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  • 1. Ball, Frank
    et al.
    Britton, Tom
    Stockholm University, Faculty of Science, Department of Mathematics.
    Leung, Ka Yin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Sirl, David
    A stochastic SIR network epidemic model with preventive dropping of edges2019In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 78, no 6, p. 1875-1951Article in journal (Refereed)
    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.

  • 2.
    Hansson, Disa
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Leung, KaYin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Britton, Tom
    Stockholm University, Faculty of Science, Department of Mathematics.
    Strömdahl, S.
    A dynamic network model to disentangle the roles of steady and casual partners for HIV transmission among MSM2019In: Epidemics, ISSN 1755-4365, E-ISSN 1878-0067, Vol. 27, p. 66-76Article in journal (Refereed)
    Abstract [en]

    HIV is a sexually transmitted infection (STI) whose transmission process is highly dependent on the sexual network structure of the population under consideration. Most sexual behaviour data is egocentric in nature. We develop a stochastic dynamic sexual network model that utilises this type of egocentric network data. The model incorporates both steady and casual sex partners, and can be seen as a stochastic form of a generalised pair-formation model. We model the spread of an infection where individuals are susceptible, infectious, or successfully treated (and unable to transmit) and derive analytical expressions for several epidemiological quantities. We use sexual behaviour and HIV prevalence data that was gathered among 403 MSM at an STI clinic in Stockholm. To accurately capture transmission dynamics for this population, we need to explicitly model both casual sex partners and steady partnerships. Our model yields an estimate for the mean time until diagnosis followed by successful treatment that is in line with literature. This study indicates that small reductions in the time to diagnosis, and thereby, beginning of treatment, may substantially reduce HIV prevalence. Moreover, we find that moderate increases in condom use with casual sex partners have greater impact on reducing prevalence than the same increases in condom use with steady sex partners. This result demonstrates the relative importance of casual contacts on the HIV transmission dynamics among MSM in Sweden. Our results highlight the importance of HIV testing and condom-use interventions, and the role that casual and steady partners play in this, in order to turn the epidemiological trend in Sweden towards decreased HIV incidence.

  • 3.
    Hansson, Disa
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Strömdahl, Susanne
    Leung, KaYin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Britton, Tom
    Stockholm University, Faculty of Science, Department of Mathematics.
    Introducing pre-exposure prophylaxis to prevent HIV acquisition among men who have sex with men in Sweden: insights from a mathematical pair-formation modelManuscript (preprint) (Other academic)
    Abstract [en]

    Objectives Since 2017, the Public health Agency of Sweden recommend that pre-exposure prophylaxis for HIV (PrEP) should be offered to high-risk individuals, in particular to men who have sex with men (MSM). The objective of this study is to develop a mathematical model investigating the effect of introducing PrEP to MSM in Sweden.

    Design A pair-formation model, including steady and casual sex partners, is developed to study the impact of introducing PrEP. Two groups are included in the model: sexually high-active MSM and sexually low-active MSM. Three mixing assumptions between the groups are considered.

    Setting A gay-friendly MSM HIV/STI-testing clinic in Stockholm, Sweden. This clinic started offering PrEP to MSM in October 2018.

    Participants The model is calibrated according to detailed sexual behaviour data gathered in 2015 among 403 MSM.

    Results By targeting sexually high-active MSM, a PrEP coverage of 3.5% of the MSM population (10% of all high-actives) would result in the long-term prevalence to drop considerably (close to 0%). While targeting only low-actives would require a PrEP coverage of 35% for a similar reduction. The main effect of PrEP is the reduced susceptibility, whereas the increased HIV-testing rate (every 3rd month) among PrEP users plays a lesser role.

    Conclusions To create a multifaceted picture of the effects of interventions against HIV, we need models that include the different stages of HIV infection and real-world data on detailed sexual behaviour to calibrate the mathematical models. Our findings conclude that targeting HIV high-risk individuals, within HIV risk populations such as MSM, with PrEP programmes could greatly decrease the long-term HIV prevalence in Sweden. Therefore, risk stratification of individuals is of importance in PrEP implementation programmes, to ensure optimising the effect and cost-effectiveness of such programmes.

  • 4.
    Leung, Ka Yin
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Ball, Frank
    Sirl, David
    Britton, Tom
    Stockholm University, Faculty of Science, Department of Mathematics.
    Individual preventive social distancing during an epidemic may have negative population-level outcomes2018In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 15, no 145, article id 20180296Article in journal (Refereed)
    Abstract [en]

    The outbreak of an infectious disease in a human population can lead to individuals responding with preventive measures in an attempt to avoid getting infected. This leads to changes in contact patterns. However, as we show in this paper, rational behaviour at the individual level, such as social distancing from infectious contacts, may not always be beneficial for the population as a whole. We use epidemic network models to demonstrate the potential negative consequences at the population level. We take into account the social structure of the population through several network models. As the epidemic evolves, susceptible individuals may distance themselves from their infectious contacts. Some individuals replace their lost social connections by seeking new ties. If social distancing occurs at a high rate at the beginning of an epidemic, then this can prevent an outbreak from occurring. However, we show that moderate social distancing can worsen the disease outcome, both in the initial phase of an outbreak and the final epidemic size. Moreover, the same negative effect can arise in real-world networks. Our results suggest that one needs to be careful when targeting behavioural changes as they could potentially worsen the epidemic outcome. Furthermore, network structure crucially influences the way that individual-level measures impact the epidemic at the population level. These findings highlight the importance of careful analysis of preventive measures in epidemic models.

  • 5.
    Leung, Ka Yin
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Utrecht University, The Netherlands; University Medical Center Utrecht, The Netherlands.
    Kretzschmar, Mirjam
    Diekmann, Odo
    Mean Field at Distance One2017In: Temporal Network Epidemiology / [ed] Naoki Masuda and Petter Holme, Singapore: Springer, 2017, p. 105-128Chapter in book (Refereed)
    Abstract [en]

    To be able to understand how infectious diseases spread on networks, it is important to understand the network structure itself in the absence of infection. In this text we consider dynamic network models that are inspired by the (static) configuration network. The networks are described by population-level averages such as the fraction of the population with k partners, k = 0, 1, 2,  This means that the bookkeeping contains information about individuals and their partners, but no information about partners of partners. Can we average over the population to obtain information about partners of partners? The answer is ‘it depends’, and this is where the mean field at distance one assumption comes into play. In this text we explain that, yes, we may average over the population (in the right way) in the static network. Moreover, we provide evidence in support of a positive answer for the network model that is dynamic due to partnership changes. If, however, we additionally allow for demographic changes, dependencies between partners arise. In earlier work we used the slogan ‘mean field at distance one’ as a justification of simply ignoring the dependencies. Here we discuss the subtleties that come with the mean field at distance one assumption, especially when demography is involved. Particular attention is given to the accuracy of the approximation in the setting with demography. Next, the mean field at distance one assumption is discussed in the context of an infection superimposed on the network. We end with the conjecture that an extension of the bookkeeping leads to an exact description of the network structure.

  • 6.
    Leung, Ka Yin
    et al.
    Utrecht University, The Netherlands; University Medical Center Utrecht, The Netherlands.
    Powers, Kimberly A.
    Kretzschmar, Mirjam
    Gender asymmetry in concurrent partnerships and HIV prevalence2017In: Epidemics, ISSN 1755-4365, E-ISSN 1878-0067, Vol. 19, p. 53-60Article in journal (Refereed)
    Abstract [en]

    The structure of the sexual network of a population plays an essential role in the transmission of HIV. Concurrent partnerships, i.e. partnerships that overlap in time, are important in determining this network structure. Men and women may differ in their concurrent behavior, e.g. in the case of polygyny where women are monogamous while men may have concurrent partnerships. Polygyny has been shown empirically to be negatively associated with HIV prevalence, but the epidemiological impacts of other forms of gender-asymmetric concurrency have not been formally explored. Here we investigate how gender asymmetry in concurrency, including polygyny, can affect the disease dynamics. We use a model for a dynamic network where individuals may have concurrent partners. The maximum possible number of simultaneous partnerships can differ for men and women, e.g. in the case of polygyny. We control for mean partnership duration, mean lifetime number of partners, mean degree, and sexually active lifespan. We assess the effects of gender asymmetry in concurrency on two epidemic phase quantities (R0 and the contribution of the acute HIV stage to R0) and on the endemic HIV prevalence. We find that gender asymmetry in concurrent partnerships is associated with lower levels of all three epidemiological quantities, especially in the polygynous case. This effect on disease transmission can be attributed to changes in network structure, where increasing asymmetry leads to decreasing network connectivity.

  • 7.
    Leung, Ka Yin
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Trapman, Pieter
    Stockholm University, Faculty of Science, Department of Mathematics.
    Britton, Tom
    Stockholm University, Faculty of Science, Department of Mathematics.
    Who is the infector? Epidemic models with symptomatic and asymptomatic cases2018In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 301, p. 190-198Article in journal (Refereed)
    Abstract [en]

    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. The current paper considers a class of epidemic models following an SEIR (Susceptible -> Exposed -> Infectious -> Recovered) structure that allows for both symptomatic and asymptomatic cases. The following question is addressed: what fraction p of those individuals getting infected are infected by symptomatic (asymptomatic) cases? This is a more complicated question than the related question for the beginning of the epidemic: what fraction of the expected number of secondary cases of a typical newly infected individual, i.e. what fraction of the basic reproduction number R-0,R- is caused by symptomatic individuals? The latter fraction only depends on the type-specific reproduction numbers, while the former fraction p also depends on timing and hence on the probabilistic distributions of latent and infectious periods of the two types (not only their means). Bounds on p are derived for the situation where these distributions (and even their means) are unknown. Special attention is given to the class of Markov models and the class of continuous-time Reed-Frost models as two classes of distribution functions for latent and infectious periods. We show how these two classes of models can exhibit very different behaviour.

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