| 1. |
- Britton, Tom, et al.
(författare)
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The early stage behaviour of a stochastic SIR epidemic with term-time forcing
- 2009
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 46:4, s. 975-992
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Tidskriftsartikel (refereegranskat)abstract
- The general stochastic SIR epidemic in a closed population under the influence of a term-time forced environment is considered. An 'environment' in this context is any external factor that influences the contact rate between individuals in the population, but is itself unaffected by the population. Here 'term-time forcing' refers to discontinuous but cyclic changes in the contact rate. The inclusion of such an environment into the model is done by replacing a single contact rate λ with a cyclically alternating renewal process with k different states denoted {A(t)}t≥0. Threshold conditions in terms of R⋆ are obtained, such that R⋆ > 1 implies that π, the probability of a large outbreak, is strictly positive. Examples are given where π is evaluated numerically from which the impact of the distribution of the time periods that Λ(t) spends in its different states is clearly seen.
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| 2. |
- Nannyonga, Betty
(författare)
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Data driven mathematical models for policy making
- 2011
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of two papers. 1. Betty Nannyonga, D.J.T. Sumpter, J.Y.T. Mugisha and L.S. Luboobi: The Dynamics,causes and possible prevention of Hepaititis E outbreaks. 2. Betty Nannyonga, D.J.T. Sumpter, andStam Nicolis: A dynamical systems approach tosocial and economic development. The first paper deals with a deterministic approach of modelling a Hepatitis E outbreak whenmalaria is endemic in a population. We design three models based on the epidemiology ofHepatitis E, malaria, and the co-infection of both diseases. We t our designed models to datathat was collected in a Hepatitis E outbreak in Kitgum district, Uganda, to estimate parameterssuch as the transmission rate, basic reproduction number and recovery rate of those aected. Inthe tting we pursue two approaches, the logistic approach when the natural mortality is zero,and a detailed tting using PottersWheel Toolbox, when natural mortality is not equal to zero.In both cases, we seek to explore how endemic malaria could aect a Hepatitis E outbreak, andsuch a disease’s ability to persist in a population over a long period of time. As a measure ofthe eect of malaria on Hepatitis E transmission, we use a modication parameter such thatwhen the estimated value is greater than unity, then malaria favours Hepatitis E, otherwisewe conclude that it inhibits its spread. In the same paper we attempt to estimate the levelof sanitation required to prevent future outbreaks, in terms of availability of latrines and safedrinking water.In the second paper, we look at the eects of child mortality and average child per woman(fertility rates) on economic development (demographic transition). We use data that is readilyavailable from Gapminder, to extract two dynamical systems, one for child mortality and grossdomestic product (GDP), and the second for child mortality, gross domestic product and averagechild per woman. The models obtained are analyzed numerically for existence and stability. Weuse the Gapminder data to obtain a model that comforms to the demographic transition. Ratherthan using data to justify the assumptions of our models, we use data directly to propose dynamicmodels for the economy. The major question is then, how can we use the model to determine thebest strategy to maximize development? We answer this question by setting constraints, wherewe assume that the economy can improve by 3% while the empirical value for child mortality istwice reduced. Then, we determine the time taken to reach the desired gross domestic product,set to that of a developed economy with low child mortality rates. These approximations makeit possible to draw some conclusions about the best strategy to invest: either directly into theeconomy, or indirectly through child health care. From the simulations we can also determinethe point at which to switch the investment strategy. We end this paper by including averagechild per woman and construct and study the model for the three variables.
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| 3. |
- Lu, Xin, et al.
(författare)
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Respondent-driven sampling on directed networks
- 2013
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Ingår i: Electronic Journal of Statistics. - 1935-7524. ; 7, s. 292-322
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Tidskriftsartikel (refereegranskat)abstract
- Respondent-driven sampling (RDS) is a widely used method for generating chain-referral samples from hidden populations. It is an extension of the snowball sampling method and can, given that some assumptions are met, generate unbiased population estimates. One key assumption, not likely to be met, is that the acquaintance network in which the recruitment process takes place is undirected, meaning that all recruiters should have the potential to be recruited by the person they recruit. Using a mean-field approach, we develop an estimator which is based on prior information about the average indegrees of estimated variables. When the indegree is known, such as for RDS studies over internet social networks, the estimator can greatly reduce estimate error and bias as compared with current methods; when the indegree is not known, which is most common for interview-based RDS studies, the estimator can through sensitivity analysis be used as a tool to account for uncertainties of network directedness and error in self-reported degree data. The performance of the new estimator, together with previous RDS estimators, is investigated thoroughly by simulations on networks with varying structures. We have applied the new estimator on an empirical RDS study for injecting drug users in New York City.
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| 4. |
- Britton, Tom, et al.
(författare)
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Dynamic Random Networks in Dynamic Populations
- 2010
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 139:3, s. 518-535
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Tidskriftsartikel (refereegranskat)abstract
- We consider a random network evolving in continuous time in which new nodes are born and old may die, and where undirected edges between nodes are created randomly and may also disappear. The node population is Markovian and so is the creation and deletion of edges, given the node population. Each node is equipped with a random social index and the intensity at which a node creates new edges is proportional to the social index, and the neighbour is either chosen uniformly or proportional to its social index in a modification of the model. We derive properties of the network as time and the node population tends to infinity. In particular, the degree-distribution is shown to be a mixed Poisson distribution which may exhibit a heavy tail (e.g. power-law) if the social index distribution has a heavy tail. The limiting results are verified by means of simulations, and the model is fitted to a network of sexual contacts.
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| 5. |
- Britton, Tom, et al.
(författare)
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Epidemic modelling : aspects where stochasticity matters
- 2009
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 22:2, s. 109-116
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Tidskriftsartikel (refereegranskat)abstract
- Epidemic models are always simplifications of real world epidemics. Which real world features to include, and which simplifications to make, depend both on the disease of interest and on the purpose of the modelling. In the present paper we discuss some such purposes for which a stochastic model is preferable to a deterministic counterpart. The two main examples illustrate the importance of allowing the infectious and latent periods to be random when focus lies on the probability of a large epidemic outbreak and/or on the initial speed, or growth rate, of the epidemic. A consequence of the latter is that estimation of the basic reproduction number R0 is sensitive to assumptions about the distributions of the infectious and latent periods when using data from the early stages of an outbreak, which we illustrate with data from the H1N1 influenza A pandemic. Some further examples are also discussed as are some practical consequences related to these stochastic aspects.
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| 6. |
- Britton, Tom, et al.
(författare)
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Graphs with specified degree distributions, simple epidemics and local vaccination strategies
- 2007
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Ingår i: Advances in Applied Probability. - : Cambridge University Press (CUP). - 0001-8678 .- 1475-6064. ; 39:4, s. 922-948
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Tidskriftsartikel (refereegranskat)abstract
- Consider a random graph, having a prespecified degree distribution F, but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose that one individual in the community is externally infected by an infectious disease and that the disease has its course by assuming that infected individuals infect their not yet infected friends independently with probability p. For this situation, we determine the values of R-0, the basic reproduction number, and tau(0), the asymptotic final size in the case of a major outbreak. Furthermore, we examine some different local vaccination strategies, where individuals are chosen randomly and vaccinated, or friends of the selected individuals are vaccinated, prior to the introduction of the disease. For the studied vaccination strategies, we determine R-v, the reproduction number, and tau(v), the asymptotic final proportion infected in the case of a major outbreak, after vaccinating a fraction v.
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| 7. |
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| 8. |
- Britton, Tom
(författare)
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Stochastic epidemic models : A survey
- 2010
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 225:1, s. 24-35
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Tidskriftsartikel (refereegranskat)abstract
- This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.
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| 9. |
- Hansson, Disa, et al.
(författare)
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Inferring individual sexual action dispositions from egocentric network data on dyadic sexual outcomes
- 2018
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Ingår i: PLOS ONE. - : Public Library of Science (PLoS). - 1932-6203. ; 13:11
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a family of models that allows us to estimate egos' unobserved action dispositions from a joint behavioural outcome of a dyadic social interaction process of both egos' and alters' action dispositions. The method is put to test on a data set containing two different types of dyadic activities of high relevance for the spread of sexually transmitted infections (STI), condom use and anal sex. The data consists of individuals older than 15 years old who visited one of the nine youth clinics in the Vastra Gotaland region of Sweden between February 2010 and March 2011 for STI testing. This is hence a group of special interest for STI interventions. We cannot find any difference in condom disposition between women and men. Condoms are initially used more often in less risky types of relationships, especially if the partner ends up as a main partner. When studying the disposition towards anal sex we do however find a difference between men and women. Women are more against practising anal sex than men while the majority of men are neutral towards anal sex.
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| 10. |
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