Immuno-epidemiology of
coccidiosis
Don Klinkenberg
Maite Severins
Hans Heesterbeek
Coccidiosis
• Caused by Eimeria spp
• Protozoan
• Intestinal infection
– sometimes lesions
– main problem: production loss
• Seven species in chickens
– location in the intestine
– no cross-immunity
Parasite classification
• After lecture notes by Kretschmar (micro/macro):
Microparasite
Macroparasite
Eimeria
Parasite lifespan
Short
Long
Short
Reproduction within
host
Rapid
None
Rapid (but dose effect)
Transmission
Direct
Indirect
Indirect
Infection events
One
Multiple
Multiple
Immunity
Complete
Partial, slowly
acquired
Accumulative, slowly
acquired
Model type
SIR type
Parasite load
???
Essential characteristics
• Transmission through environment
• Dose-dependent infectivity
• Slowly acquired immune response
– stronger upon re-infection
– reduces parasite excretion
• Within-host dynamics!
This presentation
• Model of within-host dynamics
– relation between uptake and excretion of
infectious material (oocysts)
– interaction with immune system
• Model of between-host dynamics (I)
– coupling excretion and uptake of oocysts
– interaction chickens and environment
• Model of between-host dynamics (II)
Within-host model
• Eimeria characteristics:
– transmission through oocysts
– Eimeria parasitises gut epithelial cells
– limited number of asexual generations
Eimeria cycle
Oocyst uptake (W)
Sporozoites
Oocyst excretion (Z)
Schizont I (X(1))
Gamont
Merozoites I (u(1))
Merozoites II (u(2))
Schizont II (X(2))
Eimeria cycle
Oocyst uptake (W)
Oocyst excretion (Z)
Schizont I (X(1))
Schizont II (X(2))
Eimeria cycle
Oocyst uptake (W)
Schizont I (X(1))
X
X
Schizont II (X(2))
Oocyst excretion (Z)
1
t 1
2 
t 1
 a1Wt
 1 X
Z t  2  2 X
2 
1
t
t
Adding immunity
•
•
•
•
Primarily T cell immunity
Immunity evoked by schizonts
Immunity inhibits schizont development
Keeping the model simple: one immunity
variable Y
Eimeria cycle with immunity
Oocyst uptake (W)
Oocyst excretion (Z)
+
Immunity (Y)
–
+
Schizont II (X(2))
–
Schizont I (X(1))
Eimeria cycle with immunity
Oocyst uptake (W)
X
X
Schizont I (X(1))
–
Schizont II (X(2))
+
+
–
Oocyst excretion (Z)
1
t 1
2 
t 1
 a1Wt
 1 X
Z t  2  2 X
Immunity (Y)
2 
1
t
t
Eimeria cycle with immunity
Oocyst uptake (W)
X
X
Schizont I (X(1))
–
Schizont II (X(2))
+
+
–
Oocyst excretion (Z)
1
t 1
2 
t 1
 a1Wt
 1 X
Z t  2  2 X
2 
1
t
t
f Yt 
f Yt 
Immunity (Y)

Yt 1  g Yt , X
1
t
X
2 
t

Eimeria cycle with immunity
X 1t 1  a1Wt
X 2 t 1  1 X 1t f Yt 
Z t  2  2 X 2 t f Yt 

Yt 1  g Yt , X 1t  X 2 t

1
f Y  
m
1 Y
g Y , X 1  X 2   Y    Y  X 1  X 2 




Model summary
• Discrete time
• Two asexual schizont generations
• T cell immunity against schizont
development
Model analysis
• Compare model experiments to data
– relation single dose and excretion
• saturation followed by decrease
– excretion during trickle infections
• excretion terminates after some time
– immunising effect of trickle and single
immunisation
• trickle immunisation gives better protection
Log(oocyst excretion)
Single dose and excretion
E. tenella
8
7.5
7
6.5
6
5.5
5
0
2
4
Log(oocyst uptake)
6
Model analysis
• Model experiments
– single dose and excretion
• relation between W0 and Z4
– trickle infections
– trickle vs single immunisation
Analysis: single dose
7.5
logz 4
l2
l1
6.5
a112W0
Z4 
m
1  a1W0 
5.5
l 1: logz 4=p 1+logw 0
l 2: logz 4=p 1+(1-m )logw 0-mp 2
4.5
0
2
4
6
logw 0
Analysis: single dose
E. tenella
8
6
4
2
4
6
8
Analysis: single dose
E. acervulina
8
6
4
2
4
6
8
Analysis: single dose
E. maxima
8
6
4
2
4
6
8
Model analysis
• Model experiments
– single dose and excretion
• relation between W0 and Z4
•  > 0 (naïve immunity growth)
• m ≠ 1 (non-linear immune effectiveness)
– trickle infections & immunisation
• conclusions on  and 
Conclusions within-host model
• Simple model of parasite input-output
behaviour
• Single immunity variable can explain
experimental data
• Solid basis for studying re-infection and
between-host transmission
Between-host model
• Relate excretion to uptake with oocyst
level in environment V
• Simplifying assumption: average chicken
Eimeria cycle
Oocyst uptake (W)
Oocyst excretion (Z)
+
Immunity (Y)
–
+
Schizont II (X(2))
–
Schizont I (X(1))
Eimeria cycle
outside the chickens
Environmental
oocysts (V)
×1
× a0
Oocyst excretion (Z)
Oocyst uptake (W)
×1
× a1
Immunity (Y)
+
Gamont (G)
× 2
–
+
Schizont II (X(2))
inside the chickens
–
Schizont I (X(1))
× 1
Two new parameters
• Per time step of ca. 2 days
• Uptake rate a0
– estimate from a single experiment: 0.01
• Oocyst degradation rate
– estimate from couple of articles: 0.5
Interesting variables
• Oocyst level in environment
– decrease due to degradation (+ uptake)
– increase due to excretion
• Immunity level in average chicken
– increase due to presence of schizonts
– decrease by fixed rate
• Number of infected cells as measure of
damage
– numbers of schizonts and gamonts
Basic dynamics
outside the chickens
4
5
Environmental
oocysts (V)
×1
Oocyst excretion (Z)
3
5
× a0
Oocyst uptake (W)
2
×1
× a1
Immunity (Y)
Gamont (G)
× 2
–
+
3
+
2
Schizont II (X(2))
inside the chickens
0
–
1
Schizont I (X(1))
× 1
Dynamics in single chicken cohort
• First dose of each infection generation
most important
– major change compared to previous dose
– fast decay of oocysts in environment
• Dynamics can be described in terms of
infection generations
Damage in single chicken cohort
• Cumulative damage ≈ maximum damage
11 logd
max
10
9
8
7
6
5
4
7.5
5
2.5
2.5
logv0
5
7.5
10
Conclusion on damage
• Production damage is reflected by the
maximum number of infected cells
• Damage may take local minimum with
intermediate oocyst level V0
• Mechanism
– maximum damage if a single infection
generation dominates
– minimum when generation dominance
switches
Damage in single chicken cohort
• Cumulative damage ≈ maximum damage
11 logd
max
10
9
8
37 2
6
5
4
4
7.5
5
2.5
2.5
1
schizonts II
gamonts logv
0
5
7.5
10
Discussion of the model
• Single ‘average’ chicken
• Deterministic model
• No spatial effects
Different approach
• Individual chickens
• Stochastic model
• Spatial model
• Cost:
– No continuous infection/immune level
Individual based model
• Patches interact with walking chickens
• Patches
– oocyst level empty, low, medium, high (0; 103;
105; 107)
– level rises if chicken excretes higher level
– level falls after 14 days without excretion
Individual based model
• Chickens
– walk or ‘shuffle’ each hour
– pick up maximum daily exposure (0, 101; 3; 5)
– excrete once per day depending on
• uptake -4 days
• level of immunity (no, partial, full)
• regulated by excretion templates
– immunity level may increase depending on
• time since first dose
• number and level of doses
Example: fit to data (Galmes)
1000x20
20000
control
model 1000x20
model 100000
model control
1,000,000
100,000
10,000
oocysts x10^3
1,000
100
10
1
0
0
5
10
15
20
25
30
35
40
“damage” related to initial level
High oocyst excretion
walk
shuffle
mean # excretions/chick
6
5
4
3
2
1
0
0.01
0.1
1
% initial contam ination
10
100
Local minimum
• Mechanism?
– High excretion due to serial medium doses
• medium doses require serial low doses
– If initial level is
• high: early excretion of many medium, so serial
medium doses before immunity
• intermediate: early exposure for start-up immunity,
but less serial medium exposure
• low: many chicks are not immune while others
already shed medium doses
More generalized mechanism for
local minimum damage
• Low initial level: exposure of naive chickens to
large oocyst quantities excreted by first infection
generation
• Intermediate initial level: immunity builds up
before large oocyst quantities are available
• High initial level: large oocyst quantities
available before immunity is reached
• However: relation to level of mixing yet unclear
Our coccidiosis modellers
• Deterministic continuous model
– Don Klinkenberg, Hans Heesterbeek
• Stochastic discrete model
– Maite Severins, DK, HH
• Stochastic continuous model (not shown)
– Andriy Rychahivskyy, DK, HH