The Role of Immunity and Seasonality in Cholera Epidemics

This paper presents a mathematical model for cholera epidemics which comprises seasonality, loss of host immunity, and control mechanisms acting to reduce cholera transmission. A collection of data related to cholera disease allows us to show that outbreaks in endemic areas are subject to a resonant behavior, since the intrinsic oscillation period of the disease (∼1 year) is synchronized with the annual contact rate variation. Moreover, we argue that the short period of the host immunity may be associated to secondary peaks of incidence observed in some regions (a bimodal pattern). Finally, we explore some possible mechanisms of cholera control, and analyze their efficiency. We conclude that, besides mass vaccination—which may be impracticable—improvements in sanitation system and food/personal hygiene are the most effective ways to prevent an epidemic.     

Determinants of the Final Size and Case Rate of Nosocomial Outbreaks

Different nosocomial pathogen species have varying infectivity and durations of infectiousness, while the transmission route determines the contact rate between pathogens and susceptible patients. To determine if the pathogen species and transmission route affects the size and spread of outbreaks, we perform a meta-analysis that examines data from 933 outbreaks of hospital-acquired infection representing 14 pathogen species and 8 transmission routes. We find that the mean number of cases in an outbreak is best predicted by the pathogen species and the mean number of cases per day is best predicted by the species-transmission route combination. Our fitted model predicts the largest mean number of cases for Salmonella outbreaks (22.3) and the smallest mean number of cases for Streptococci outbreaks (8.5). The largest mean number of cases per day occurs during Salmonella outbreaks spread via the environment (0.33) and the smallest occurs for Legionella outbreaks spread by multiple transmission routes (0.005). When combined with information on the frequency of outbreaks these findings could inform the design of infection control policies in hospitals.     

On the Use of Human Mobility Proxies for Modeling Epidemics

Human mobility is a key component of large-scale spatial-transmission models of infectious diseases. Correctly modeling and quantifying human mobility is critical for improving epidemic control, but may be hindered by data incompleteness or unavailability. Here we explore the opportunity of using proxies for individual mobility to describe commuting flows and predict the diffusion of an influenza-like-illness epidemic. We consider three European countries and the corresponding commuting networks at different resolution scales, obtained from (i) official census surveys, (ii) proxy mobility data extracted from mobile phone call records, and (iii) the radiation model calibrated with census data. Metapopulation models defined on these countries and integrating the different mobility layers are compared in terms of epidemic observables. We show that commuting networks from mobile phone data capture the empirical commuting patterns well, accounting for more than 87% of the total fluxes. The distributions of commuting fluxes per link from mobile phones and census sources are similar and highly correlated, however a systematic overestimation of commuting traffic in the mobile phone data is observed. This leads to epidemics that spread faster than on census commuting networks, once the mobile phone commuting network is considered in the epidemic model, however preserving to a high degree the order of infection of newly affected locations. Proxies'' calibration affects the arrival times'' agreement across different models, and the observed topological and traffic discrepancies among mobility sources alter the resulting epidemic invasion patterns. Results also suggest that proxies perform differently in approximating commuting patterns for disease spread at different resolution scales, with the radiation model showing higher accuracy than mobile phone data when the seed is central in the network, the opposite being observed for peripheral locations. Proxies should therefore be chosen in light of the desired accuracy for the epidemic situation under study.     

Epidemics with partial immunity to reinfection

We obtain analytical results about epidemics generated by the partial immunity model of Gomes et al. [3], in which infection confers partial immunity to reinfection. When the demographic process is excluded, the behavior switches from epidemic to endemic as the basic reproduction number R₀ crosses the reinfection threshold . We derive formulas for two quantities characterizing the size of the epidemic below the reinfection threshold: the attack rate A, which is the fraction of the population infected at least once, and the final size Z, which is the average number of infections per individual. We also derive a system of differential equations which can be used to obtain more detailed information, such as the fraction of the population infected n times throughout the epidemic, for every n.     

A Tuberculosis Model with Seasonality

The statistical data of tuberculosis (TB) cases show seasonal fluctuations in many countries. A TB model incorporating seasonality is developed and the basic reproduction ratio R ₀ is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if R ₀<1, and there exists at least one positive periodic solution and the disease is uniformly persistent if R ₀>1. Numerical simulations indicate that there may be a unique positive periodic solution which is globally asymptotically stable if R ₀>1. Parameter values of the model are estimated according to demographic and epidemiological data in China. The simulation results are in good accordance with the seasonal variation of the reported cases of active TB in China.     

Epidemics with general generation interval distributions

We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her “age” of infection. We focus first on early outbreak stages when stochastic effects dominate and show that epidemics tend to happen faster than deterministic calculations predict. If an outbreak is sufficiently large, stochastic effects are negligible and we modify the standard ordinary differential equation (ODE) model to accommodate age-of-infection effects. We avoid the use of partial differential equations which typically appear in related models. We introduce a “memoryless” ODE system which approximates the true solutions. Finally, we analyze the transition from the stochastic to the deterministic phase.     

Generality of the Final Size Formula for an Epidemic of a Newly Invading Infectious Disease

The well-known formula for the final size of an epidemic was published by Kermack and McKendrick in 1927. Their analysis was based on a simple susceptible-infected-recovered (SIR) model that assumes exponentially distributed infectious periods. More recent analyses have established that the standard final size formula is valid regardless of the distribution of infectious periods, but that it fails to be correct in the presence of certain kinds of heterogeneous mixing (e.g., if there is a core group, as for sexually transmitted diseases). We review previous work and establish more general conditions under which Kermack and McKendrick's formula is valid. We show that the final size formula is unchanged if there is a latent stage, any number of distinct infectious stages and/or a stage during which infectives are isolated (the durations of each stage can be drawn from any integrable distribution). We also consider the possibility that the transmission rates of infectious individuals are arbitrarily distributed—allowing, in particular, for the existence of super-spreaders—and prove that this potential complexity has no impact on the final size formula. Finally, we show that the final size formula is unchanged even for a general class of spatial contact structures. We conclude that whenever a new respiratory pathogen emerges, an estimate of the expected magnitude of the epidemic can be made as soon the basic reproduction number ℝ₀ can be approximated, and this estimate is likely to be improved only by more accurate estimates of ℝ₀, not by knowledge of any other epidemiological details.     

On the Minute Size of Mitochondria

In very small systems chemical reactions may, it is suggested,take on a periodic or oscillatory character. This would meanthat organelles such as mitochondria might become the centerof elastic and electromagnetic radiation. This possibility hasconsequences relevant to the problems of uptake, cell microstructureand protein synthesis, amongst other things.     

On the Optimal Size of Marine Reserves

The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. This study examines the impact of the creation of marine protected areas, from both economic and biological perspectives. The consequences of reserve establishment on the long-run equilibrium fish biomass and fishery catch levels are evaluated. We include reserve size as control variable to maximize catch at equilibrium. A continuous time model is used to simulate the effects of reserve size on fishing catch. Fish movements between the sites is assumed to take place at a faster time scale than the variation of the stock and the change of the fleet size. We take advantage of these two time scales to derive a reduced model governing the dynamics of the total fish stock and the fishing effort. Simulation results suggest that the establishment of a protected marine reserve will always lead to an increase in total fish biomass, an optimal size of a marine reserve can achieve to maximize the catch at equilibrium.     

Flexible Modeling of Epidemics with an Empirical Bayes Framework

Seasonal influenza epidemics cause consistent, considerable, widespread loss annually in terms of economic burden, morbidity, and mortality. With access to accurate and reliable forecasts of a current or upcoming influenza epidemic’s behavior, policy makers can design and implement more effective countermeasures. This past year, the Centers for Disease Control and Prevention hosted the “Predict the Influenza Season Challenge”, with the task of predicting key epidemiological measures for the 2013–2014 U.S. influenza season with the help of digital surveillance data. We developed a framework for in-season forecasts of epidemics using a semiparametric Empirical Bayes framework, and applied it to predict the weekly percentage of outpatient doctors visits for influenza-like illness, and the season onset, duration, peak time, and peak height, with and without using Google Flu Trends data. Previous work on epidemic modeling has focused on developing mechanistic models of disease behavior and applying time series tools to explain historical data. However, tailoring these models to certain types of surveillance data can be challenging, and overly complex models with many parameters can compromise forecasting ability. Our approach instead produces possibilities for the epidemic curve of the season of interest using modified versions of data from previous seasons, allowing for reasonable variations in the timing, pace, and intensity of the seasonal epidemics, as well as noise in observations. Since the framework does not make strict domain-specific assumptions, it can easily be applied to some other diseases with seasonal epidemics. This method produces a complete posterior distribution over epidemic curves, rather than, for example, solely point predictions of forecasting targets. We report prospective influenza-like-illness forecasts made for the 2013–2014 U.S. influenza season, and compare the framework’s cross-validated prediction error on historical data to that of a variety of simpler baseline predictors.     

Seasonality of toxoplasmosis]

The indices of seasonal changes in the proportion of population allergopositive to toxoplasmosis were determined by analyzing the results of intracutaneous tests made in 61,324 pregnant women in Novokuznetsk between 1964 and 1974. Indices exceeding the average monthly level were registered in March-July and in September-October. Taking into account the modal term during which allergization develops in a patient from the moment of toxoplasmic invasion, a high risk of toxoplasmosis infection is likely to be present mainly during winter and spring (December-May), as well as summer (July-August) periods. Researchers should pay attention to the nature of the seasonal prevalence of the epidemic process of toxoplasmosis.     

On the Regulation of Pack Size in Wolves

Wolves live in territorial packs of up to 20 animals. To gain insight into the regulation of wolf populations it is necessary to understand the regulation of pack size. Based on a long-time study of the social behaviour of a wolf pack in a large enclosure, a model of the regulation of pack size is constructed. Ecological factors such as prey size and prey biomass have an influence on wolf mortality, as well as on aggressive, sexual and spatial behaviour within the pack.     

On the Scaling of Tooth Size in Mammals

We must establish the allometric regularities of functionalscalingin interspecific, "mouse-to elephant" plots in orderto provide criteria for the recognition of special adaptationsunrelated to the requirements of size. The qualitative literaturesuggests that postcanine tooth areas of herbivorous mammalsshould increase with positive allometry in such plots. Thispositive allometry might reflect the demands of metabolism orthe ecological strategies of large vs. small hervivores embodiedin Levins' concept of environmental grain. Plots of postcaninearea vs. body size display the expected postive allometry inall groups studied: hystricomorph rodents, suine artiodactyls(pigs, peccaries, and hippos), cervoid artiodactyls (deer, s.l),and four groups of primates considered separately (lemuroids,ceboids, cercopithecoids, and great apes). Sketchy data foraustralopithecines also indicate positive allometry and therelatively larger cheek teeth of robust forms may only reflecttheir larger body size and not the dietary differences so oftenadvocated. Phyletic dwarfs of large herbivores display negativeallometry (relatively larger cheek teeth in dwarfs) in oppositionto the interspecific trend.     

On the Size of African Riverine Fish Faunas

SYNOPSIS. An apparent anomaly exists in the size of riverinefish faunas of the Nile and Zaire; the Nile while considerablylonger, appears depauperate when compared with the Zaire. Thisparadox is explained when discharge, not length, is used asa measure of river size. Indeed, the number of freshwater fishspecies in African rivers is more closely related to dischargethan to length or catchment area. Discharge is directly proportionalto terrestrial productivity of a river basin, which in turnaffects total biomass of fish and number of species. Changesin the size of rivers during the geologic past affected theircapacity to sustain diverse fish faunas. Rivers flowing throughespecially arid lands during the late- Pleistocene were reducedin discharge, and concomitantly, fish faunas. Immigration offish from refuge rivers during the Holocene partially restoredthese diminished faunas. We propose that fish are more mobilethan they seem, and that the distinctiveness of riverine fishfaunas may be maintained by competitive pressure from establishedresidents, rather than by limited dispersal abilities of fish.Theories of the distribution of fish in Africa are considered,and we suggest that discharge as affected by climatic stabilityis largely responsible for the size of African riverine fishfaunas.