Possible counter-intuitive impact of local vaccine mandates for vaccine-preventable infectious diseases.

We modeled the impact of local vaccine mandates on the spread of vaccine-preventable infectious diseases, which in the absence of vaccines will mainly affect children. Examples of such diseases are measles, rubella, mumps, and pertussis. To model the spread of the pathogen, we used a stochastic SIR (susceptible, infectious, recovered) model with two levels of mixing in a closed population, often referred to as the household model.

Modelling: Understanding pandemics and how to control them.

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

Commentary on the use of the reproduction number during the COVID-19 pandemic.

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text].

The risk for a new COVID-19 wave and how it depends on , the current immunity level and current restrictions.

The COVID-19 pandemic has hit different regions differently. The current disease-induced immunity level in a region approximately equals the cumulative fraction infected, which primarily depends on two factors: (i) the initial potential for COVID-19 in the region ( ), and (ii) the preventive measures put in place. Using a mathematical model including heterogeneities owing to age, social activity and susceptibility, and allowing for time-varying preventive measures, the risk for a new epidemic wave and its doubling time are investigated.

Key questions for modelling COVID-19 exit strategies.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented.

A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2.

Despite various levels of preventive measures, in 2020, many countries have suffered severely from the coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Using a model, we show that population heterogeneity can affect disease-induced immunity considerably because the proportion of infected individuals in groups with the highest contact rates is greater than that in groups with low contact rates. We estimate that if = 2.

SIR epidemics and vaccination on random graphs with clustering.

In this paper we consider Susceptible [Formula: see text] Infectious [Formula: see text] Recovered (SIR) epidemics on random graphs with clustering. To incorporate group structure of the underlying social network, we use a generalized version of the configuration model in which each node is a member of a specified number of triangles. SIR epidemics on this type of graph have earlier been investigated under the assumption of homogeneous infectivity and also under the assumption of Poisson transmission and recovery rates.

Who is the infector? Epidemic models with symptomatic and asymptomatic cases.

What role do asymptomatically infected individuals play in the transmission dynamics? There are many diseases, such as norovirus and influenza, where some infected hosts show symptoms of the disease while others are asymptomatically infected, i.e. do not show any symptoms.

Branching process approach for epidemics in dynamic partnership network.

We study the spread of sexually transmitted infections (STIs) and other infectious diseases on a dynamic network by using a branching process approach. The nodes in the network represent the sexually active individuals, while connections represent sexual partnerships. This network is dynamic as partnerships are formed and broken over time and individuals enter and leave the sexually active population due to demography.

Inferring R0 in emerging epidemics-the effect of common population structure is small.

When controlling an emerging outbreak of an infectious disease, it is essential to know the key epidemiological parameters, such as the basic reproduction number R0 and the control effort required to prevent a large outbreak. These parameters are estimated from the observed incidence of new cases and information about the infectious contact structures of the population in which the disease spreads. However, the relevant infectious contact structures for new, emerging infections are often unknown or hard to obtain.

Reproduction numbers for epidemic models with households and other social structures II: Comparisons and implications for vaccination.

In this paper we consider epidemic models of directly transmissible SIR (susceptible → infective → recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of households or of households and workplaces. We review most reproduction numbers defined in the literature for these models, including the basic reproduction number R0 introduced in the companion paper of this, for which we provide a simpler, more elegant derivation. Extending previous work, we provide a complete overview of the inequalities among these reproduction numbers and resolve some open questions.

Stochastic SIR epidemics in a population with households and schools.

We study the spread of stochastic SIR (Susceptible [Formula: see text] Infectious [Formula: see text] Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school and one household. In the independent partition model, the partitions of the population into schools and households are independent of each other.

Five challenges for spatial epidemic models.

Infectious disease incidence data are increasingly available at the level of the individual and include high-resolution spatial components. Therefore, we are now better able to challenge models that explicitly represent space. Here, we consider five topics within spatial disease dynamics: the construction of network models; characterising threshold behaviour; modelling long-distance interactions; the appropriate scale for interventions; and the representation of population heterogeneity.

Eight challenges for network epidemic models.

Networks offer a fertile framework for studying the spread of infection in human and animal populations. However, owing to the inherent high-dimensionality of networks themselves, modelling transmission through networks is mathematically and computationally challenging. Even the simplest network epidemic models present unanswered questions.

Five challenges for stochastic epidemic models involving global transmission.

The most basic stochastic epidemic models are those involving global transmission, meaning that infection rates depend only on the type and state of the individuals involved, and not on their location in the population. Simple as they are, there are still several open problems for such models. For example, when will such an epidemic go extinct and with what probability (questions depending on the population being fixed, changing or growing)? How can a model be defined explaining the sometimes observed scenario of frequent mid-sized epidemic outbreaks? How can evolution of the infectious agent transmission rates be modelled and fitted to data in a robust way?

Stochastic epidemics in growing populations.

Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that three different scenarios may occur: (i) an epidemic never takes off, (ii) an epidemic gets going and grows but at a slower rate than the community thus still being negligible in terms of population fractions, or (iii) an epidemic takes off and grows quicker than the community eventually leading to an endemic equilibrium.

Inferring global network properties from egocentric data with applications to epidemics.

Social networks are often only partly observed, and it is sometimes desirable to infer global properties of the network from 'egocentric' data. In the current paper, we study different types of egocentric data, and show which global network properties are consistent with data. Two global network properties are considered: the size of the largest connected component (the giant) and the size of an epidemic outbreak taking place on the network.

Reproduction numbers for epidemic models with households and other social structures. I. Definition and calculation of R0.

The basic reproduction number R(0) is one of the most important quantities in epidemiology. However, for epidemic models with explicit social structure involving small mixing units such as households, its definition is not straightforward and a wealth of other threshold parameters has appeared in the literature. In this paper, we use branching processes to define R(0), we apply this definition to models with households or other more complex social structures and we provide methods for calculating it.

The nosocomial transmission rate of animal-associated ST398 meticillin-resistant Staphylococcus aureus.

The global epidemiology of meticillin-resistant Staphylococcus aureus (MRSA) is characterized by different clonal lineages with different epidemiological behaviour. There are pandemic hospital clones (hospital-associated (HA-)MRSA), clones mainly causing community-acquired infections (community-associated (CA-)MRSA, mainly USA300) and an animal-associated clone (ST398) emerging in European and American livestock with subsequent spread to humans. Nosocomial transmission capacities (R(A)) of these different MRSA types have never been quantified.

Analysis of a stochastic SIR epidemic on a random network incorporating household structure.

This paper is concerned with a stochastic SIR (susceptible-->infective-->removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities.

A useful relationship between epidemiology and queueing theory: the distribution of the number of infectives at the moment of the first detection.

In this paper we establish a relation between the spread of infectious diseases and the dynamics of so called M/G/1 queues with processor sharing. The relation between the spread of epidemics and branching processes, which is well known in epidemiology, and the relation between M/G/1 queues and birth death processes, which is well known in queueing theory, will be combined to provide a framework in which results from queueing theory can be used in epidemiology and vice versa. In particular, we consider the number of infectious individuals in a standard SIR epidemic model at the moment of the first detection of the epidemic, where infectious individuals are detected at a constant per capita rate.

Reproduction numbers for epidemics on networks using pair approximation.

One way to describe the spread of an infection on a network is by using the method of pair approximation. This method is a deterministic pair-based variant of the usual methods used to describe the progress of an epidemic in randomly mixing populations. However, although the ideas of pair approximation are intuitively clear, it is not straightforward to make all assumptions used explicit.

On analytical approaches to epidemics on networks.

One way to describe the spread of an infection on a network is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g.

A branching model for the spread of infectious animal diseases in varying environments.

This paper is concerned with a stochastic model, describing outbreaks of infectious diseases that have potentially great animal or human health consequences, and which can result in such severe economic losses that immediate sets of measures need to be taken to curb the spread. During an outbreak of such a disease, the environment that the infectious agent experiences is therefore changing due to the subsequent control measures taken. In our model, we introduce a general branching process in a changing (but not random) environment.