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  • 1.
    Andersson, Patrik
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Lindenstrand, David
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A stochastic SIS epidemic with demography: initial stages and time to extinction2011Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 62, nr 3, s. 333-348Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study an open population stochastic epidemic model from the time of introduction of the disease, through a possible outbreak and to extinction. The model describes an SIS (susceptible–infective–susceptible) epidemic where all individuals, including infectious ones, reproduce at a given rate. An approximate expression for the outbreak probability is derived using a coupling argument. Further, we analyse the behaviour of the model close to quasi-stationarity, and the time to disease extinction, with the aid of a diffusion approximation. In this situation the number of susceptibles and infectives behaves as an Ornstein–Uhlenbeck process, centred around the stationary point, for an exponentially distributed time before going extinct.

  • 2. Ball, Frank
    et al.
    Britton, Tom
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Leung, Ka Yin
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Sirl, David
    A stochastic SIR network epidemic model with preventive dropping of edges2019Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 78, nr 6, s. 1875-1951Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A Markovian Susceptible Infectious Recovered (SIR) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size N, assuming that the degrees of individuals are bounded. A central limit theorem is conjectured for the final size of the epidemic. The results are obtained for both the Molloy-Reed (in which the degrees of individuals are deterministic) and Newman-Strogatz-Watts (in which the degrees of individuals are independent and identically distributed) versions of the configuration model. The two versions yield the same limiting deterministic model but the asymptotic variances in the central limit theorems are greater in the Newman-Strogatz-Watts version. The basic reproduction number R0 and the process of susceptible individuals in the limiting deterministic model, for the model with dropping of edges, are the same as for a corresponding SIR model without dropping of edges but an increased recovery rate, though, when R0>1, the probability of a major outbreak is greater in the model with dropping of edges. The results are specialised to the model without dropping of edges to yield conjectured central limit theorems for the final size of Markovian SIR epidemics on configuration-model networks, and for the size of the giant components of those networks. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations are good, even for moderate N.

  • 3. Ball, Frank
    et al.
    Britton, Tom
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Sirl, David
    A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon2013Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 66, nr 4-5, s. 979-1019Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form a network. Clustering is obtained by forming small completely connected subgroups, and positive (negative) degree correlation is obtained by connecting a fraction of the stubs with stubs of similar (dissimilar) degree. An SIR (Susceptible Infective Recovered) epidemic model is defined on this network. Asymptotic properties of both the network and the epidemic, as the population size tends to infinity, are derived: the degree distribution, degree correlation and clustering coefficient, as well as a reproduction number , the probability of a major outbreak and the relative size of such an outbreak. The theory is illustrated by Monte Carlo simulations and numerical examples. The main findings are that (1) clustering tends to decrease the spread of disease, (2) the effect of degree correlation is appreciably greater when the disease is close to threshold than when it is well above threshold and (3) disease spread broadly increases with degree correlation when is just above its threshold value of one and decreases with when is well above one.

  • 4. Ball, Frank
    et al.
    Britton, Tom
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Sirl, David
    Household epidemic models with varying infection response2011Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, nr 2, s. 309-337Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper is concerned with SIR (susceptible -> infected -> removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to partial immunity, and in the second, the infection status of an individual depends on the infection status of its infector and on whether the individual was infected by a within- or between-household contact. The first scenario may be modelled using a multitype household epidemic model, and the second scenario by a model we denote by the infector-dependent-severity household epidemic model. Large population results of the two models are derived, with the focus being on the distribution of the total numbers of mild and severe cases in a typical household, of any given size, in the event that the epidemic becomes established. The aim of the paper is to investigate whether it is possible to determine which of the two underlying explanations is causing the varying response when given final size household outbreak data containing mild and severe cases. We conduct numerical studies which show that, given data on sufficiently many households, it is generally possible to discriminate between the two models by comparing the Kullback-Leibler divergence for the two fitted models to these data.

  • 5.
    Britton, Tom
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Neal, Peter
    University of Manchester.
    The time to extinction for an SIS-household-epidemic model2010Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 61, nr 6, s. 763-769Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We analyse a Markovian SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission.

  • 6.
    Fransson, Carolina
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Trapman, Pieter
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    SIR epidemics and vaccination on random graphs with clustering2019Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 78, nr 7, s. 2369-2398Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we consider Susceptible Infectious 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. We extend known results from literature by relaxing the assumption of homogeneous infectivity both in individual infectivity and between different kinds of neighbours. An important special case of the epidemic model analysed in this paper is epidemics in continuous time with arbitrary infectious period distribution. We use branching process approximations of the spread of the disease to provide expressions for the basic reproduction number R0, the probability of a major outbreak and the expected final size. In addition, the impact of random vaccination with a perfect vaccine on the final outcome of the epidemic is investigated. We find that, for this particular model, R0 equals the perfect vaccine-associated reproduction number. Generalizations to groups larger than three are discussed briefly.

  • 7.
    Geli, Patricia
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Modeling the Mechanism of Postantibiotic Effect and Determining Implications for Dosing Regimens2009Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 59, nr 5, s. 1416-1432Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A stochastic model is proposed to explain one possible underlying mechanism of the postantibiotic effect (PAE). This phenomenon, of continued inhibition of bacterial growth after removal of the antibiotic drug, is of high relevance in the context of optimizing dosing regimens. One clinical implication of long PAE lies in the possibility of increasing intervals between drug administrations. The model describes the dynamics of synthesis, saturation and removal of penicillin binding proteins (PBPs). High fractions of saturated PBPs are in the model associated with a lower growth capacity of bacteria. An analytical solution for the bivariate probability of saturated and unsaturated PBPs is used as a basis to explore optimal antibiotic dosing regimens. Our finding that longer PAEs do not necessarily promote for increased intervals between doses, might help for our understanding of data provided from earlier PAE studies and for the determination of the clinical relevance of PAE in future studies.

  • 8.
    Hössjer, Ola
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On the eigenvalue effective size of structured populations2015Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 71, nr 3, s. 595-646Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A general theory is developed for the eigenvalue effective size () of structured populations in which a gene with two alleles segregates in discrete time. Generalizing results of Ewens (Theor Popul Biol 21:373-378, 1982), we characterize in terms of the largest non-unit eigenvalue of the transition matrix of a Markov chain of allele frequencies. We use Perron-Frobenius Theorem to prove that the same eigenvalue appears in a linear recursion of predicted gene diversities between all pairs of subpopulations. Coalescence theory is employed in order to characterize this recursion, so that explicit novel expressions for can be derived. We then study asymptotically, when either the inverse size and/or the overall migration rate between subpopulations tend to zero. It is demonstrated that several previously known results can be deduced as special cases. In particular when the coalescence effective size exists, it is an asymptotic version of in the limit of large populations.

  • 9.
    Hössjer, Ola
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Ryman, Nils
    Stockholms universitet, Naturvetenskapliga fakulteten, Zoologiska institutionen.
    Quasi equilibrium, variance effective size and fixation index for populations with substructure2014Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 69, nr 5, s. 1057-1128Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we develop a method for computing the variance effective size , the fixation index and the coefficient of gene differentiation of a structured population under equilibrium conditions. The subpopulation sizes are constant in time, with migration and reproduction schemes that can be chosen with great flexibility. Our quasi equilibrium approach is conditional on non-fixation of alleles. This is of relevance when migration rates are of a larger order of magnitude than the mutation rates, so that new mutations can be ignored before equilibrium balance between genetic drift and migration is obtained. The vector valued time series of subpopulation allele frequencies is divided into two parts; one corresponding to genetic drift of the whole population and one corresponding to differences in allele frequencies among subpopulations. We give conditions under which the first two moments of the latter, after a simple standardization, are well approximated by quantities that can be explicitly calculated. This enables us to compute approximations of the quasi equilibrium values of , and . Our findings are illustrated for several reproduction and migration scenarios, including the island model, stepping stone models and a model where one subpopulation acts as a demographic reservoir. We also make detailed comparisons with a backward approach based on coalescence probabilities.

  • 10. Kozlov, Vladimir
    et al.
    Radosavljevic, Sonja
    Stockholms universitet, Naturvetenskapliga fakulteten, Stockholm Resilience Centre.
    Tkachev, Vladimir
    Wennergren, Uno
    Global stability of an age-structured population model on several temporally variable patches2021Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 83, nr 6-7, artikel-id 68Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number R0R0 for time-independent and periodical models and establish the permanence dichotomy: if R0≤1R0≤1, extinction on all patches is imminent, and if R0>1R0>1, permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.

  • 11.
    Kurasov, Pavel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Mugnolo, Delio
    Wolf, Verena
    Analytic solutions for stochastic hybrid models of gene regulatory networks2021Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 82, nr 1-2, artikel-id 9Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely large. Therefore hybrid models, in which protein counts are replaced by average protein concentrations, have become a popular alternative. The evolution of the corresponding probability density functions is given by a coupled system of hyperbolic PDEs. This system has Markovian nature but its hyperbolic structure makes it difficult to apply standard functional analytical methods. We are able to prove convergence towards the stationary solution and determine such equilibrium explicitly by combining abstract methods from the theory of positive operators and elementary ideas from potential analysis.

  • 12.
    Lashari, Abid Ali
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Trapman, Pieter
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Branching process approach for epidemics in dynamic partnership network2018Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 76, nr 1-2, s. 265-294Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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. We assume that individuals enter the sexually active network with a random number of partners, chosen according to a suitable distribution and that the maximal number of partners that an individual can have at a time is finite. We discuss two different branching process approximations for the initial stages of an outbreak of the STI. In the first approximation we ignore some dependencies between infected individuals. We compute the offspring mean of this approximating branching process and discuss its relation to the basic reproduction number R0. The second branching process approximation is asymptotically exact, but only defined if individuals can have at most one partner at a time. For this model we compute the probability of a minor outbreak of the epidemic starting with one or few initial cases. We illustrate complications caused by dependencies in the epidemic model by showing that if individuals have at most one partner at a time, the probabilities of extinction of the two approximating branching processes are different. This implies that ignoring dependencies in the epidemic model leads to a wrong prediction of the probability of a large outbreak. Finally, we analyse the first branching process approximation if the number of partners an individual can have at a given time is unbounded. In this model we show that the branching process approximation is asymptomatically exact as the population size goes to infinity.

  • 13. Ouboter, Tanneke
    et al.
    Meester, Ronald
    Trapman, Pieter
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Stochastic SIR epidemics in a population with households and schools2016Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 72, nr 5, s. 1177-1193Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the spread of stochastic SIR (Susceptible Infectious 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. This model corresponds to the well-studied household-workplace model. In the hierarchical model which we introduce here, members of the same household are also members of the same school. We introduce computable branching process approximations for both types of populations and use these to compare the probabilities of a large outbreak. The branching process approximation in the hierarchical model is novel and of independent interest. We prove by a coupling argument that if all households and schools have the same size, an epidemic spreads easier (in the sense that the number of individuals infected is stochastically larger) in the independent partition model. We also show by example that this result does not necessarily hold if households and/or schools do not all have the same size.

  • 14. Schaller, David
    et al.
    Geiß, Manuela
    Chávez, Edgar
    González Laffitte, Marcos
    López Sánchez, Alitzel
    Stadler, Bärbel M. R.
    Valdivia, Dulce I.
    Hellmuth, Marc
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hernández Rosales, Maribel
    Stadler, Peter F.
    Corrigendum to “Best match graphs”2021Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 82, nr 6, artikel-id 47Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    Two errors in the article Best Match Graphs (Geiß et al. in JMB 78: 2015–2057, 2019) are corrected. One concerns the tacit assumption that digraphs are sink-free, which has to be added as an additional precondition in Lemma 9, Lemma 11, Theorem 4. Correspondingly, Algorithm 2 requires that its input is sink-free. The second correction concerns an additional necessary condition in Theorem 9 required to characterize best match graphs. The amended results simplify the construction of least resolved trees for n-cBMGs, i.e., Algorithm 1. All other results remain unchanged and are correct as stated.

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  • 15. Schaller, David
    et al.
    Geiß, Manuela
    Stadler, Peter F.
    Hellmuth, Marc
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Complete Characterization of Incorrect Orthology Assignments in Best Match Graphs2021Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 82, nr 20Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Genome-scale orthology assignments are usually based on reciprocal best matches. In the absence of horizontal gene transfer (HGT), every pair of orthologs forms a reciprocal best match. Incorrect orthology assignments therefore are always false positives in the reciprocal best match graph. We consider duplication/loss scenarios and characterize unambiguous false-positive (u-fp) orthology assignments, that is, edges in the best match graphs (BMGs) that cannot correspond to orthologs for any gene tree that explains the BMG. Moreover, we provide a polynomial-time algorithm to identify all u-fp orthology assignments in a BMG. Simulations show that at least 75% of all incorrect orthology assignments can be detected in this manner. All results rely only on the structure of the BMGs and not on any a priori knowledge about underlying gene or species trees.

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  • 16. Schaller, David
    et al.
    Lafond, Manuel
    Stadler, Peter F.
    Wieseke, Nicolas
    Hellmuth, Marc
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Indirect identification of horizontal gene transfer2021Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 83, nr 1, artikel-id 10Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Several implicit methods to infer horizontal gene transfer (HGT) focus on pairs of genes that have diverged only after the divergence of the two species in which the genes reside. This situation defines the edge set of a graph, the later-divergence-time (LDT) graph, whose vertices correspond to genes colored by their species. We investigate these graphs in the setting of relaxed scenarios, i.e., evolutionary scenarios that encompass all commonly used variants of duplication-transfer-loss scenarios in the literature. We characterize LDT graphs as a subclass of properly vertex-colored cographs, and provide a polynomial-time recognition algorithm as well as an algorithm to construct a relaxed scenario that explains a given LDT. An edge in an LDT graph implies that the two corresponding genes are separated by at least one HGT event. The converse is not true, however. We show that the complete xenology relation is described by an rs-Fitch graph, i.e., a complete multipartite graph satisfying constraints on the vertex coloring. This class of vertex-colored graphs is also recognizable in polynomial time. We finally address the question “how much information about all HGT events is contained in LDT graphs” with the help of simulations of evolutionary scenarios with a wide range of duplication, loss, and HGT events. In particular, we show that a simple greedy graph editing scheme can be used to efficiently detect HGT events that are implicitly contained in LDT graphs.

  • 17.
    Svensson, Åke
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Who was the infector-probabilities in the presence of variability in latent and infectious times.2013Ingår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 68, nr 4, s. 951-967Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The probability that an observed infection has been transmitted from a particular member of a set of potential infectors is calculated. The calculations only use knowledge of the times of infection. It is shown that the probabilities depend on individual variability in latent and infectious times. The analysis are based on different background information and different assumptions on the progress of infectivity. The results are illustrated by numerical calculations and simulations.

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