1 / 21

Infectious disease, heterogeneous populations and public healthcare: the role of simple models

Infectious disease, heterogeneous populations and public healthcare: the role of simple models. SIAM CSE 2009 K.A. Jane White Centre for Mathematical Biology University of Bath United Kingdom. Presentation overview. Motivating the use of simple models Infectious disease modelling

plato-larsen
Download Presentation

Infectious disease, heterogeneous populations and public healthcare: the role of simple models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Infectious disease, heterogeneous populations and public healthcare: the role of simple models SIAM CSE 2009 K.A. Jane White Centre for Mathematical Biology University of Bath United Kingdom

  2. Presentation overview • Motivating the use of simple models • Infectious disease modelling • Case study 1: treatment of infections • Case study 2: prevention of infections • Concluding remarks Co-workers Vicki Brown, Centre for Mathematical Biology Matt Dorey, Health Protection Agency Dushyant Mital, Milton Keynes General Hospital Steven White, Centre for Ecology & Hydrology

  3. What categorises a simple model? • Captures key components of real system • Can be used to address specific questions • Model lends itself to analytical techniques: ODEs, PDEs, integral equations, integro-difference/differential equations; nonlinear, low dimension. • Equivalent to, derived from or motivated by, higher dimensional systems more directly linked to data

  4. Aside: equivalence of models Modelling spread of insects into discrete spatial locations e.g. pests in agriculture Coupled map lattice Integro-difference system Pattern formation Speed of invasion taken as an indicator function

  5. Infectious disease modelling Public Healthcare Treatment Effective Affordable Available Prevention Intervention Education Social Contact Epidemiology

  6. Nonlinear incidence Dealing with social contact structure I: The simple modelling approach Compartmental model Population split according to infection status: Susceptible (S), Infected (I), etc. Mass action assumption Rate of infection (incidence) bilinearly dependent on S & I Generally unrealistic for structured contacts.

  7. Dealing with social contact structure II: Linking nonlinear incidence to infection on networks Irregular networks e.g. Scale free Good to represent sexual contact network From Andrea Galeotti University of Essex

  8. Per capita infection rate Time Infecteds Time Data from simulation on scale free network Fitted curve (glm) Infection on scale free network p=1.05; q=0.71 b = 0.00016

  9. Case study 1: Treatment of Infections

  10. Previous work White et al. (2005) JID Vicious and virtuous circles in the dynamics of infectious disease and the provision of healthcare Modelling included: Age structure Sex Activity classes Model structure: Coupled PDEs involving integrals. Analysed using simulations Model outcome: Regions of containment, outbreak and bistability.

  11. pl Symptomatic Infected Susceptible g g (1-p)l d s Asymptomatic Infected Treated The simple version Collapse to a 2-D system

  12. Infection incidence Maximum healthcare provision Hysteresis effect Tmax Simple model can quantify basins of attraction in bistable region

  13. Outbreak Bistability Containment Containment and outbreak requirements N I N=Tmax II Tmax Simple model can quantify transitions between outbreak and containment of infection

  14. Gonorrhoea Symptoms appear 1 week after infection Treatment effective after 1 day Chlamydia Symptoms appear 2 weeks after infection Treatment effective after 1 week N=Tmax Tmax Outbreak Bistability Containment Common Infections N N N=Tmax Tmax

  15. http://images.parenthood.com/hpv-vaccine.jpg Case study II: Prevention of Infection • HPV (Human papillomaviruses) vaccination • HPV-16 and HPV-18 causal factor in cervical cancer • 80% of women infected with HPV at some time • Recent vaccination strategy in England • vaccinate pre-teenage girls (3 doses, £240) • catch up for 16-18 year old girls.

  16. The Simple Modelling Approach • Ignore age and optimal control • Understand behaviour of key parameter groupings • Ignore age, include optimal control • Understand interaction of control with behaviours of first model • Include both age and optimal control • Most realistic system for given problem

  17. Waning immunity Onset sexual activity I. Ignore age and optimal control p=Proportion vaccinated Infection eradicated if • Eradication more likely, for fixed p, if • Vaccination protection is long lasting • Slower rate of becoming sexually active

  18. Females p p h a Asymmetric vaccination has small impact on infection prevalence between sexes Important to consider impact of sexual debut p Males a

  19. II. Ignore age, include optimal control Optimal Control Time In cases where constant control gives persistence of infection, optimal control can eradicate infection. Time III. Still to do!

  20. Concluding remarks • Simple models equivalent to high dimensional systems provide useful analytical techniques • Simple models parameterised from high dimensional systems can be used to analyse more complex problems • Building up complexity of model allows systematic exploration of interactions

More Related