Heterogeneity and herd immunity In response to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), some politicians have been keen exploit the idea of achieving immunity. Countering this possibility are estimates derived from work on historical vaccination studies, which suggest that may only be achieved at an unacceptable cost lives. Because human populations far homogeneous, Britton et al. show by introducing age activity heterogeneities into population models for SARS-CoV-2, can...

Networks offer a fertile framework for studying the spread of infection in human and animal populations. However, owing to inherent high-dimensionality networks themselves, modelling transmission through is mathematically computationally challenging. Even simplest network epidemic models present unanswered questions. Attempts improve practical usefulness by including realistic features contact host–pathogen biology (e.g. waning immunity) have made some progress, but robust analytical results...

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

In this paper we consider a stochastic SIR (susceptible→infective→removed) epidemic model in which individuals may make infectious contacts two ways, both within ‘households’ (which for ease of exposition are assumed to have equal size) and along the edges random graph describing additional social contacts. Heuristically motivated branching process approximations described, lead threshold parameter methods calculating probability major outbreak, given few initial infectives, expected...

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 not straightforward and a wealth other threshold parameters has appeared literature. In this paper, we use branching processes to define R(0), apply households or more complex structures provide methods calculating it.

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

In this paper we consider a model for the spread of stochastic SIR (Susceptible $\to$ Infectious Recovered) epidemic on network individuals described by random intersection graph. Individuals belong to number cliques, each size, and infection can be transmitted between two if only there is clique they both to. Both sizes cliques an individual belongs follow mixed Poisson distributions. An infinite-type branching process approximation (with type being given length individual's infectious...

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

Abstract Most countries are suffering severely from the ongoing covid-19 pandemic despite various levels of preventive measures. A common question is if and when a country or region will reach herd immunity h . The classical level C defined as =1−1 /R 0 , where R basic reproduction number, for estimated to lie somewhere in range 2.2-3.5 depending on region. It shown here that disease-induced D after an outbreak has taken place country/region with set measures put place, actually...

What role do asymptomatically infected individuals play in the transmission dynamics? There are many diseases, such as norovirus and influenza, where some hosts show symptoms of disease while others infected, i.e. not any symptoms. The current paper considers a class epidemic models following an SEIR (Susceptible → Exposed Infectious Recovered) structure that allows for both symptomatic asymptomatic cases. question is addressed: what fraction ρ those getting by (asymptomatic) cases? This...

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

We consider long-range percolation on ℤd, where the probability that two vertices at distance r are connected by an edge is given p(r) = 1 − exp[−λ(r)] ∈ (0, 1) and presence or absence of different edges independent. Here, λ(r) a strictly positive, nonincreasing, regularly varying function. investigate asymptotic growth size k-ball around origin, $|\mathcal{B}_{k}|$, is, number within graph-distance k for → ∞, λ(r). show conditioned origin being in (unique) infinite cluster, nonempty classes...

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

We introduce a new 1-dependent percolation model to describe and analyze the spread of an epidemic on general directed locally finite graph. assign two-dimensional random weight vector each vertex graph in such way that weights different vertices are independent identically distributed, but two entries assigned need not be independent. The probability for edge open depends its end vertices, but, conditionally weights, states edges other. In epidemiological setting, represent individuals...

We consider a branching population where individuals have independent and identically distributed (i.i.d.) life lengths (not necessarily exponential) constant birth rates. let N t denote the size at time . further assume that all individuals, their times, are equipped with exponential clocks parameter δ. interested in genealogical tree stopped first T when one of these rings. This question has applications epidemiology, genetics, ecology, queueing theory. show that, conditional on {...

In this paper we consider a stochastic SIR (susceptible→infective→removed) epidemic model in which individuals may make infectious contacts two ways, both within ‘households’ (which for ease of exposition are assumed to have equal size) and along the edges random graph describing additional social contacts. Heuristically motivated branching process approximations described, lead threshold parameter methods calculating probability major outbreak, given few initial infectives, expected...

We study long-range percolation on the hierarchical lattice of order $N$, where any edge length $k$ is present with probability $p_k=1-\exp(-\beta^{-k} \alpha)$, independently all other edges. For fixed $\beta$, we show that $\alpha_c(\beta)$ (the infimum those $\alpha$ for which an infinite cluster exists a.s.) non-trivial if and only $N < \beta N^2$. Furthermore, uniqueness component continuity as a function $\beta$. This means phase diagram this model well understood.