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Background It sparked considerable attention from international media when Denmark lifted restrictions against COVID-19 in February 2022 amidst widespread transmission of the new SARS-CoV-2 Omicron variant and a steep rise in reported COVID-19 mortality based on the 30-day COVID-19 death count. Aim Our aim was to investigate how coincidental infections affected COVID-19 mortality estimates following the introduction of the Omicron variant in late 2021. Methods We compared the 30-day COVID-19 death count with the observed mortality using three alternative mortality estimation methods; (i) a mathematical model to correct the 30-day COVID-19 death count for coincidental deaths, (ii) the Causes of Death Registry (CDR) and (iii) all-cause excess mortality. Results There was a substantial peak in the 30-day COVID-19 death count following the emergence of the Omicron variant in late 2021. However, there was also a substantial change in the proportion of coincidental deaths, increasing from 10–20% to around 40% of the recorded COVID-19 deaths. The high number of 30-day COVID-19 deaths was not reflected in the number of COVID-19 deaths in the CDR and the all-cause excess mortality surveillance. Conclusion Our analysis showed a distinct change in the mortality pattern following the introduction of Omicron in late 2021 with a markedly higher proportion of people estimated to have died with, rather than of, COVID-19 compared with mortality patterns observed earlier in the COVID-19 pandemic. Our findings highlight the importance of incorporating alternative mortality surveillance methods to more correctly estimate the burden of COVID-19 as the pandemic continues to evolve.

Background The COVID-19 pandemic is one of the most serious global public health threats of recent times. Understanding SARS-CoV-2 transmission is key for outbreak response and to take action against the spread of disease. Transmission within the household is a concern, especially because infection control is difficult to apply within this setting. Aim The objective of this observational study was to investigate SARS-CoV-2 transmission in Danish households during the early stages of the COVID-19 pandemic. Methods We used comprehensive administrative register data from Denmark, comprising the full population and all COVID-19 tests from 27 February 2020 to 1 August 2020, to estimate household transmission risk and attack rate. Results We found that the day after receiving a positive test result within the household, 35% (788/2,226) of potential secondary cases were tested and 13% (98/779) of these were positive. In 6,782 households, we found that 82% (1,827/2,226) of potential secondary cases were tested within 14 days and 17% (371/2,226) tested positive as secondary cases, implying an attack rate of 17%. We found an approximate linear increasing relationship between age and attack rate. We investigated the transmission risk from primary cases by age, and found an increasing risk with age of primary cases for adults (aged ≥ 15 years), while the risk seems to decrease with age for children (aged Conclusions Although there is an increasing attack rate and transmission risk of SARS-CoV-2 with age, children are also able to transmit SARS-CoV-2 within the household.

BackgroundThe Covid-19 pandemic is one of the most serious global public health threats in recent times. Understanding transmission of SARS-CoV-2 is of utmost importance to be able to respond to outbreaks and take action against spread of the disease. Transmission within the household is a concern, especially because infection control is difficult to apply within the household domain.MethodsWe used comprehensive administrative register data from Denmark, comprising the full population and all COVID-19 tests, to estimate household transmission risk and attack rate.ResultsWe studied the testing dynamics for COVID-19 and found that the day after receiving a positive test result within the household, 35% of potential secondary cases were tested and 13% of these were positive. After a primary case in 6,782 households, 82% of potential secondary cases were tested within 14 days, of which 17% tested positive as secondary cases, implying an attack rate of 17%. Among primary cases, those aged 0-24 were underrepresented when compared with the total population. We found an approximately linearly increasing relationship between attack rate and age. We investigated the transmission risk from primary cases by age, and found an increasing risk with age of primary cases for adults, while the risk seems to decrease with age for children.ConclusionsAlthough there is an increasing attack rate and transmission risk of SARS-CoV-2 with age, children are also able to transmit SARS-CoV-2 within the household.

The competition between two pathogen strains during the course of an epidemic represents a fundamental step in the early evolution of emerging diseases as well as in the antigenic drift process of influenza. The outcome of the competition, however, depends not only on the epidemic properties of the two strains but also on the timing and size of the introduction, characteristics that are poorly captured by deterministic mean-field epidemic models. We describe those aspects of the competition that can be determined from the mean-field models giving the range of possible final sizes of susceptible hosts and cumulated attack rates that could be observed after an epidemic with two cross-reacting strains. In the limit where the size of the initial infection goes to zero, the possible outcomes lie on a (one dimensional) curve in the outcome space.

In the century since the 1918 influenza pandemic, insights have been sought to explain the pandemic’s signature pattern of high death rates in young adults and low death rates in the elderly and infants. Our understanding of the origin and evolution of the pandemic has shifted considerably. We review evidence of the characteristic age-related pattern of death during the 1918 pandemic relative to the “original antigenic sin” hypothesis. We analyze age-stratified mortality data from Copenhagen around 1918 to identify break points associated with unusual death risk. Whereas infants had no meaningful risk elevation, death risk gradually increased, peaking for young adults 20–34 years of age before dropping sharply for adults ages 35–44 years, suggesting break points for birth cohorts around 1908 and 1878. Taken together with data from previous studies, there is strong evidence that those born before 1878 or after 1908 were not at increased risk of dying of 1918 pandemic influenza. Although the peak death risk coincided with the 1889–1892 pandemic, the 1908 and 1878 break points do not correspond with known pandemics. An increasing number of interdisciplinary studies covering fields such as virology, phylogenetics, death, and serology offer exciting insights into patterns and reasons for the unusual extreme 1918 pandemic mortality risk in young adults.

Mounting epidemiological evidence supports the occurrence of a mild herald pandemic wave in the spring and summer of 1918 in North America and Europe, several months before the devastating autumn outbreak that killed an estimated 2% of the global population. These epidemiological findings corroborate the anecdotal observations of contemporary clinicians who reported widespread influenza outbreaks in spring and summer 1918, with sporadic occurrence of unusually severe clinical manifestations in young adults. Initially seen as controversial, these findings were eventually confirmed by retrospective identification of influenza specimens collected from U.S. soldiers who died from acute respiratory infections in May-August 1918. Other studies found that having an episode of influenza illness during the spring herald wave was highly protective in the severe autumn wave. Here, we conduct a systematic review of the clinical, epidemiological, and virological evidence supporting the global occurrence of mild herald waves of the 1918 pandemic and place these historic observations in the context of pandemic preparedness. Taken together, historic experience with the 1918 and subsequent pandemics shows that increased severity in second and later pandemic waves may be the rule rather than the exception. Thus, a sustained pandemic response in the first years following a future pandemic is critical; conversely, multiwave pandemic patterns allow for more time to rollout vaccines and antivirals.

Objectives We evaluated the effect of an antibiotic stewardship programme (ASP) on the use of antibiotics and resistance levels of Escherichia coli using a method that allowed direct comparison between an intervention hospital and a control hospital. Methods The study was conducted as a retrospective controlled interrupted time series (ITS) at two university teaching hospitals, intervention and control, with 736 and 552 beds, respectively. The study period was between January 2008 and September 2014. We used ITS analysis to determine significant changes in antibiotic use and resistance levels of E. coli. Results were directly compared with data from the control hospital utilizing a subtracted time series (STS). Results Direct comparison with the control hospital showed that the ASP was associated with a significant change in the level of use of cephalosporins [-151 DDDs/1000 bed-days (95% CI -177, -126)] and fluoroquinolones [-44.5 DDDs/1000 bed-days (95% CI -58.9, -30.1)]. Resistance of E. coli showed a significant change in slope for cefuroxime [-0.13 percentage points/month (95% CI -0.21, -0.057)] and ciprofloxacin [-0.15 percentage points/month (95% CI -0.26, -0.038)]. Conclusions The ASP significantly reduced the use of cephalosporins and fluoroquinolones, with concomitant decreasing levels of E. coli resistance to cefuroxime and ciprofloxacin. The same development was not observed at the control hospital.

Pathogens that consist of multiple antigenic variants are a serious public health concern. These infections, which include dengue virus, influenza and malaria, generate substantial morbidity and mortality. However, there are considerable theoretical challenges involved in modelling such infections. As well as describing the interaction between strains that occurs as a result cross-immunity and evolution, models must balance biological realism with mathematical and computational tractability. Here we review different modelling approaches, and suggest a number of biological problems that are potential candidates for study with these methods. We provide a comprehensive outline of the benefits and disadvantages of available frameworks, and describe what biological information is preserved and lost under different modelling assumptions. We also consider the emergence of new disease strains, and discuss how models of pathogens with multiple strains could be developed further in future. This includes extending the flexibility and biological realism of current approaches, as well as interface with data.

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{R}_{0}}$\end{document}: There is a unique positive solution giving the size of the epidemic if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{R}_{0}}$\end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{R}_{0}}$\end{document}. For other mixing patterns, the relation may be reversed.

Background. The 1918‐1919 A/H1N1 influenza pandemic killed 50 million people worldwide. Historical records suggest that an early pandemic wave struck Europe during the summer of 1918. Methods. 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. Results. AlargeepidemicoccurredinCopenhagenduringthesummerof1918;theagedistributionofdeathswas 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. Conclusions. TheCopenhagensummerwavemayhavebeencausedbyaprecursorA/H1N1pandemicvirusthat 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. Recent studies of the 1918 “Spanish” influenza pan

When introducing new antibiotic guidelines for empirical treatment of bacteremia, it is imperative to evaluate the performance of the new guideline. We examined the utility of administrative data to evaluate the effect of new antibiotic guidelines and the prognostic impact of appropriate empirical treatment. We categorized 2,008 adult patients diagnosed with bacteremia between 2010 and 2012 according to whether they received cephalosporins or fluoroquinolones (old regimen) or not (new regimen). We used administrative data to extract individual level data on mortality, readmission, and appropriateness of treatment, and computed adjusted hazard ratios (HRs) and 95 % confidence intervals (CIs) for 30-day mortality and post-discharge readmission by regimen and appropriateness of treatment. In total, 945 (47.1 %) were treated by the old regimen and 1,063 (52.9 %) by the new. The median length of stay (8 days) did not differ by regimen and neither did the proportion of those receiving appropriate empirical treatment (84.1 % vs. 85.5 %). However, fewer patients with the new regimen were admitted to the intensive care unit (ICU; 3.8 % vs. 12.0 %) and they had lower 30-day mortality (16.4 % vs. 23.4 %). The adjusted 30-day mortality HR for appropriate versus inappropriate treatment was 0.79 (95 % CI 0.62–1.01) and 0.83 (95 % CI 0.66–1.05) for the new versus the old regimen. The HR for 30-day readmission for appropriate versus inappropriate treatment was 0.91 (95 % CI 0.73–1.13) and 1.05 (95 % CI 0.87–1.25) for the new versus the old regimen. This study demonstrates that administrative data can be useful for evaluating the effect and quality of new bacteremia treatment guidelines.

Phenotypic variation is common in most pathogens, yet the mechanisms that maintain this diversity are still poorly understood. We asked whether continuous host variation in susceptibility helps maintain phenotypic variation, using experiments conducted with a baculovirus that infects gypsy moth (Lymantria dispar) larvae. We found that an empirically observed tradeoff between mean transmission rate and variation in transmission, which results from host heterogeneity, promotes long-term coexistence of two pathogen types in simulations of a population model. This tradeoff introduces an alternative strategy for the pathogen: a low-transmission, low-variability type can coexist with the high-transmission type favoured by classical non-heterogeneity models. In addition, this tradeoff can help explain the extensive phenotypic variation we observed in field-collected pathogen isolates, in traits affecting virus fitness including transmission and environmental persistence. Similar heterogeneity tradeoffs might be a general mechanism promoting phenotypic variation in any pathogen for which hosts vary continuously in susceptibility.

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 ρ 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.

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.

Between major pandemics, the influenza A virus changes its antigenic properties by accumulating point mutations (drift) mainly in the RNA genes that code for the surface proteins hemagglutinin (HA) and neuraminidase (NA). The successful strain (variant) that will cause the next epidemic is selected from a reduced number of progenies that possess relatively high transmissibility and the ability to escape from the immune surveillance of the host. In this paper, we analyse a one-dimensional model of influenza A drift (Z. Angew. Math. Mech. 76 (2) (1996) 421) that generalizes the classical SIR model by including mutation as a diffusion process in a phenotype space of variants. The model exhibits traveling wave solutions with an asymptotic wave speed that matches well those obtained from numerical simulations. As exact solutions for these waves are not available, asymptotic estimates for the amplitudes of infected and recovered classes are provided through an exponential approximation based on the smallness of the diffusion constant. Through this approximation, we find simple scaling properties to several parameters of relevance to the epidemiology of the disease.

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.

We analyze an epidemiological model consisting of a linear chain of three cocirculating influenza A strains that provide hosts exposed to a given strain with partial immune cross-protection against other strains. In the extreme case where infection with the middle strain prevents further infections from the other two strains, we reduce the model to a six-dimensional kernel capable of showing self-sustaining oscillations at relatively high levels of cross-protection. Dimensional reduction has been accomplished by a transformation of variables that preserves the eigenvalue responsible for the transition from damped oscillations to limit cycle solutions.

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; 1212 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, fever38 °C, weight loss and sick leave. Data were analysed by logistic regression. CDI patients2 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 diarrhoea15 days (59% vs. 73%) as the predominant symptoms. CDI patients ≥2 years old reported duration of diarrhoea15 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 patients2 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.

SUMMARYTo identify risk factors forClostridium difficileinfection (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 toxigenicC. difficileand 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

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.

We study a population exposed to a lethal infectious disease. Host response is carried at one locus with two alleles while the pathogen occurs in two variants. Based on an Si-type epidemic model we derive explicit equations for the dynamics of each genotype. By assuming small variations in both host and disease, we obtain a separation in time scales between epidemic and evolutionary processes. This allows us to describe explicitly the changes in host and disease gene frequencies. The resulting model has a rich behaviour including multiple stable states and oscillations. However, in the oscillatory situation the model is degenerate excluding the possibility of limit cycles. We show that the degeneracy can only be removed by frequency dependent selection in the pathogen, for example by including direct interaction of virus in a free-living stage. The qualitative conclusions extend to an SIR-type epidemic model, where recovery with immunity from the disease is possible.

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.

Pregnancy has been identified as a risk factor for severe illness and death during all the influenza pandemics of the 20th century and in the 2009–2010 influenza A(H1N1) pandemic. In the 1957 influenza pandemic, ∼50% of the deaths in women of childbearing age occurred in pregnant women and resulted from primary viral pneumonia following influenza infection [1–3]. Similarly, although pregnant women comprise ∼1% of the US population today, they accounted for 5% of influenza-related deaths during the 2009 pandemic; furthermore, pregnant women were at elevated risk for admission to intensive care units and preterm delivery [4–6]. In contrast to the risk of maternal illness during pregnancy, the impact of influenza on the fetus and likelihood of miscarriage has been less studied [7]. Although studies have shown that maternal influenza vaccination improves fetal and infant outcomes [8, 9], little is known about whether maternal influenza infection has the potential to terminate pregnancies, and comprehensive data are lacking on the association between influenza and birth outcomes. This issue could have important implications for public health strategies and clinical care for pandemics as well as seasonal epidemics. Investigating the impact of influenza on pregnancy is a challenge, because miscarriages may not be directly linked to influenza when patients are referred to clinics, especially if miscarriage occurs several weeks after primary viral infection. In addition, early pregnancy loss may occur unbeknownst to women who have not yet discovered that they are pregnant. Clinical reports from the 1918 pandemic period support a link between influenza and elevated maternal morbidity, mortality, pregnancy loss, and preterm labor [10–12]. In a 1919 report of 1350 pregnant women with influenza, 26% of case subjects miscarried (the largest proportion in the first trimester), whereas 52% of pneumonia-complicated case subjects miscarried [13]. This phenomenon associated with the 1918 pandemic appears to have been geographically widespread; a preponderance of miscarriages following pandemic peak activity was described in the Philippines [14], and an increase in miscarriages in women 5–9 months pregnant followed by a baby boom was reported in Norway [15]. In more recent literature, a possible association was noted between seasonal influenza A(H3N2) and a cluster of miscarriages [16]. Small observational studies of pregnant women infected with the 2009 pandemic influenza A(H1N1) virus reported preterm deliveries and fetal deaths [17, 18]. Despite these geographically limited reports and case series, the association between maternal influenza and pregnancy loss has not been quantified. In this study, we utilized historical epidemiological records from the 1918 influenza pandemic in 3 Scandinavian countries and the United States to examine the relationship between influenza and pregnancy outcomes at the population level. We hypothesized that if influenza infection in pregnant women can cause miscarriages on a large scale, then a decline in births would occur within 9 months of the peak pandemic activity. Data from contemporaneous national surveillance systems were acquired from library archives to elucidate the potential temporal associations between influenza activity and birth patterns, and to quantify the risk of miscarriage associated with influenza infection.

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 [16]). 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.

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.

A new modeling framework for particle dispersal is explored in the context of the particles being fungal spores dispersed within a field. The model gives rise to both exponentially decreasing and polynomially decreasing two-dimensional densities of deposited fungal spores. We reformulate the model in terms of time to deposition, and show how this concept is equivalent to the deposition rate for fungal spores. Special cases where parameter values for wind and gravitation lead to exponentially or polynomially decreasing densities are discussed, and formulas for one- and two-dimensional densities of deposited spores are given explicitly in terms of parameters for diffusion, wind, gravitation, and spore release height.

We develop a simple ordinary differential equation model to study the epidemiological consequences of the drift mechanism for influenza A viruses. Improving over the classical SIR approach, we introduce a fourth class (C) for the cross-immune individuals in the population, i.e., those that recovered after being infected by different strains of the same viral subtype in the past years. The SIRC model predicts that the prevalence of a virus is maximum for an intermediate value of R(0), the basic reproduction number. Via a bifurcation analysis of the model, we discuss the effect of seasonality on the epidemiological regimes. For realistic parameter values, the model exhibits a rich variety of behaviors, including chaos and multi-stable periodic outbreaks. Comparison with empirical evidence shows that the simulated regimes are qualitatively and quantitatively consistent with reality, both for tropical and temperate countries. We find that the basins of attraction of coexisting cycles can be fractal sets, thus predictability can in some cases become problematic even theoretically. In accordance with previous studies, we find that increasing cross-immunity tends to complicate the dynamics of the system.

Influenza in humans is characterised by strongly annual dynamics and antigenic evolution leading to partial escape from prior host immunity. The variability of new epidemic strains depends on the amount of virus currently circulating. In this paper, the amount of antigenic variation produced each year is dependent on the epidemic size. Our model reduces to a one-dimensional map and a full mathematical analysis is presented. This simple system suggests some basic principles which may be more generally applicable. In particular, for diseases with antigenic drift, vaccination may be doubly beneficial. Not only does it protect the population through classical herd immunity, but the overall case reduction reduces the chance of new variants being produced; hence, subsequent epidemics may be milder as a result of this positive feedback. Also, a disease with a high innate rate of antigenic variation will always be able to invade a susceptible population, whereas a disease with less potential for variation may require several introduction events to become endemic.

The persistence of Influenza A in the human population relies on continual changes in the viral surface antigens allowing the virus to reinfect the same hosts every few years. The epidemiology of such a drifting virus is modeled by a discrete season-to-season map. During the epidemic season only one strain is present and its transmission dynamics follows a standard epidemic model. After the season, cross-immunity to next year's virus is determined from the proportion of hosts that were infected during the season. A partial analysis of this map shows the existence of oscillations where epidemics occur at regular or irregular intervals.

We develop simple epidemic models of co-circulating strains of an infectious disease in which the strains interact immunologically via cross-protective acquired immune responses. Two limiting forms of cross-protective immunity are explored: reduction of infectivity on infection with a strain that against which a degree of cross-protective immunity exists from prior excposure to a heterologous strain, and reduction of susceptibility to infection after exposure to the second strain. After developing a generic model framework capable of representing both forms of action, we show that model formulation can be simplified for some simple cross-immunity structures in the case of infectivity reduction. We then discuss equilbria and stability properties of the generic model, before investigating in detail the special case of allele-based cross-immunity, where antigenic relatedness depends on the number of alleles shared between two strains of a haploid pathogen. For this system, we present conditions for the stability of the symmetric and boundary equilibria in the case of purely infectivity-mediated cross-immunity, and illustrate numerically the wide range of complex limit cycle or chaotic dynamics that dominate a large region of parameter space. Finally, we describe the similarities between the dynamics exhibited by systems with each form of immunity action, and discuss biological applications of such models.

We develop a model that describes the dynamics of a finite number of strains that confer partial cross-protection among strains. The immunity structure of the host population is captured by an index-set notation where the index specifies the set of strains to which the host has been exposed. This notation allows us to derive threshold conditions for the invasion of a new strain and to show the existence of an endemic multi-strain equilibrium in a special case. The dynamics of systems consisting of more than two strains can exhibit sustained oscillations caused by an overshoot in the immunity to a specific strain if cross-protection is sufficiently strong.

We study a hybrid zone between two populations of a diploid organism. The populations differ at one locus. Homozygotes have equal fitnesses and the heterozygote fitness is reduced by β + δ (β is the birth rate deviation and δ is the death rate deviation). The populations extend along a one dimensional continuous habitat, and migration occurs by diffusion of individuals. The model is formulated as a set of simple continuous time demographic models without age structure for the three genotypes, and the system is transformed into three new variables, the total population size N, the gene frequency p, and the deviation from Hardy-Weinberg proportions F. The gene frequency in a steady state cline always follows a hyperbolic tangent closely. Analysis of the asymptotic behavior of the cline far from the hybrid zone suggests a qualitative prediction of the shape of N, p and F over the zone. For weak selection the shape is determined by a central steepness of $$\sqrt {\beta + \delta /4D} $$ , as observed by Bazykin in 1969, where D is the diffusion coefficient. For strong selection the cline is less steep than the Bazykin cline, and the form is dominated by the migration process. The steepness at the center of the cline is close to $$\sqrt {b/4D} $$ where b is the birth rate of homozygotes.

Using for each genotype an SIR-type model of disease transmission dynamics, we describe natural selection in a continuously breeding diploid host whose disease susceptibility and resistance are carried at one locus with two alleles. The system is transformed into variables that for each disease class describe the number of individuals, the gene frequency, and the deviation from Hardy-Weinberg proportions as measured by Wright′s fixation index. An assumption of small variation in disease response among genotypes (slow selection) separates the system to first-order into three blocks. One block describes the population-wide disease dynamics, the second considers the fixation index in each class, and the third block provides the change in gene frequencies. The first two blocks settle to equilibrium at a rate determined by the population turnover time while the last block after a while is dominated by a slowly changing variable, the average gene frequency. The dynamics of the gene frequency take the usual form for a continuous time slow selection model, and this provides explicit, epidemiologically justified expressions for the genotypic fitnesses. We apply the method to other disease transmission patterns (SEI and SIS) and discuss how suitable time averages extend our results to diseases with temporally varying incidence.

Using asymptotic expansions in the ratio between the duration of infection and host lifetime, equilibrium conditions are analyzed for an SIR-type epidemic model with age-dependent mortality and age-independent disease transmission. Disease incidence at equilibrium depends on the distribution of lifetimes. Incidence is maximal if host life span is fixed and, for vanishing higher moments, it decreases with increasing variance of the distribution. The spectrum of the linearization about the endemic equilibrium has two dominant components, one near 0 and one with a large imaginary part. All roots of the characteristic equation have a negative real part so the model is always stable. The roots with a large imaginary part dominate in most cases, indicating that the approach to equilibrium will be through slowly damped oscillations.