only a few years of exposure especially showed a decrease in FVC and peak expiratory flow. The effect of current organic dust exposure was more evident for nonsmokers than for ex-smokers and current smokers. CONCLUSION: The major finding of this study was an independent effect of overall mean organic dust exposure and the number of years of organic dust exposure on the MEFV curve.

Adult↗

PubMed1998

Market influences on internal medicine residents' decisions to subspecialize.

BACKGROUND: Managed care reduces the demand for internal medicine subspecialists, but little empirical information is available on how increasing managed care may be affecting residents' training choices. OBJECTIVE: To determine whether increased managed care penetration into an area where residents train was associated with a decreased likelihood that residents who completed general internal medicine training pursued subspecialty training. DESIGN: Secondary logistic regression analysis of data from the 1993 cohort of general internal medicine residents. SETTING: U.S. residency training sites. PARTICIPANTS: 2263 U.S. medical school graduates who completed general internal medicine residency training in 1993. MEASUREMENTS: The outcome variable (enrollment in subspecialty training) was derived from the Graduate Medical Education Tracking Census of the Association of American Medical Colleges (AAMC). Health maintenance organization (HMO) penetration (possible range, 0.0 to 1.0; higher values indicate greater penetration) was taken from the Interstudy Competitive Edge Database. Individual and medical school covariates were taken from the AAMC's Student and Applicant Information Management System database and the National Institutes of Health Information for Management Planning, Analysis, and Coordination system. The U.S. Census division was included as a control covariate. RESULTS: 980 participants (43%) enrolled in subspecialty training. Logistic regression analyses indicated a nonlinear association between managed care penetration into a training area and the odds of subspecialization. Increasing managed care penetration was associated with decreasing odds of subspecialization when penetration exceeded 0.15. The choice of subspecialty training increased as HMO penetration increased from 0 to 0.15. CONCLUSIONS: Local market forces locally influenced the career decisions of internal medicine residents, but the influence was small compared with the effects of age and sex. These results suggest that market forces help to achieve more desirable generalist-to-specialist physician ratios in internal medicine.

Age Factors↗

PubMed2006

[Prediction of bone strength using a CT based finite element method].

Hip fractures are the most serious complication of osteoporosis and have been recognized as a major public health problem. In elderly persons, hip fractures occur as a result of increased fragility of the proximal femur due to osteoporosis. It is essential to precisely quantify the strength of the proximal femur in order to estimate the fracture risk and plan preventive interventions. Computed tomography (CT)-based finite element analysis could possibly achieve precise assessment of the strength of the proximal femur. We have developed a three dimensional simulation model that could accurately predict the strength and surface strains of the proximal femur using a CT-based finite element method. The axial CT scans of the proximal femora were obtained with a calibration phantom, from which the 3D finite element models were constructed. Materially nonlinear finite element analyses were performed. The yield and fracture loads were calculated, while the sites where elements failed and the distributions of the principal strains and stresses were determined. The simulation is patient specific and could provide us of a useful tool to evaluate fracture risk in patients with osteoporosis. The technology utilized in this method would make a rapid progress in accordance with the progress of both imaging and computer technologies and much more precise prediction of the fracture risk will be realized in the near future.

Aged↗

PubMed2004

A biomechanical study of lumbar fusion based on a three-dimensional nonlinear finite element method.

Biomechanical analyses under compression, flexion, and extension loading were performed to evaluate the stability of interbody, posterolateral, posterior, and facet fusions using a nonlinear three-dimensional finite element method. The effects of facet fusion on other lumbar fusions were also examined. A three-dimensional L4-L5 motion segment model was developed that took into consideration the material nonlinearities of ligaments and annular fibers and the contact nonlinearities of facet joints. Of all models of fusion, maximum rigidity was obtained in the interbody fusion model. In the posterolateral, posterior, and facet fusion models under compression, axial displacement and flexion rotation were induced. In combination with facet fusion, the interbody, posterolateral, and posterior fusion models demonstrated a decrease in axial displacement of about 6%, 1%, and 5%, respectively, under compression and a decrease in rotation angle of about 22%, 12%, and 48%, respectively, under flexion-extension loading. Stress concentration moved principally toward the fusion site, indicating increased load transfer across the fusion mass. Our findings suggest that a more solid fixation can be expected from lumbar fusion--especially in posterior fusion--if facet fusion is performed.

Compressive Strength↗

PubMed1995

Spatial heterogeneity, nonlinear dynamics and chaos in infectious diseases.

There is currently considerable interest in the role of nonlinear phenomena in the population dynamics of infectious diseases. Childhood diseases such as measles are particularly well documented dynamically, and have recently been the subject of analyses (of both models and notification data) to establish whether the pattern of epidemics is chaotic. Though the spatial dynamics of measles have also been extensively studied, spatial and nonlinear dynamics have only recently been brought together. The present review concentrates mainly on describing this synthesis. We begin with a general review of the nonlinear dynamics of measles models, in a spatially homogeneous environment. Simple compartmental models (specifically the SEIR model) can behave chaotically, under the influence of strong seasonal 'forcing' of infection rate associated with patterns of schooling. However, adding observed heterogeneities such as age structure can simplify the deterministic dynamics back to limit cycles. By contrast all current strongly seasonally forced stochastic models show large amplitude irregular fluctuations, with many more 'fadeouts' of infection that is observed in real communities of similar size. This indicates that (social and/or geographical) spatial heterogeneity is needed in the models. We review the exploration of this problem with nonlinear spatiotemporal models. The few studies to date indicate that spatial heterogeneity can help to increase the realism of models. However, a review of nonlinear analyses of spatially subdivided measles data show that more refinements of the models (particularly in representing the impact of human demographic changes on infection dynamics) are required. We conclude with a discussion of the implication of these results for the dynamics of infectious diseases in general and, in particular, the possibilities of cross fertilization between human disease epidemiology and the study of plant and animal diseases.

Communicable Diseases↗