[Show abstract][Hide abstract] ABSTRACT: Population epidemiological models where hosts can be infected sequentially by different strains have the potential to help us understand many important diseases. Researchers have in recent years started to develop and use such models, but the extra layer of complexity from multiple strains brings with it many technical challenges. It is therefore hard to build models which have realistic assumptions yet are tractable. Here we outline some of the main challenges in this area. First we begin with the fundamental question of how to translate from complex small-scale dynamics within a host to useful population models. Next we consider the nature of so-called “strain space”. We describe two key types of host heterogeneities, and explain how models could help generate a better understanding of their effects. Finally, for diseases with many strains, we consider the challenge of modelling how immunity accumulates over multiple exposures.
[Show abstract][Hide abstract] ABSTRACT: Vaccination has been one of the most successful public health measures since the introduction of basic sanitation. Substantial mortality and morbidity reductions have been achieved via vaccination against many infections, and the list of diseases that are potentially controllable by vaccines is growing steadily. We introduce key challenges for modeling in shaping our understanding and guiding policy decisions related to vaccine preventable diseases.
[Show abstract][Hide abstract] ABSTRACT: This study examined the association between prenatal exposure to pandemic influenza and cardiovascular events in adulthood.
Using Danish surveillance data to identify months when influenza activity was highest during three previous pandemics (1918, 1957, and 1968), persons were defined as exposed/unexposed based on whether they were in utero during peak months of one of the pandemics. Episodes of acute myocardial infarction (MI) and stroke were identified in the Danish National Registry of Patients covering all Danish hospitals since 1977.
Information from Danish national registries on all persons with a Civil Personal Registry number and birthdates in 1915 through 1922, 1954 through 1960, and 1966 through 1972 was collected.
Crude incidence rate ratios (IRRs) were calculated per pandemic. Generalized linear models were fit to estimate IRRs adjusted for sex.
For acute MI, sex-adjusted IRRs for persons in utero during peaks of the 1918, 1957, and 1968 pandemics, compared with those born afterward, were 1·02 (95% confidence interval (CI): 0·99, 1·05), 0·96 (95% CI: 0·87, 1·05), and 1·18 (95% CI: 0·96, 1·45), respectively. For stroke, the corresponding IRRs were 0·99 (95% CI: 0·97, 1·02), 0·99 (95% CI: 0·92, 1·05), and 0·85 (95% CI: 0·77, 0·94), respectively.
There was generally no evidence of an association between prenatal influenza exposure and acute MI or stroke in adulthood. However, survivor bias and left truncation of outcomes for the 1918 pandemic are possible, and the current young ages of persons included in the analyses for the 1957 and 1968 pandemics may warrant later re-evaluation.
Influenza and Other Respiratory Viruses 01/2014; 8(1):83-90. · 1.47 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Deterministic models have a long history of being applied to the study of infectious disease epidemiology. We highlight and discuss nine challenges in this area. The first two concern the endemic equilibrium and its stability. We indicate the need for models that describe multi-strain infections, infections with time-varying infectivity, and those where superinfection is possible. We then consider the need for advances in spatial epidemic models, and draw attention to the lack of models that explore the relationship between communicable and non-communicable diseases. The final two challenges concern the uses and limitations of deterministic models as approximations to stochastic systems.
[Show abstract][Hide abstract] ABSTRACT: Clostridium difficile infection (CDI) is gradually being recognised as a cause of morbidity in the community. We investigated the incidence and clinical characteristics of CDI in a community setting and characterised the C. difficile strains by toxin gene profiling and polymerase chain reaction (PCR) ribotyping. Patients included in the study had attended general practice, primarily because of diarrhoea; CDI patients (259 patients; 121 <2 years of age) had positive cultures for toxigenic C. difficile and non-CDI patients (455 patients) were culture-negative. Outcome variables included the frequency and duration of diarrhoea, vomiting, stomach ache, fever >38 °C, weight loss and sick leave. Data were analysed by logistic regression. CDI patients <2 and ≥2 years of age with C. difficile as the only enteropathogen in the faecal sample reported slimy stools (65 % vs. 62 %), stomach ache (60 % vs. 75 %), weight loss (50 % vs. 76 %) and duration of diarrhoea >15 days (59 % vs. 73 %) as the predominant symptoms. CDI patients ≥2 years old reported duration of diarrhoea >15 days more often compared to non-CDI patients (73 % vs. 27 %, p < 0.0001). The annual incidence of CDI was 518 and 23/100,000 for patients <2 and ≥2 years of age, respectively, and 46/100,000 in the subgroup of patients ≥60 years of age. CDI was characterised by stomach ache and persistent diarrhoea, often leading to weight loss. This emphasises the importance of diagnosing CDI not only in hospitalised patients, but also in individuals ≥2 years of age attending general practice because of gastrointestinal symptoms, especially in the elderly, where the incidence of CDI is high.
European Journal of Clinical Microbiology 12/2013; · 3.02 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: SUMMARY To identify risk factors for Clostridium difficile infection (CDI) in Danish patients consulting general practice with gastrointestinal symptoms, a prospective matched case-control study was performed; cases (N = 259) had positive cultures for toxigenic C. difficile and controls (N = 455) negative cultures. Data were analysed by conditional logistic regression. In patients aged ⩾2 years (138 cases), hospitalization [odds ratio (OR) 8·4, 95% confidence interval (CI) 3·1-23], consumption of beef (OR 5·5, 95% CI 2·0-15), phenoxymethylpenicillin (OR 15, 95% CI 2·7-82), dicloxacillin (OR 27, 95% CI 3·6-211), and extended spectrum penicillins (OR 9·2, 95% CI 1·9-45) were associated with CDI. In patients aged <2 years none of these were associated with CDI, but in a subgroup analysis contact with animals was associated with CDI (OR 8·1, 95% CI 1·0-64). This study emphasizes narrow-spectrum penicillins, and suggests beef consumption, as risk factors for CDI in adults, and indicates a different epidemiology of CDI in infants.
Epidemiology and Infection 09/2013; · 2.49 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Understanding the biological mechanisms underlying episodic outbreaks of infectious diseases is one of mathematical epidemiology's major goals. Historic records are an invaluable source of information in this enterprise. Pertussis (whooping cough) is a re-emerging infection whose intermittent bouts of large multiannual epidemics interspersed between periods of smaller-amplitude cycles remain an enigma. It has been suggested that recent increases in pertussis incidence and shifts in the age-distribution of cases may be due to diminished natural immune boosting. Here we show that a model that incorporates this mechanism can account for a unique set of pre-vaccine-era data from Copenhagen. Under this model, immune boosting induces transient bursts of large amplitude outbreaks. In the face of mass vaccination, the boosting model predicts larger and more frequent outbreaks than do models with permanent or passively-waning immunity. Our results emphasize the importance of understanding the mechanisms responsible for maintaining immune memory for pertussis epidemiology.
PLoS ONE 08/2013; 8(8):e72086. · 3.53 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The average age of infection is expected to vary during seasonal epidemics in a way that is predictable from the epidemiological features, such as the duration of infectiousness and the nature of population mixing. However, it is not known whether such changes can be detected and verified using routinely collected data. We examined the correlation between the weekly number and average age of cases using data on pre-vaccination measles and rotavirus. We show that age-incidence patterns can be observed and predicted for these childhood infections. Incorporating additional information about important features of the transmission dynamics improves the correspondence between model predictions and empirical data. We then explored whether knowledge of the age-incidence pattern can shed light on the epidemiological features of diseases of unknown aetiology, such as Kawasaki disease (KD). Our results indicate KD is unlikely to be triggered by a single acute immunizing infection, but is consistent with an infection of longer duration, a non-immunizing infection or co-infection with an acute agent and one with longer duration. Age-incidence patterns can lend insight into important epidemiological features of infections, providing information on transmission-relevant population mixing for known infections and clues about the aetiology of complex paediatric diseases.
Proceedings of the Royal Society B: Biological Sciences 03/2012; 279(1739):2736-43. · 5.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the final size equation for an epidemic in a subdivided population with general mixing patterns among subgroups. The equation is determined by a matrix with the same spectrum as the next generation matrix and it exhibits a threshold controlled by the common dominant eigenvalue, the basic reproduction number R0. There is a unique positive solution giving the size of the epidemic if and only if R0 exceeds unity. When mixing heterogeneities arise only from variation in contact rates and proportionate mixing, the final size of the epidemic in a heterogeneously mixing population is always smaller than that in a homogeneously mixing population with the same basic reproduction number R0. For other mixing patterns, the relation may be reversed.
Bulletin of Mathematical Biology 10/2011; 73(10):2305-21. · 2.02 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Although pregnancy is a recognized risk factor for severe influenza infection, the effect of influenza on miscarriages and births remains unclear. We examined the relationship between influenza and birth rates during the 1918 pandemic in the United States, Denmark, Sweden, and Norway.
We compiled monthly birth rates from 1911 through 1930 in 3 Scandinavian countries and the United States, identified periods of unusually low or high birth rates, and quantified births as "missing" or "in excess" of the normal expectation. Using monthly influenza data, we correlated the timing of peak pandemic exposure and depressions in birth rates, and identified pregnancy stages at risk of influenza-related miscarriage.
Birth rates declined in all study populations in spring 1919 by a mean of 2.2 births per 1000 persons, representing a 5%-15% drop below baseline levels (P < .05). The 1919 natality depression reached its trough 6.1-6.8 months after the autumn pandemic peak, suggesting that missing births were attributable to excess first trimester miscarriages in ∼1 in 10 women who were pregnant during the peak of the pandemic. Pandemic-related mortality was insufficient to explain observed patterns.
The observed birth depressions were consistent with pandemic influenza causing first trimester miscarriages in ∼1 in 10 pregnant women. Causality is suggested by temporal synchrony across geographical areas.
The Journal of Infectious Diseases 10/2011; 204(8):1157-64. · 5.85 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Measuring the burden of historic pandemics is not straightforward and often must be based on suboptimal mortality data. For example, the critical 1918 pandemic global burden estimate was based on excess in annual all-cause mortality--calculated as the difference between deaths during 1918-1920 and the surrounding 3-year periods. One intriguing result was a ∼ 40-fold between-country variation in pandemic mortality burden: ∼ 0.2% of Danes died, compared to ∼ 8% of populations in some Indian provinces (Murray et al., 2006 ). Using the same methodology and data source we explore the robustness of this methodology for different age-groups. For infants the country estimates varied 100-fold, from 15 to 1500 excess deaths/10,000 population, while for adults ≥ 45 years estimates ranged from -70 to 170/10,000 population. In contrast, estimates for children, 1-14 years, and adults aged 15-44 years, were far more stable. We next used detailed mortality data from Copenhagen to compare such estimates to the more precise estimates obtained from monthly mortality time series data and respiratory deaths. We found that the all-cause annual method substantially underestimated due to an unexplained depression in all-cause mortality in Denmark in 1918 and deaths caused by other epidemic diseases during the baseline periods. We conclude that country estimates for infants and older adults were highly variable by the Murray method due to substantial variability in annual all-cause mortality. A more precise 1918 pandemic burden estimate would be gotten from either focusing analysis on persons age 1-44 who suffered 95% of all pandemic deaths and had a substantial rise over their baseline mortality level, or if possible focus analysis on annual respiratory deaths. For less severe pandemics, including the ongoing 2009 H1N1 pandemic, the use of all-cause mortality data requires careful consideration of excess deaths in defined pandemic periods and a focus on age groups known to be at risk.
[Show abstract][Hide abstract] ABSTRACT: The 1918 influenza pandemic was associated with an unusual age pattern of mortality, with most deaths occurring among young adults. Few studies have addressed changes in the age distribution for influenza-related mortality in the pre-pandemic and post-pandemic period, which has implications for pandemic preparedness. In the present paper, we analyse the age patterns of influenza-related excess mortality in the decades before and after the 1918 pandemic, using detailed historic surveillance data from Copenhagen.
Weekly age-specific rates of respiratory mortality and influenza-like-illnesses were compiled for 1904-1937. Seasonal excess rates of morbidity and mortality attributable to influenza were calculated using a seasonal regression approach. To characterize the age patterns of influenza-related deaths in individual seasons, we used two rate ratio (RR) measures representing ratios of excess mortality rates between age groups and influenza seasons.
Individuals aged 15-64 years experienced sharply elevated excess respiratory mortality rates in the 1918-1919 and 1919-1920 pandemic periods, compared to pre-pandemic seasons (RR for excess mortality in the fall of 1918 = 67 relative to inter-pandemic seasons). Of all excess respiratory deaths occurring during 1918-1919, 84% were reported in individuals 15-64 years. By contrast, seniors over 65 years of age experienced no measurable excess mortality during 1918-1919 and moderate excess mortality in the recrudescent pandemic wave of 1919-1920. The first post-pandemic season associated with high excess mortality rates in individuals over 65 years was 1928-1929, with 73% of excess deaths occurring among seniors. We estimate that the age patterns of influenza-related mortality returned to pre-pandemic levels after 1925, based on trends in the rate ratio of excess respiratory mortality in people under and over 65 years.
The unusual elevation of excess respiratory mortality rates in young and middle-aged adults was confined to the first three years of A/H1N1 virus circulation 1918-1920; the rapid return to "epidemic" mortality pattern in this age group was probably due to high attack rates and build-up of immunity. In contrast, seniors were completely spared from pandemic mortality during 1918-1919, likely due to childhood exposure to an A/H1-like influenza virus. The rise in excess mortality rates in seniors in the recrudescent pandemic wave of 1919-1920 may suggest the emergence of an early influenza A/H1N1 drift variant. Subsequent drift events may have been associated with the particularly severe 1928-1929 epidemic in Denmark and elsewhere.
[Show abstract][Hide abstract] ABSTRACT: Seasonal variation in infection transmission is a key determinant of epidemic dynamics of acute infections. For measles, the best-understood strongly immunizing directly transmitted childhood infection, the perception is that term-time forcing is the main driver of seasonality in developed countries. The degree to which this holds true across other acute immunizing childhood infections is not clear. Here, we identify seasonal transmission patterns using a unique long-term dataset with weekly incidence of six infections including measles. Data on age-incidence allow us to quantify the mean age of infection. Results indicate correspondence between dips in transmission and school holidays for some infections, but there are puzzling discrepancies, despite close correspondence between average age of infection and age of schooling. Theoretical predictions of the relationship between amplitude of seasonality and basic reproductive rate of infections that should result from term-time forcing are also not upheld. We conclude that where yearly trajectories of susceptible numbers are perturbed, e.g. via waning of immunity, seasonality is unlikely to be entirely driven by term-time forcing. For the three bacterial infections, pertussis, scarlet fever and diphtheria, there is additionally a strong increase in transmission during the late summer before the end of school vacations.
Proceedings of the Royal Society B: Biological Sciences 10/2009; 276(1676):4111-8. · 5.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The 1918-1919 A/H1N1 influenza pandemic killed approximately 50 million people worldwide. Historical records suggest that an early pandemic wave struck Europe during the summer of 1918.
We obtained surveillance data that were compiled weekly, during 1910-1919, in Copenhagen, Denmark; the records included medically treated influenza-like illnesses (ILIs), hospitalizations, and deaths by age. We used a Serfling seasonal regression model to quantify excess morbidity and mortality, and we estimated the reproductive number (R) for the summer, fall, and winter pandemic waves.
A large epidemic occurred in Copenhagen during the summer of 1918; the age distribution of deaths was characteristic of the 1918-1919 A/H1N1 pandemic overall. That summer wave accounted for 29%-34% of all excess ILIs and hospitalizations during 1918, whereas the case-fatality rate (0.3%) was many-fold lower than that of the fall wave (2.3%). Similar patterns were observed in 3 other Scandinavian cities. R was substantially higher in summer (2.0-5.4) than in fall (1.2-1.6) in all cities.
The Copenhagen summer wave may have been caused by a precursor A/H1N1 pandemic virus that transmitted efficiently but lacked extreme virulence. The R measured in the summer wave is likely a better approximation of transmissibility in a fully susceptible population and is substantially higher than that found in previous US studies. The summer wave may have provided partial protection against the lethal fall wave.
The Journal of Infectious Diseases 02/2008; 197(2):270-8. · 5.78 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Cross-immunity among related strains can account for the selection producing the slender phylogenetic tree of influenza A and B in humans. Using a model of seasonal influenza epidemics with drift (Andreasen, 2003. Dynamics of annual influenza A epidemics with immuno-selection. J. Math. Biol. 46, 504-536), and assuming that two mutants arrive in the host population sequentially, we determine the threshold condition for the establishment of the second mutant in the presence of partial cross-protection caused by the first mutant and their common ancestors. For fixed levels of cross-protection, the chance that the second mutant establishes increases with rho the basic reproduction ratio and some temporary immunity may be necessary to explain the slenderness of flu's phylogenetic tree. In the presence of moderate levels of temporary immunity, an asymmetric situation can arise in the season after the two mutants were introduced and established: if the offspring of the new mutant arrives before the offspring of the resident type, then the mutant-line may produce a massive epidemic suppressing the original lineage. However, if the original lineage arrives first then both strains may establish and the phylogenetic tree may bifurcate.
Theoretical Population Biology 10/2006; 70(2):164-73. · 1.53 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We use a mathematical model to study the evolution of influenza A during the epidemic dynamics of a single season. Classifying strains by their distance from the epidemic-originating strain, we show that neutral mutation yields a constant rate of antigenic evolution, even in the presence of epidemic dynamics. We introduce host immunity and viral immune escape to construct a non-neutral model. Our population dynamics can then be framed naturally in the context of population genetics, and we show that departure from neutrality is governed by the covariance between a strain's fitness and its distance from the original epidemic strain. We quantify the amount of antigenic evolution that takes place in excess of what is expected under neutrality and find that this excess amount is largest under strong host immunity and long epidemics.
Proceedings of the Royal Society B: Biological Sciences 07/2006; 273(1592):1307-16. · 5.29 Impact Factor