L16 - Epidemiology (2) Flashcards
Describe the SIR model and how it differs from the SI model of disease spread
SIR - (Susceptible, Infected, Removed)
- Same as SI model but Removed compartment added
- Removed = plant killed or infected tissue stops being infectious (epidemiologically inert)
Give the 3 mathematical equations related to SIR modelling, describing each term
1) dS/dt = - Beta x IS
2) dI/dt = Beta x IS - mu x I
3) dR/dt = mu x I
(Beta = infection rate)
(Mu = loss of infectivity rate)
What are the key results of the SIR model?
- Disease eventually burns itself out, I = 0 as t = infinity
- Not all plants infected by end of epidemic
Describe the biology of Citrus canker, which will be used as a case study in this lecture
Give:
- pathogen name
- host species
- method of transmission
- symptoms of disease
- draw a sketch of the pathogen’s lifecycle
- Bacterial disease - Xanthomonas axonopodis
- Affects multiple citrus species (grapefruit, lime, lemon etc…)
- Airborne, primarily wind-blown rain
- Bacteria penetrate in wet conditions via stomata
- Pre-existing wounds caused by Asian citrus leaf miner (Phyllocnistis citrella) allow direct penetration
- Erumpent lesions on leaves, stems + fruit
- Causes defoliation, reduced fruit quality, premature fruit drop
- See sketch on 2nd lecture page
Define the basic reproductive number, Ro, how to calculate it and describe its significance
Ro = Avr. no. of of secondary infections generated by one infected individual in a completely susceptible population
Calculation:
- Ro = overall rate of infection x infectious period
- Ro = (Beta x N)/Mu
Significance:
- Ro > 1: disease can invade (epidemic)
- Ro < 1: disease cannot invade (no epidemic)
Describe an area largely affected by Citrus canker
- Multiple introductions of exotic pest to Florida
- Entered in 1995, citrus production reduced 1/3 in one decade
What are the control options for Citrus Canker/lack of control options?
Genetic:
- no resistant forms found
Chemical
- Cu-based bactericides reduce Beta
- Pesticides control leaf miner
- None close to 100%
Which disease model seems applicable and what are the implications?
- Disease reduces fruit yield but doesn’t kill tree
- SI model applicable as Mu = 0
- Implies eventual infection of all trees, even if Beta reduced
What manual control can be applied by growers to reduce the spread of Citrus Canker and how does this change the model used?
- Roguing done - infected hosts scouted and removed/killed by growers
- Move from SI to SIR model
- Mu determined by rate of roguing
Is increasing the frequency of roguing enough to control Citrus Canker disease?
Ro = (Beta x N)/Mu
- Mu can be increased by more roguing
- Increasing roguing frequency doesn’t increase Mu indefinitely
- Further Mu increase requires immediately killing infected hosts
- Infectious but non-symptomatic trees make this hard
Describe a more specific model for Citrus Canker that advances from the SIR model
SCIR Model:
- SIR model + C category
- C = Cryptic (infectious but not yet symptomatic)
- I = Infected (infectious and symptomatic)
- Symptoms developed at rate γ
- Cannot rogue class C plants
Give the four mathematical equations for the SCIR model
1) dS/dt = - βIS - βCS
2) dC/dt = βIS + βCS - γC
3) dI/dt = γC - μI
4) dR/dt = μI
Give an expression for Ro in the SCIR model
Explain the limitations of roguing given this expression
Ro = Ro(C) + Ro(S)
= (βN)/γ + (βN)/μ
- Ro(C) and Ro(S) are separate components for cryptic and symptomatic infection
- Roguing only affects Ro(S)
- Ro(C) > 1 means roguing alone not successful
- Potential for chemical control to reduce Ro(C) but too expensive
Explain a technique that was used to try to reduce the spread of Citrus Canker by reducing Ro(C)
- Rogue infected trees + simultaneously cull nearby trees
- Need to develop optimal radius of control
How can the optimal radius of culling for control be determined?
- Spatial model needed
- Model the “dispersal kernel” of infection
- E.g. exponential kernel K(d) = e^-(d/a), ‘a’ fitted to data
- Multiple models used to find minimum epidemic impact w.r.t cull radius
What happened in Florida to try and control the spread of Citrus Canker?
Did it work? Why/why not
- Culling radius implemented
Radius = 125ft in 1998
Radius = 1900ft in 2001
- not politically popular (killing potentially healthy trees)
Failed control due to :
- pre-2001 radius too small
- legal challenges by homeowners against culling
- widespread pathogen dispersal by hurricanes
- 1900ft also wrong radius (done on basic epidemiology)
