# Modelling Infectious Disease

• View
27

• Category

## Documents

Embed Size (px)

DESCRIPTION

Modelling Infectious Disease. … And other uses for Compartment Models. Plumbing. Tracking the concentration of dissolved particles through pipes. A simple conceptual model. Amount of solutes at the start = x(t=0)=x(0)=18 Concentration of solutes at any time = x / V - PowerPoint PPT Presentation

### Text of Modelling Infectious Disease

Modelling Infectious Disease

Modelling Infectious Disease And other uses for Compartment Models1PlumbingTracking the concentration of dissolved particles through pipesA simple conceptual modelraterateVolumeAmount of solutes at the start = x(t=0)=x(0)=18Concentration of solutes at any time = x/VWater coming in removes an amount of x at a constant rateNeed a model to calculate x(t)A simple mathematical model

rrVThe SolutionX(0) = 18r = 10V = 100

Varying the rate of flow

Compartments & Flow

rrrrV1V2V3Changes in Concentration7Evaluate the ModelChoose some parametersV1 = 80V2 = 100V3 = 120r = 20Define the initial conditionsx1(0) = 10x2(0) = 0x3(0) = 0http://math.fullerton.edu/mathews/N310/projects2/p14.htm (read from More Background onwards)

8Results

9General Framework10Any pattern you likeLandSeaAir11From plumbing to infectious diseasesInfectious DiseaseSusceptible pool of people

Infected pool of people

Recovered pool of peopleSIR13SIRbSIvIInfection Rate:Contact rateInfection probabilityRecovery Rate

If D is the duration of infection:v = 1/D

14A typical flu epidemicEach infected person infects a susceptible every 2 days so bN=1/2 (N = S+I+R)Infections last on average 3 days so v=1/3London has 7.5 million people10 infected people introduced See accompanying notes on parameter meanings

15R0 as a useful statisticR0 is the basic reproductive number of the diseaseSimilar to the r and R that appear in population modelsR0 = N*b*Duration = N(b/v)If R0 > 1 epidemicIf R0 < 1 disease dies out naturally16Changes to Infection Rate

b=0.5/Nv=1/3

b=2/Nv=1/3

17Modifications are (almost) endlessSusceptibleExposedInfectedRecoveredSEIRSusceptibleCarrierInfectedRecoveredCarrier Type Diseases: TB, Typhoid18Typhoid Mary1869-1938Healthy carrier of typhoidInfected 47 people in the USQuarantined twice under the mental health actWe still do this!!e.g. TB

19Smallpox (Variola)Enveloped DNA virusgenus Orthopox

Remains a biological threatHuge vaccine stocks are held by many Governments

20Legrand et al. 2004, Epidemiol Infect, vol 132, pp19-25Uninfectedcontacts(located)Vaccinated successfullyExposed contacts(missed)SusceptibleInfectiousRemovedExposed contacts(located)Quarantine21Time to Invervention is crucial

22Endemic InfectionsThese are persistent infections in the population that tick along at a relatively stable level, never going extinct.This happens when the number of Infectious people remains constant

23Minimum Vaccination NumberAlso known as Herd ImmunityAt equilibrium (stable state)

R0S = 1

Vaccinate proportion q of population

R0(1-q)=1

1-q=1/R0

qc=1-(1/R0)

This is the minimum % of the pop that have to be vaccinated in order to stop the spread of the disease24Immunisation ThresholdsDiseaseR0Thresholdqc=1-(1/R0)Measles1593%Smallpox786%Mumps580%25ConclusionsCompartment models are versatileFlow of liquids between tanksDiffusion of nutrients across sediment boundariesSpread of disease through populationsEndless elaborations can be madeSpatial structurePopulation structure26Further ReadingThe bible and for a link from SIR to population models:Anderson & May. 1979. Population biology of infectious diseases: Part 1. Nature 280, 361-367.May & Anderson. 1979. Population biology of infectious diseases: Part 2. Nature 280, 455-461.For an evolutionary spin:Brown et al. 2008. Evolution of virulence: triggering host inflammation allows invading pathogens to exclude competitors.Fitting models to real data:Keeling & Grenfell, 2001. Understanding the persistence of measles: reconciling theory, simulation and observation. Proc Roy Soc B 269, 335-343.Indeed, anything by Bryan Grenfell is worth reading: http://www.cidd.psu.edu/people/bio_grenfell.html Foot-and-mouth disease:Tildesley et al. 2006. Optimal reactive vaccination strategies for a foot-and-mouth outbreak in the UK. Nature 440, 83-86. (and refs therein, esp the first 2)The original article:Kermack & McKendrick 1927. http://links.jstor.org/sici?sici=0950-1207%2819270801%29115%3A772%3C700%3AACTTMT%3E2.0.CO%3B2-Z

27Tasks for next tutorialWhy do some infectious diseases such as measles epidemics cycle?Intrinsic (properties of the infective process itself)Extrinsic (environmental)See Bryan Grenfells research on measles as a starter http://www.princeton.edu/eeb/people/display_person.xml?netid=grenfell&display=All

Recommended

Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Healthcare
Documents
##### Emerging infectious disease
Health & Medicine
Documents