Department of Mathematics

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Browsing Department of Mathematics by Author "Andersson, Mikael"

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    Household Epidemics: Modelling Effects of Early Stage Vaccination
    (Wiley, 2009) Shaban, Nyimvua; Andersson, Mikael; Svensson, Åke; Britton, Tom
    A Markovian susceptible - infectious - removed (SIR) epidemic model is considered in a community partitioned into households. A vaccination strategy, which is implemented during the early stages of the disease following the detection of infected individuals is proposed. In this strategy, the detection occurs while an individual is infectious and other susceptible household members are vaccinated without further delay. Expressions are derived for the influence on the reproduction numbers of this vaccination strategy for equal and unequal household sizes. We fit previously estimated parameters from influenza and use household distributions for Sweden and Tanzania census data. The results show that the reproduction number is much higher in Tanzania (6 compared with 2) due to larger households, and that infected individuals have to be detected (and household members vaccinated) after on average 5 days in Sweden and after 3.3 days in Tanzania, a much smaller difference.
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    Network Epidemics and Early Stage Vaccination: The Effects of Infectious and Vaccination Delay Periods and Their Randomness
    (2011) Shaban, Nyimvua; Andersson, Mikael; Svensson, Åke; Britton, Tom
    It is known that the distributions of the latent and infectious periods affect the dynamics of the spread of an infectious disease. Here we consider the SEIR epidemic model describing the spread of an infectious disease giving life-long immunity in a community whose social structure can be represented by a simple random graph having a pre-specified degree distribution. Two real time vaccination strategies, based on tracing and vaccinating the friends of infectious individuals during the early stages of an epidemic, are proposed. The first strategy considers vaccination of each friend of a detected infectious individual independently with probability ρ. The second strategy sets an upper bound on the number of friends an individual can infect before being detected. We derive both the basic reproduction number and the strategy-specific reproduction numbers and show that these reproduction numbers decrease when the variances of the infectious period and the time to detection increase. Under the assumption that detection may only occur after the latent period, the reproduction numbers are independent of the distribution of the latent period.
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    Networks, Epidemics and Vaccination through Contact Tracing
    (Elsevier, 2008) Shaban, Nyimvua; Andersson, Mikael; Svensson, Åke; Britton, Tom
    We consider a (social) network whose structure can be represented by a simple random graph having a pre-specified degree distribution. A Markovian SIR epidemic model is defined on such a social graph. We then consider two real-time vaccination models for contact tracing during the early stages of an epidemic outbreak. The first model considers vaccination of each friend of an infectious individual (once identified) independently with probability ρ. The second model is related to the first model but also sets a bound on the maximum number an infectious individual can infect before being identified. Expressions are derived for the influence on the reproduction number of these vaccination models. We give some numerical examples and simulation results based on the Poisson and heavy-tail degree distributions where it is shown that the second vaccination model has a bigger advantage compared to the first model for the heavy-tail degree distribution.