The pluses and minuses of R0

Understanding the challenges to COVID-19 vaccines and treatment options, herd immunity and probability of reinfection

Unlike pandemics in the past, the outbreak of coronavirus disease 2019 (COVID-19), which rapidly spread worldwide, was met with a different approach to control and measures implemented across affected countries. The lack of understanding of the fundamental nature of the outbreak continues to make COVID-19 challenging to manage for both healthcare practitioners and the scientific community. Challenges to vaccine development and evaluation, current therapeutic options, convalescent plasma therapy, herd immunity, and the emergence of reinfection and new variants remain the major obstacles to combating COVID-19. This review discusses these challenges in the management of COVID-19 at length and highlights the mechanisms needed to provide better understanding of this pandemic.

Estimation of basic reproduction number (R0) of African swine fever (ASF) in mid-size commercial pig farms in Vietnam

African swine fever (ASF) is a devastating disease affecting the global swine industry. Recently, it has spread to many countries in Africa, Europe, Asia, and the Caribbean, leaving severe damage to local, regional, national, and global economies. Due to its highly complex molecular characteristics and pathogenesis, the development of a successful vaccine has been an unmet challenge. Therefore, ASF control relies solely on biosecurity, rapid detection, and elimination. Epidemiological information obtained from natural ASF outbreaks is critical for designing and implementing ASF control measures. Basic reproduction number (R₀), an epidemiological metric used to describe the contagiousness or transmissibility of infectious agents, is an important epidemiological tool. In this study, we have calculated R₀ for the in-farm spread of ASF among fattening pigs and sows in two midsize commercial pig farms, HY1 and HY2, that practice the spot removal approach in controlling ASF outbreaks in Vietnam. The R₀ values for the sows and fattening pigs were 1.78 (1.35–2.35) and 4.76 (4.18–5.38) for HY1 and 1.55 (1.08–2.18) and 3.8 (3.33–4.28) for HY2. This is the first study to evaluate the transmission potential of ASF in midsize commercial pig farms in Vietnam. Based on the R₀ values, we predict that the spot removal approach could be used to successfully control ASF outbreaks in midsize commercial sow barns but not in fattening pens.

Capturing complex interactions in disease ecology with simplicial sets

Network approaches have revolutionized the study of ecological interactions. Social, movement and ecological networks have all been integral to studying infectious disease ecology. However, conventional (dyadic) network approaches are limited in their ability to capture higher-order interactions. We present simplicial sets as a tool that addresses this limitation. First, we explain what simplicial sets are. Second, we explain why their use would be beneficial in different subject areas. Third, we detail where these areas are: social, transmission, movement/spatial and ecological networks and when using them would help most in each context. To demonstrate their application, we develop a novel approach to identify how pathogens persist within a host population. Fourth, we provide an overview of how to use simplicial sets, highlighting specific metrics, generative models and software. Finally, we synthesize key research questions simplicial sets will help us answer and draw attention to methodological developments that will facilitate this.

Why the Spectral Radius? An intuition-building introduction to the basic reproduction number

The basic reproduction number [Formula: see text] is a fundamental concept in mathematical epidemiology and infectious disease modeling. Loosely speaking, it describes the number of people that an infectious person is expected to infect. The basic reproduction number has profound implications for epidemic trajectories and disease control strategies. It is well known that the basic reproduction number can be calculated as the spectral radius of the next generation matrix, but why this is the case may not be intuitively obvious. Here, we walk through how the discrete, next generation process connects to the ordinary differential equation disease system of interest, linearized at the disease-free equilibrium. Then, we use linear algebra to develop a geometric explanation of why the spectral radius of the next generation matrix is an epidemic threshold. Finally, we work through a series of examples that help to build familiarity with the kinds of patterns that arise in parameter combinations produced by the next generation method. This article is intended to help new infectious disease modelers develop intuition for the form and interpretation of the basic reproduction number in their disease systems of interest.

Parameter estimation and uncertainty quantification using information geometry

In this work, we: (i) review likelihood-based inference for parameter estimation and the construction of confidence regions; and (ii) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar curvature, to supplement typical techniques for uncertainty quantification, such as Bayesian methods, profile likelihood, asymptotic analysis and bootstrapping. These techniques from information geometry provide data-independent insights into uncertainty and identifiability, and can be used to inform data collection decisions. All code used in this work to implement the inference and information geometry techniques is available on GitHub.

Transmission dynamics of ectoparasitic gyrodactylids (Platyhelminthes, Monogenea): An integrative review

Parasite transmission is the ability of pathogens to move between hosts. As a key component of the interaction between hosts and parasites, it has crucial implications for the fitness of both. Here, we review the transmission dynamics of Gyrodactylus species, which are monogenean ectoparasites of teleost fishes and a prominent model for studies of parasite transmission. Particularly, we focus on the most studied host–parasite system within this genus: guppies, Poecilia reticulata, and G. turnbulli/G. bullatarudis. Through an integrative literature examination, we identify the main variables affecting Gyrodactylus spread between hosts, and the potential factors that enhance their transmission. Previous research indicates that Gyrodactylids spread when their current conditions are unsuitable. Transmission depends on abiotic factors like temperature, and biotic variables such as gyrodactylid biology, host heterogeneity, and their interaction. Variation in the degree of social contact between hosts and sexes might also result in distinct dynamics. Our review highlights a lack of mathematical models that could help predict the dynamics of gyrodactylids, and there is also a bias to study only a few species. Future research may usefully focus on how gyrodactylid reproductive traits and host heterogeneity promote transmission and should incorporate the feedbacks between host behaviour and parasite transmission.

Pathogens Spillover from Honey Bees to Other Arthropods

Honey bees, and pollinators in general, play a major role in the health of ecosystems. There is a consensus about the steady decrease in pollinator populations, which raises global ecological concern. Several drivers are implicated in this threat. Among them, honey bee pathogens are transmitted to other arthropods populations, including wild and managed pollinators. The western honey bee, Apis mellifera, is quasi-globally spread. This successful species acted as and, in some cases, became a maintenance host for pathogens. This systematic review collects and summarizes spillover cases having in common Apis mellifera as the mainteinance host and some of its pathogens. The reports are grouped by final host species and condition, year, and geographic area of detection and the co-occurrence in the same host. A total of eighty-one articles in the time frame 1960-2021 were included. The reported spillover cases cover a wide range of hymenopteran host species, generally living in close contact with or sharing the same environmental resources as the honey bees. They also involve non-hymenopteran arthropods, like spiders and roaches, which are either likely or unlikely to live in close proximity to honey bees. Specific studies should consider host-dependent pathogen modifications and effects on involved host species. Both the plasticity of bee pathogens and the ecological consequences of spillover suggest a holistic approach to bee health and the implementation of a One Health approach.

What the reproductive number R0 can and cannot tell us about COVID-19 dynamics

The reproductive number R (or R0, the initial reproductive number in an immune-naïve population) has long been successfully used to predict the likelihood of pathogen invasion, to gauge the potential severity of an epidemic, and to set policy around interventions. However, often ignored complexities have generated confusion around use of the metric. This is particularly apparent with the emergent pandemic virus SARS-CoV-2, the causative agent of COVID-19. We address some misconceptions about the predictive ability of the reproductive number, focusing on how it changes over time, varies over space, and relates to epidemic size by referencing the mathematical definition of R and examples from the current pandemic. We hope that a better appreciation of the uses, nuances, and limitations of R and R0 facilitates a better understanding of epidemic spread, epidemic severity, and the effects of interventions in the context of SARS-CoV-2.

ECIEN-2020 study: the effect of COVID-19 on admissions for non-COVID-19 diseases

BACKGROUND

The pandemic caused by severe acute respiratory coronavirus 2 (SARS-CoV-2) has had great effects on health systems worldwide, not only in relation to coronavirus disease 2019 (COVID-19) cases but also affecting patients with other pathologies.

METHODS

ECIEN-2020 is an observational study conducted in a tertiary referral hospital in Navarra, Spain. It describes the effects of COVID-19 pandemic and the preventive measures adopted, in pediatric admissions for non-COVID-19 diseases. Admissions during March-June 2020 (first wave of the COVID-19 pandemic in Spain) are described and compared with the same quarter in 2019. A sub-analysis was performed delving into epidemiology. Patient characteristics (age, sex, past medical history), disease characteristics (symptoms, duration of symptoms, previous consultation in Primary Care Health Center), and admission characteristics (place and average stay) were analyzed.

RESULTS

A 33% reduction in the number of pediatric hospital admissions was observed, decreasing from 529 hospitalizations in 2019 to 353 in 2020 (P < 0.001). This highlights a 48% reduction in patients admitted for pulmonary diseases. There were no significant changes in average hospital-stay, percentage of intensive care unit admissions, or in admissions for other reasons. Percentage of patients admitted among those seen in the emergency department rose from 5.1% in 2019 to 10.9% in 2020, whereas the total number of consultations in the emergency department decreased by 68%.

CONCLUSION

The pandemic and the measures adopted due to SARS-CoV-2 have significantly decreased pediatric admissions for non-COVID-19 diseases, especially due to a reduction in the hospitalization for respiratory diseases.

Spatiotemporal multi-disease transmission dynamic measure for emerging diseases: an application to dengue and zika integrated surveillance in Thailand

Background

New emerging diseases are public health concerns in which policy makers have to make decisions in the presence of enormous uncertainty. This is an important challenge in terms of emergency preparation requiring the operation of effective surveillance systems. A key concept to investigate the dynamic of infectious diseases is the basic reproduction number. However it is difficult to be applicable in real situations due to the underlying theoretical assumptions.

Methods

In this paper we propose a robust and flexible methodology for estimating disease strength varying in space and time using an alternative measure of disease transmission within the hierarchical modeling framework. The proposed measure is also extended to allow for incorporating knowledge from related diseases to enhance performance of surveillance system.

Results

A simulation was conducted to examine robustness of the proposed methodology and the simulation results demonstrate that the proposed method allows robust estimation of the disease strength across simulation scenarios. A real data example is provided of an integrative application of Dengue and Zika surveillance in Thailand. The real data example also shows that combining both diseases in an integrated analysis essentially decreases variability of model fitting.

Conclusions

The proposed methodology is robust in several simulated scenarios of spatiotemporal transmission force with computing flexibility and practical benefits. This development has potential for broad applicability as an alternative tool for integrated surveillance of emerging diseases such as Zika.

Complexity of the Basic Reproduction Number (R0)

The basic reproduction number (R₀), also called the basic reproduction ratio or rate or the basic reproductive rate, is an epidemiologic metric used to describe the contagiousness or transmissibility of infectious agents. R₀ is affected by numerous biological, sociobehavioral, and environmental factors that govern pathogen transmission and, therefore, is usually estimated with various types of complex mathematical models, which make R₀ easily misrepresented, misinterpreted, and misapplied. R₀ is not a biological constant for a pathogen, a rate over time, or a measure of disease severity, and R₀ cannot be modified through vaccination campaigns. R₀ is rarely measured directly, and modeled R₀ values are dependent on model structures and assumptions. Some R₀ values reported in the scientific literature are likely obsolete. R₀ must be estimated, reported, and applied with great caution because this basic metric is far from simple.

The Impact of Selective Predation on Host-Parasite SIS Dynamics

While models of host-parasite interactions are widespread in the theoretical literature, we still have limited understanding of the impact of community dynamics on infectious disease dynamics. When the wider host ecology is taken into account, the underlying inter-species feedbacks can lead to counter-intuitive results. For example, the 'healthy herd' hypothesis posits that the removal of a predator species may not be beneficial for a prey population infected by an endemic disease. In this work, we focus on the effects of including a predator species in a susceptible-infected-susceptible model. Specifically, a key role is played by predator selectivity for either healthy or infected prey. We explored both cases and found important differences in the asymptotic behaviours of the system. Independently from selectivity, large portions of parameter space allow for the coexistence of the three species. However, when predators feed mainly on susceptible prey we find that a fold bifurcation can occur, leading to a region of bi-stability between coexistence and parasite extinction. Conversely, when predator selection is strongly towards infected prey, total prey population density can be maximal when the three species coexist, consistent with the 'healthy herd' hypothesis. Our work further highlights the importance of community interactions to infectious disease dynamics.

A general theory for target reproduction numbers with applications to ecology and epidemiology

A general framework for threshold parameters in population dynamics is developed using the concept of target reproduction numbers. This framework identifies reproduction numbers and other threshold parameters in the literature in terms of their roles in population control. The framework is applied to the analysis of single and multiple control strategies in ecology and epidemiology, and this provides new biological insights.

Complexity of the Basic Reproduction Number (R0)

The basic reproduction number (R₀), also called the basic reproduction ratio or rate or the basic reproductive rate, is an epidemiologic metric used to describe the contagiousness or transmissibility of infectious agents. R₀ is affected by numerous biological, sociobehavioral, and environmental factors that govern pathogen transmission and, therefore, is usually estimated with various types of complex mathematical models, which make R₀ easily misrepresented, misinterpreted, and misapplied. R₀ is not a biological constant for a pathogen, a rate over time, or a measure of disease severity, and R₀ cannot be modified through vaccination campaigns. R₀ is rarely measured directly, and modeled R₀ values are dependent on model structures and assumptions. Some R₀ values reported in the scientific literature are likely obsolete. R₀ must be estimated, reported, and applied with great caution because this basic metric is far from simple.

Implications of asymptomatic carriers for infectious disease transmission and control

For infectious pathogens such as Staphylococcus aureus and Streptococcus pneumoniae, some hosts may carry the pathogen and transmit it to others, yet display no symptoms themselves. These asymptomatic carriers contribute to the spread of disease but go largely undetected and can therefore undermine efforts to control transmission. Understanding the natural history of carriage and its relationship to disease is important for the design of effective interventions to control transmission. Mathematical models of infectious diseases are frequently used to inform decisions about control and should therefore accurately capture the role played by asymptomatic carriers. In practice, incorporating asymptomatic carriers into models is challenging due to the sparsity of direct evidence. This absence of data leads to uncertainty in estimates of model parameters and, more fundamentally, in the selection of an appropriate model structure. To assess the implications of this uncertainty, we systematically reviewed published models of carriage and propose a new model of disease transmission with asymptomatic carriage. Analysis of our model shows how different assumptions about the role of asymptomatic carriers can lead to different conclusions about the transmission and control of disease. Critically, selecting an inappropriate model structure, even when parameters are correctly estimated, may lead to over- or under-estimates of intervention effectiveness. Our results provide a more complete understanding of the role of asymptomatic carriers in transmission and highlight the importance of accurately incorporating carriers into models used to make decisions about disease control.

Bi-logistic model for disease dynamics caused by Mycobacterium tuberculosis in Russia

In this work, we explore epidemiological dynamics by the example of tuberculosis in Russian Federation. It has been shown that the epidemiological dynamics correlates linearly with the virulence of Mycobacterium tuberculosis during the period 1987-2012. To construct an appropriate model, we have analysed (using LogLet decomposition method) epidemiological World Health Organization (WHO) data (period 1980-2014) and obtained, as result of their integration, a curve approximated by a bi-logistic function. This fact allows a subdivision of the whole population into parts, each of them satisfies the Verhulst-like models with different constant virulences introduced into each subsystem separately. Such a subdivision could be interconnected with the heterogeneous structure of mycobacterial population that has a high ability of adaptation to the host and strong mutability.

An epidemic model with noisy parameters

We analyse an SIR model where the epidemiological parameters are subject to small amplitude random fluctuations. We derive a final size equation and extend the result to an SEIR model. We use a small amplitude perturbation to estimate the expected final size of the SIR model and its variance, and compare the result with numerical simulations. We show that although individual realisations may exhibit considerable variation around solutions of the deterministic model, the mean of the final size distribution is in good agreement with the deterministic final size, and its standard deviation is small compared to the mean.

The many guises of R0 (a didactic note)

The basic reproduction number R0 is, by definition, the expected life time number of offspring of a newborn individual. An operationalization entails a specification of what events are considered as "reproduction" and what events are considered as "transitions from one individual-state to another". Thus, an element of choice can creep into the concretization of the definition. The aim of this note is to clearly expose this possibility by way of examples from both population dynamics and infectious disease epidemiology.

From within-host interactions to epidemiological competition: a general model for multiple infections

Many hosts are infected by several parasite genotypes at a time. In these co-infected hosts, parasites can interact in various ways thus creating diverse within-host dynamics, making it difficult to predict the expression and the evolution of virulence. Moreover, multiple infections generate a combinatorial diversity of cotransmission routes at the host population level, which complicates the epidemiology and may lead to non-trivial outcomes. We introduce a new model for multiple infections, which allows any number of parasite genotypes to infect hosts and potentially coexist in the population. In our model, parasites affect one another's within-host growth through density-dependent interactions and by means of public goods and spite. These within-host interactions determine virulence, recovery and transmission rates, which are then integrated in a transmission network. We use analytical solutions and numerical simulations to investigate epidemiological feedbacks in host populations infected by several parasite genotypes. Finally, we discuss general perspectives on multiple infections.

Analysis of the transmission of Trypanosoma cruzi infection through hosts and vectors

Calculating epidemiological measures of infection by Trypanosoma cruzi, the causative agent of Chagas disease, is complex, because it involves several species, different stages of infection in humans and multiple transmission routes. Using the next-generation matrix method, we analysed a model which considers the three stages of human infection, triatomines and dogs (the main domestic reservoirs of T. cruzi when triatomines are present) and the main transmission routes. We derived R 0 and type-reproduction numbers T. We deduced formulas for the number of new infections generated through each transmission route by each infected individual. We applied our findings in Argentine Gran Chaco. The expressions achieved allowed quantifying the high infectivity of dogs and emphasizing the epidemiological importance of the long and asymptomatic chronic indeterminate stage in humans in the spread of the infection. According to the model, it is expected that one infected human infects 21 triatomines, that 100 infected triatomines are necessary to infect one human and 34 to infect a dog, and that each dog infects on average one triatomine per day. Our results may allow quantifying the effect of control measures on infected humans, triatomines and dogs (or other highly infected vertebrate) or on a specific route of transmission, in other scenarios.

The risk of incomplete personal protection coverage in vector-borne disease

Personal protection (PP) techniques, such as insecticide-treated nets, repellents and medications, include some of the most important and commonest ways used today to protect individuals from vector-borne infectious diseases. In this study, we explore the possibility that a PP intervention with partial coverage may have the counterintuitive effect of increasing disease burden at the population level, by increasing the biting intensity on the unprotected portion of the population. To this end, we have developed a dynamic model which incorporates parameters that describe the potential effects of PP on vector searching and biting behaviour and calculated its basic reproductive rate, R0. R0 is a well-established threshold of disease risk; the higher R0 is above unity, the stronger the disease onset intensity. When R0 is below unity, the disease is typically unable to persist. The model analysis revealed that partial coverage with popular PP techniques can realistically lead to a substantial increase in the reproductive number. An increase in R0 implies an increase in disease burden and difficulties in eradication efforts within certain parameter regimes. Our findings therefore stress the importance of studying vector behavioural patterns in response to PP interventions for future mitigation of vector-borne diseases.

Estimating the Basic Reproductive Number (R0) for African Swine Fever Virus (ASFV) Transmission between Pig Herds in Uganda

African swine fever (ASF) is a highly contagious, lethal and economically devastating haemorrhagic disease of domestic pigs. Insights into the dynamics and scale of virus transmission can be obtained from estimates of the basic reproduction number (R₀). We estimate R₀ for ASF virus in small holder, free-range pig production system in Gulu, Uganda. The estimation was based on data collected from outbreaks that affected 43 villages (out of the 289 villages with an overall pig population of 26,570) between April 2010 and November 2011. A total of 211 outbreaks met the criteria for inclusion in the study. Three methods were used, specifically; (i) GIS- based identification of the nearest infectious neighbour based on the Euclidean distance between outbreaks, (ii) epidemic doubling time, and (iii) a compartmental susceptible-infectious (SI) model. For implementation of the SI model, three approaches were used namely; curve fitting (CF), a linear regression model (LRM) and the SI/N proportion. The R₀ estimates from the nearest infectious neighbour and epidemic doubling time methods were 3.24 and 1.63 respectively. Estimates from the SI-based method were 1.58 for the CF approach, 1.90 for the LRM, and 1.77 for the SI/N proportion. Since all these values were above one, they predict the observed persistence of the virus in the population. We hypothesize that the observed variation in the estimates is a consequence of the data used. Higher resolution and temporally better defined data would likely reduce this variation. This is the first estimate of R₀ for ASFV in a free range smallholder pig keeping system in sub-Saharan Africa and highlights the requirement for more efficient application of available disease control measures.

Transmissibility of the Ice Bucket Challenge among globally influential celebrities: retrospective cohort study

OBJECTIVES

To estimate the transmissibility of the Ice Bucket Challenge among globally influential celebrities and to identify associated risk factors.

DESIGN

Retrospective cohort study.

SETTING

Social media (YouTube, Facebook, Twitter, Instagram).

PARTICIPANTS

David Beckham, Cristiano Ronaldo, Benedict Cumberbatch, Stephen Hawking, Mark Zuckerberg, Oprah Winfrey, Homer Simpson, and Kermit the Frog were defined as index cases. We included contacts up to the fifth generation seeded from each index case and enrolled a total of 99 participants into the cohort.

MAIN OUTCOME MEASURES

Basic reproduction number R0, serial interval of accepting the challenge, and odds ratios of associated risk factors based on fully observed nomination chains; R0 is a measure of transmissibility and is defined as the number of secondary cases generated by a single index in a fully susceptible population. Serial interval is the duration between onset of a primary case and onset of its secondary cases.

RESULTS

Based on the empirical data and assuming a branching process we estimated a mean R0 of 1.43 (95% confidence interval 1.23 to 1.65) and a mean serial interval for accepting the challenge of 2.1 days (median 1 day). Higher log (base 10) net worth of the participants was positively associated with transmission (odds ratio 1.63, 95% confidence interval 1.06 to 2.50), adjusting for age and sex.

CONCLUSIONS

The Ice Bucket Challenge was moderately transmissible among a group of globally influential celebrities, in the range of the pandemic A/H1N1 2009 influenza. The challenge was more likely to be spread by richer celebrities, perhaps in part reflecting greater social influence.

The basic reproduction number obtained from Jacobian and next generation matrices - A case study of dengue transmission modelling

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Estimating the basic reproduction number from surveillance data on past epidemics

In this paper, we consider the basic reproduction number, R0, a parameter that characterizes the transmission potential of an epidemic, and explore a novel way for estimating it. We introduce a stochastic process which takes as starting points the classical SIR (susceptibles-infected-removed) models, deterministic and stochastic. The estimation method rests on an extremum property of the deterministic SIR model, and could be applied to past surveillance data on epidemic outbreaks, data gathered at different locations or in different years. Our estimators take into account some practical limitations, in particular the fact that data are collected at preassigned times. We derive asymptotic properties of the estimators and perform a simulation study to assess their small sample behavior. We illustrate the method on real data (from the USA Centers for Disease Control and Prevention site) and we point to various extensions to our approach, as well as practical implementation issues.

Mycobacterium bovis: characteristics of wildlife reservoir hosts

Mycobacterium bovis is the cause of tuberculosis in animals and sometimes humans. Many developed nations have long-standing programmes to eradicate tuberculosis in livestock, principally cattle. As disease prevalence in cattle decreases these efforts are sometimes impeded by passage of M. bovis from wildlife to cattle. In epidemiological terms, disease can persist in some wildlife species, creating disease reservoirs, if the basic reproduction rate (R0) and critical community size (CCS) thresholds are achieved. Recognized wildlife reservoir hosts of M. bovis include the brushtail possum (Trichosurus vulpecula) in New Zealand, European badger (Meles meles) in Great Britain and Ireland, African buffalo (Syncerus caffer) in South Africa, wild boar (Sus scrofa) in the Iberian Peninsula and white-tailed deer (Odocoileus virginianus) in Michigan, USA. The epidemiological concepts of R0 and CCS are related to more tangible disease/pathogen characteristics such as prevalence, pathogen-induced pathology, host behaviour and ecology. An understanding of both epidemiological and disease/pathogen characteristics is necessary to identify wildlife reservoirs of M. bovis. In some cases, there is a single wildlife reservoir host involved in transmission of M. bovis to cattle. Complexity increases, however, in multihost systems where multiple potential reservoir hosts exist. Bovine tuberculosis eradication efforts require elimination of M. bovis transmission between wildlife reservoirs and cattle. For successful eradication identification of true wildlife reservoirs is critical, as disease control efforts are most effective when directed towards true reservoirs.

Using the basic reproduction number to assess the effects of climate change in the risk of Chagas disease transmission in Colombia

The dynamics of vector-borne diseases has often been linked to climate change. However the commonly complex dynamics of vector-borne diseases make it very difficult to predict risk based on vector or host distributions. The basic reproduction number (R0) integrates all factors that determine whether a pathogen can establish or not. To obtain R0 for complex vector-borne diseases one can use the next-generation matrix (NGM) approach. We used the NGM to compute R0 for Chagas disease in Colombia incorporating the effect of temperature in some of the transmission routes of Trypanosoma cruzi. We used R0 to generate a risk map of present conditions and a forecast risk map at 20 years from now based on mean annual temperature (data obtained from Worldclim). In addition we used the model to compute elasticity and sensitivity indexes on all model parameters and routes of transmission. We present this work as an approach to indicate which transmission pathways are more critical for disease transmission but acknowledge the fact that results and projections strongly depend on better knowledge of entomological parameters and transmission routes. We concluded that the highest contribution to R0 comes from transmission of the parasites from humans to vectors, which is a surprising result. In addition,parameters related to contacts between human and vectors and the efficiency of parasite transmission between them also show a prominent effect on R0.

Predicting and controlling infectious disease epidemics using temporal networks

Infectious diseases can be considered to spread over social networks of people or animals. Mainly owing to the development of data recording and analysis techniques, an increasing amount of social contact data with time stamps has been collected in the last decade. Such temporal data capture the dynamics of social networks on a timescale relevant to epidemic spreading and can potentially lead to better ways to analyze, forecast, and prevent epidemics. However, they also call for extended analysis tools for network epidemiology, which has, to date, mostly viewed networks as static entities. We review recent results of network epidemiology for such temporal network data and discuss future developments.

Molecular evolution and emergence of avian gammacoronaviruses

Coronaviruses, which are single stranded, positive sense RNA viruses, are responsible for a wide variety of existing and emerging diseases in humans and other animals. The gammacoronaviruses primarily infect avian hosts. Within this genus of coronaviruses, the avian coronavirus infectious bronchitis virus (IBV) causes a highly infectious upper-respiratory tract disease in commercial poultry. IBV shows rapid evolution in chickens, frequently producing new antigenic types, which adds to the multiple serotypes of the virus that do not cross protect. Rapid evolution in IBV is facilitated by strong selection, large population sizes and high genetic diversity within hosts, and transmission bottlenecks between hosts. Genetic diversity within a host arises primarily by mutation, which includes substitutions, insertions and deletions. Mutations are caused both by the high error rate, and limited proof reading capability, of the viral RNA-dependent RNA-polymerase, and by recombination. Recombination also generates new haplotype diversity by recombining existing variants. Rapid evolution of avian coronavirus IBV makes this virus extremely difficult to diagnose and control, but also makes it an excellent model system to study viral genetic diversity and the mechanisms behind the emergence of coronaviruses in their natural host.

On the definition and the computation of the type-reproduction number T for structured populations in heterogeneous environments

In the context of mathematical epidemiology, the type-reproduction number (TRN) for a specific host type is interpreted as the average number of secondary cases of that type produced by the primary cases of the same host type during the entire course of infection. Here, it must be noted that T takes into account not only the secondary cases directly transmitted from the specific host but also the cases indirectly transmitted by way of other types, who were infected from the primary cases of the specific host with no intermediate cases of the target host. Roberts and Heesterbeek (Proc R Soc Lond B 270:1359-1364, 2003) have shown that T is a useful measure when a particular single host type is targeted in the disease control effort in a community with various types of host, based on the fact that the sign relation sign(R₀-1) = sign(T-1) holds between the basic reproduction number R₀ and T. In fact, T can be seen as an extension of R₀ in a sense that the threshold condition of the total population growth can be formulated by the reproduction process of the target type only. However, the original formulation is limited to populations with discrete state space in constant environments. In this paper, based on a new perspective of R₀ in heterogeneous environments (Inaba in J Math Biol 2011), we give a general definition of the TRN for continuously structured populations in heterogeneous environments and show some examples of its computation and applications.

Epidemiology and transmission dynamics of the 1918-19 pandemic influenza in Florence, Italy

To investigate the 1918/19 influenza pandemic daily number of new hospitalizations in the only hospital in Florence (Central Italy) were analyzed. In order to describe the transmission dynamics of the 1918/1919 pandemic influenza a compartmental epidemic model was used. Model simulations show a high level of agreement with the observed epidemic data. By assuming both latent and infectious period equal to 1.5 days, the estimated basic reproduction number was R(0)(1) = 1.03 (95% CI: 1.00-1.08) during the summer wave and R(0)(2) = 1.38 (95% CI: 1.32-1.48) during the fall wave. Varying the length of the generation time or the estimation method, R(0)(2) ranges from 1.32 to 1.71. The hospitalization rate was found significantly different between summer and fall waves. Notably, the estimated basic reproductive numbers are lower compared to those observed in other countries, while the age distribution of deaths resulted to be consistent with the patterns generally observed during of the 1918-1919 pandemic. Our knowledge on past pandemics, as for the 1918-19 Spanish influenza, would help improving mathematical modeling accuracy and understanding the mechanisms underlying the dynamics of future pandemics.

Modelling the Dynamics of Host-Parasite Interactions: Basic Principles

Mathematical modelling is a valuable tool for the analysis of the infectious diseases spread. Dynamical models may help to represent and summarize available knowledge on transmission and disease evolution, to test assumptions and analyse scenarios, and to predict outcomes of the host-pathogen interactions. This chapter aims at introducing basic concepts and methods of epidemiological modelling, in order to provide a starting point for further developments. After positioning modelling in the process of disease investigation, we first present the main principles of model building and analysis, using simple biological and also mathematical systems. We then provide an overview of the methods that can be employed to describe more complex systems. Last, we illustrate how the modelling approach may help for different practical purposes, including evaluation of control strategies. A brief conclusion discusses the challenge of including genetic and molecular variability in epidemiological modelling.

The failure of R0

The basic reproductive ratio, R(0), is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R(0) < 1, the disease dies out, whereas if R(0) > 1, the disease persists. R(0) has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, R(0) is flawed. Diseases can persist with R(0) < 1, while diseases with R(0) > 1 can die out. We show that the same model of malaria gives many different values of R(0), depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of R(0) for a variety of diseases, and examine some of the alternatives that have been proposed. If R(0) is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.

Early estimation of the reproduction number in the presence of imported cases: pandemic influenza H1N1-2009 in New Zealand

We analyse data from the early epidemic of H1N1-2009 in New Zealand, and estimate the reproduction number . We employ a renewal process which accounts for imported cases, illustrate some technical pitfalls, and propose a novel estimation method to address these pitfalls. Explicitly accounting for the infection-age distribution of imported cases and for the delay in transmission dynamics due to international travel, was estimated to be (95% confidence interval: ). Hence we show that a previous study, which did not account for these factors, overestimated . Our approach also permitted us to examine the infection-age at which secondary transmission occurs as a function of calendar time, demonstrating the downward bias during the beginning of the epidemic. These technical issues may compromise the usefulness of a well-known estimator of - the inverse of the moment-generating function of the generation time given the intrinsic growth rate. Explicit modelling of the infection-age distribution among imported cases and the examination of the time dependency of the generation time play key roles in avoiding a biased estimate of , especially when one only has data covering a short time interval during the early growth phase of the epidemic.

The model of Kermack and McKendrick for the plague epidemic in Bombay and the type reproduction number with seasonality

The figure showing how the model of Kermack and McKendrick fits the data from the 1906 plague epidemic in Bombay is the most reproduced figure in books discussing mathematical epidemiology. In this paper we show that the assumption of constant parameters in the model leads to quite unrealistic numerical values for these parameters. Moreover the reports published at the time show that plague epidemics in Bombay occurred in fact with a remarkable seasonal pattern every year since 1897 and at least until 1911. So the 1906 epidemic is clearly not a good example of epidemic stopping because the number of susceptible humans has decreased under a threshold, as suggested by Kermack and McKendrick, but an example of epidemic driven by seasonality. We present a seasonal model for the plague in Bombay and compute the type reproduction numbers associated with rats and fleas, thereby extending to periodic models the notion introduced by Roberts and Heesterbeek.

Maintenance, spillover and spillback transmission of bovine tuberculosis in multi-host wildlife complexes: a New Zealand case study

The causative agent of bovine tuberculosis (bTB; Mycobacterium bovis) has a broad host range. The role of each animal species in spreading the disease depends on how transmission occurs, on the abundance of each host, and on the interactions between hosts. This paper explores differences in the roles individual host species can play in allowing M. bovis infection to persist and spread within a multi-species complex, using New Zealand as a case study. In New Zealand, four wild mammal species are frequently infected. Of these the brushtail possum is now regarded as the only true "maintenance" host. Red deer and ferrets can become maintenance hosts where their densities are exceptionally high, but more often they are "spillover" hosts, with most infection arising from moderately frequent inter-species transmission from possums. The latter situation is even more strongly the case for feral pigs. Spillover hosts may occasionally play a crucial epidemiological role by transmitting infection back to a potential maintenance host (spillback). Three key factors make spillback transmission far more epidemiologically important than its low frequency of occurrence might suggest--amplification of the reservoir of bTB, far greater spatial spread than by the maintenance host, and greater persistence of bTB in long-lived spillover hosts extending the risk of spillback far into the future. The risk of spillback is undoubtedly low, but it nonetheless determines the nature, scale and duration of management required. Eradication of the disease may require management of both the infection in maintenance hosts and reduction or elimination of any risk of spillback.

Strategies for antiviral stockpiling for future influenza pandemics: a global epidemic-economic perspective

Influenza pandemics present a global threat owing to their potential mortality and substantial economic impacts. Stockpiling antiviral drugs to manage a pandemic is an effective strategy to offset their negative impacts; however, little is known about the long-term optimal size of the stockpile under uncertainty and the characteristics of different countries. Using an epidemic-economic model we studied the effect on total mortality and costs of antiviral stockpile sizes for Brazil, China, Guatemala, India, Indonesia, New Zealand, Singapore, the UK, the USA and Zimbabwe. In the model, antivirals stockpiling considerably reduced mortality. There was greater potential avoidance of expected costs in the higher resourced countries (e.g. from $55 billion to $27 billion over a 30 year time horizon for the USA) and large avoidance of fatalities in those less resourced (e.g. from 11.4 to 2.3 million in Indonesia). Under perfect allocation, higher resourced countries should aim to store antiviral stockpiles able to cover at least 15 per cent of their population, rising to 25 per cent with 30 per cent misallocation, to minimize fatalities and economic costs. Stockpiling is estimated not to be cost-effective for two-thirds of the world's population under current antivirals pricing. Lower prices and international cooperation are necessary to make the life-saving potential of antivirals cost-effective in resource-limited countries.

Identifying genetic markers of adaptation for surveillance of viral host jumps

Adaptation is often thought to affect the likelihood that a virus will be able to successfully emerge in a new host species. If so, surveillance for genetic markers of adaptation could help to predict the risk of disease emergence. However, adaptation is difficult to distinguish conclusively from the other processes that generate genetic change. In this Review we survey the research on the host jumps of influenza A, severe acute respiratory syndrome-coronavirus, canine parvovirus and Venezuelan equine encephalitis virus to illustrate the insights that can arise from combining genetic surveillance with microbiological experimentation in the context of epidemiological data. We argue that using a multidisciplinary approach for surveillance will provide a better understanding of when adaptations are required for host jumps and thus when predictive genetic markers may be present.

The virulence-transmission trade-off in vector-borne plant viruses: a review of (non-)existing studies

The adaptive hypothesis invoked to explain why parasites harm their hosts is known as the trade-off hypothesis, which states that increased parasite transmission comes at the cost of shorter infection duration. This correlation arises because both transmission and disease-induced mortality (i.e. virulence) are increasing functions of parasite within-host density. There is, however, a glaring lack of empirical data to support this hypothesis. Here, we review empirical investigations reporting to what extent within-host viral accumulation determines the transmission rate and the virulence of vector-borne plant viruses. Studies suggest that the correlation between within-plant viral accumulation and transmission rate of natural isolates is positive. Unfortunately, results on the correlation between viral accumulation and virulence are very scarce. We found only very few appropriate studies testing such a correlation, themselves limited by the fact that they use symptoms as a proxy for virulence and are based on very few viral genotypes. Overall, the available evidence does not allow us to confirm or refute the existence of a transmission-virulence trade-off for vector-borne plant viruses. We discuss the type of data that should be collected and how theoretical models can help us refine testable predictions of virulence evolution.

Real-time epidemic monitoring and forecasting of H1N1-2009 using influenza-like illness from general practice and family doctor clinics in Singapore

Background

Reporting of influenza-like illness (ILI) from general practice/family doctor (GPFD) clinics is an accurate indicator of real-time epidemic activity and requires little effort to set up, making it suitable for developing countries currently experiencing the influenza A (H1N1 -2009) pandemic or preparing for subsequent epidemic waves.

Methodology/Principal Findings

We established a network of GPFDs in Singapore. Participating GPFDs submitted returns via facsimile or e-mail on their work days using a simple, standard data collection format, capturing: gender; year of birth; “ethnicity”; residential status; body temperature (°C); and treatment (antiviral or not); for all cases with a clinical diagnosis of an acute respiratory illness (ARI). The operational definition of ILI in this study was an ARI with fever of 37.8°C or more. The data were processed daily by the study co-ordinator and fed into a stochastic model of disease dynamics, which was refitted daily using particle filtering, with data and forecasts uploaded to a website which could be publicly accessed. Twenty-three GPFD clinics agreed to participate. Data collection started on 2009-06-26 and lasted for the duration of the epidemic. The epidemic appeared to have peaked around 2009-08-03 and the ILI rates had returned to baseline levels by the time of writing.

Conclusions/Significance

This real-time surveillance system is able to show the progress of an epidemic and indicates when the peak is reached. The resulting information can be used to form forecasts, including how soon the epidemic wave will end and when a second wave will appear if at all.

The importance of age dependent mortality and the extrinsic incubation period in models of mosquito-borne disease transmission and control

Nearly all mathematical models of vector-borne diseases have assumed that vectors die at constant rates. However, recent empirical research suggests that mosquito mortality rates are frequently age dependent. This work develops a simple mathematical model to assess how relaxing the classical assumption of constant mortality affects the predicted effectiveness of anti-vectorial interventions. The effectiveness of mosquito control when mosquitoes die at age dependent rates was also compared across different extrinsic incubation periods. Compared to a more realistic age dependent model, constant mortality models overestimated the sensitivity of disease transmission to interventions that reduce mosquito survival. Interventions that reduce mosquito survival were also found to be slightly less effective when implemented in systems with shorter EIPs. Future transmission models that examine anti-vectorial interventions should incorporate realistic age dependent mortality rates.

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect

Infectious diseases are responsible for the extinction of a number of species. In conventional epidemic models, the transition from endemic population persistence to extirpation takes place gradually. However, if host demographics exhibits a strong Allee effect (AE) (population decline at low densities), extinction can occur abruptly in a catastrophic population crash. This might explain why species suddenly disappear even when they used to persist at high endemic population levels. Mathematically, the tipping point towards population collapse is associated with a saddle-node bifurcation. The underlying mechanism is the simultaneous population size depression and the increase of the extinction threshold due to parasite pathogenicity and Allee effect. Since highly pathogenic parasites cause their own extinction but not that of their host, there can be another saddle-node bifurcation with the re-emergence of two endemic equilibria. The implications for control interventions are discussed, suggesting that effective management may be possible for ℛ(0)≫1.

The consequences of spatial structure for the evolution of pathogen transmission rate and virulence

The distribution of organisms in space can be an important mediator of species interactions, but its evolutionary effects on those interactions are only beginning to be explored. These effects may be especially relevant to pathogen-host interactions. A detailed understanding of how and when spatial structure will affect the evolution of pathogen traits is likely to aid our ability to control rapidly emerging infectious diseases. Here we review a growing body of theoretical studies suggesting that spatial structure can lead to the evolution of an intermediate pathogen transmission rate and virulence. We explain the results of these studies in terms of a competition-persistence trade-off. These studies strongly suggest that local host interactions, local host dispersal, and relatively low host reproduction rates create a host population spatial structure that enforces this trade-off and leads to the evolution of lower pathogen transmission rates and virulence. They also suggest that when spatial structure exists, it can dominate over the shape of the transmission-virulence trade-off in determining pathogen traits. We also identify important areas of future research, including quantifying pathogen fitness in a spatial context in order to gain a more mechanistic understanding of the effects of spatial structure and observationally and experimentally testing theoretical predictions.