Computational Sustainability - PowerPoint Presentation

Slide1

Computational Sustainability March 12, 2010 at 1:25PM – 2:40PM 1150 Snee Hall Optimizing Intervention Strategies in Food Animal Systems: modeling production, health and food safety

Elva Cha, DVM, PhD candidate, Rebecca Smith, DVM, PhD candidate, Zhao Lu, PhD, Research Associate and Cristina Lanzas, DVM, PhD, Research Associate and

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ö

T. Gröhn, DVM, MPVM, MS, PhD

Department of Population Medicine and Diagnostic Sciences,

College of Veterinary Medicine, Cornell UniversitySlide2

Perhaps I should start with “ a disclaimer”… If I understood correctly, your approach is to assume the model is 'correct', then optimize the system. As veterinarians, our responsibility is to build a model based on subject matter representing reality.Of course, our goal is to find the optimal way to control disease (not necessarily eradication). And sometimes we need to learn the economically optimal way to coexist with them.Slide3

Food Supply Veterinary Medicine….all aspects of veterinary medicine's involvement in food supply systems, from traditional agricultural production to consumption.

Modeling production, health and food safety

:

1. Optimizing health and management decisions

2.

Mathematical modeling of

zoonotic

infectious diseases

(such as

L.

monozytogenes

, E. coli, MDR salmonella and

paratuberculosis

).Slide4

Three examples …Modeling production and health:Project 1. “Optimal Clinical Mastitis Management in Dairy cows.” Elva

Cha’s

PhD research

Project 2.

“

Cost Effective Control Strategies for The Reduction of

Johne’s

Disease on Dairy Farms.” Zhao Lu, Research Associate and Becky

Smith’s PhD

research

2. Modeling Food Safety:

Project 3.

“Food Animal Systems-Based Mathematical Models of Antibiotic Resistance among

Commensal

Bacteria.” Cristina Lanzas, Research AssociateSlide5

Let’s start with…1. Modeling production and health: Our overall goal is to develop a comprehensive economic model, dynamic model (DP), to assist farmers in making treatment and culling decisions.

Our 1

st

example:

Elva

Cha’s

PhD research: “Optimal Clinical Mastitis Management in Dairy cows”Slide6

Mastitis (inflammation in mammary gland)Common, costly disease (major losses: milk yield, conception rates, and culling). The question we address is whether it is better to treat animals at the time CM is first observed or whether it is worthwhile collecting more information related to the nature of the pathogen involved (Gram-positive or Gram-negative, or even the actual pathogen), and then make a treatment decision.

More information would seem to be of benefit

when deciding what to do with diseased cows,

but

unless the additional tests provide a different recommended outcome,

they are only an extra cost.

Slide7

Objective:We will build upon our existing Dynamic Programming model. This work requires us to determine the risk and consequences of CM (milk loss, delayed conception, mortality) as functions of cow characteristics, including the disease history and disease prognosis of the cow.

To do this

To determine the economically optimal amount of information needed to make mastitis treatment decisionsSlide8

How do we address our objective?We will compare 2 modelsModel 1 which will identify cows based on generic (non-specific) mastitisAnd Model 2, whereby if a cow has mastitis, it will be specified as gram-positive, gram-negative or other types of mastitisWe will then compare the profit of each modelWhat is this model?Slide9

The modelsThe models will calculate the optimal policy for each individual cowThis can be done by ‘dynamic programming’Slide10

Dynamic programmingNumerical method for solving sequential decision problemsBased on the ‘Bellman principal of optimality’In our case, the ‘system’ is dairy cows, observed over an infinite time horizon split into ‘stages’ i.e. months of a cow’s lifeSlide11

Dynamic programming At each stage, the state of the system is observedE.g. pregnancy status, disease status, milk yieldAnd a decision is madeReplace, keep (treat and inseminate) or sellThis decision influences stochastically the state to be observed at the next stage

Depending on the state and decision, a reward is gainedSlide12

Dynamic programmingValue function is the expected total rewards from the current stage until the end of the horizonOptimal decisions depending on stage and state are determined backwards step by stepSlide13

Structure of the hierarchic Markov process optimization modelSlide14

Parameters in our modelFor each type of mastitisRisk of mastitisRepeated risk of mastitisEffect on milk yieldEffect on conceptionEffect on mortality and cullingSlide15

LimitationsNow we can only study 3 different types of mastitis, although we have data for very specific types of mastitis! (i.e. >3!)Why is this a limitation? Can’t we simply expand the model?Slide16

Implications of a larger modelBy expanding the model, we will encounter the ‘curse of dimensionality’An opportunity cost of including another disease, and hence the parameters associated with itThe model increases as a power function, not by a factor of 1, 2 or 3…This makes computations even more challenging and time consumingSlide17

The curse of dimensionalityexample: Houben et al. 1994 State variables:

Age (monthly intervals, 204 levels)

Milk yield, present lactation (15 levels)

Milk yield, previous lactation (15 levels)

Length of calving interval (8 levels)

Mastitis, present lactation (4 levels)

Mastitis, previous lactation (4 levels)

Clinical mastitis (yes/no)

Total state space 6,821,724 statesSlide18

The curse of dimensionalityexample: Gröhn et al. 2003 State variables: Parity

(12 levels)

Conception in month

(10 levels)

Stage of lactation (20 levels)

Milk yield (5 levels)

Month of

calving (12 levels)

Disease index

(212 levels)

Total state space 144,000 x 212= 30,528,000Slide19

Structure of the hierarchic Markov process optimization model: First level: 5 milk yield levelsSecond level: 8 possible lactations and 2 carry-over mastitis states from previous lactation (yes/no).Third level: 20 lactation

stages (max calving interval of 20 months).

5 temporary milk yield levels

(relative to permanent milk yield),

9 pregnancy status levels

(0=open, 1-7 months pregnant, and 8=to be dried off), one involuntary culled state

13 mastitis states:

0=no mastitis

1 = 1

st

occurrence of CM (observed at the end of the stage),

2, 3, 4 = 1, 2, 3 and more months after 1

st

CM,

5 = 2

nd

CM,

6, 7, 8 = 1, 2, 3 and more months after 2

nd

CM,

9 = 3

rd

CM,

10, 11, 12 = 1, 2, 3 and more months after 3

rd

CM,

CM events > 3 assigned same penalties as if they were 3

rd

occurrence.

After deleting impossible stage-state combinations, the model described 560,725 stage-state combinations.Slide20

If we were able to overcome the curse of dimensionality … No longer only generic guidelines for the generic cow. The DP recommendations could be tailored to the individual cow in real time according to her cow characteristics and economics of the herd.Slide21

Project 2: “Cost Effective Control Strategies for The Reduction of Johne’s Disease on Dairy Farms”Zhao Lu, PhD, Research Associate, and Becky Smith, DVM, PhD studentSlide22

Johne’s disease (paratuberculosis)Johne’s disease is a chronic, infectious, intestinal disease caused by infection with Mycobacterium avium subspecies paratuberculosis (

MAP

).

Infection process of

paratuberculosis

on a dairy cow:

Transient shedding

Latency

Low shedding

High shedding

Infection status

Disease status

No clinical signs

Sub-clinical

Clinical

InfectionSlide23

Issues of Johne’s diseaseEconomic loss: > 200 million $ per year (Ott, 1999) due to the reduced milk production, lower slaughter value, etc.Public health: a potential association between Johne’s disease and human Crohn’s disease has been debated. Control of

Johne’s

disease:

Test and cull strategies, i.e., to cull/remove infectious animals form herd by test-positive results using diagnostic testing methods, such as culture and ELISA tests.

Improved hygiene management;

Vaccination.

However, it is difficult to control JD spread:

Long incubation period;

Low diagnostic test sensitivity for animals shedding low levels of MAP;

Cross reactivity of

Johne’s

disease vaccines with tuberculosis (TB).Slide24

Modeling of MAP transmission on a dairy herdA deterministic compartmental model (Mitchell et al., 2008). The test-based culling rates of low and high shedders are denoted by δ1 and δ2, respectively.

X

1

Susceptible

-





d

X

2

Resistant



d

Tr

Transient



d



()

H

Latent



d



Y

1

Low



d



Y

2

High



d



1



2



Slide25

Evaluation of effectiveness of test-based culling in Johne’s disease controlThe reproduction ratio R0 was derived and a global parameter uncertainty analysis was performed to determine the effectiveness of test-based culling intervention (Lu et al., 2008)Slide26

A stochastic multi-group model(Evaluation of effectiveness of test-based culling)

Calves

Heifers

Cows

Slide27

Optimal control of Johne’s disease:economic modelObjective function (cost function): Profit: selling milk, culling cows (meat);Cost: raising first and second-year calves/heifers; diagnostic testing; Lost: false-positive testing results. Control: various scenarios of test-based culling rates and management

Constraints: a system of dynamic equations.

Compartment model providing numbers of calves, heifers, and cows in each compartment, which are needed in the objective functional (cost function).

A deterministic, discrete time economic model has been developed to find optimal test-based culling rates with large (6 and 12 month) time steps. Slide28

What do we want?(Optimal control of test-based culling rates)A deterministic, continuous time economic model. Analytical studies of linear controls (test-based culling rates);Numerical search of optimal test-based culling rates.

A stochastic economic model.

Reasons: more realistic (variable prevalence and fadeout due to random events)

Optimal culling rates using stochastic differential equations;

Numerical simulations of optimal culling rates for the mean of cost function.

Economic analysis of

Johne’s

disease vaccines.

Mathematical modeling of imperfect

Johne’s

vaccines is in progress.

Slide29

Modeling the efficacy of an imperfect vaccine with multiple effectsVaccines are often imperfect They may not prevent all infectionsThey may have effects other than decreasing susceptibilityEfficacy can be considered as the proportional effect on a rate or probability parameter in a compartmental model5 vaccine effects:Vertical transmission

Horizontal transmission

Susceptibility

Infectiousness

Duration of latency

Duration of low-infectious period

Progression of clinical symptomsSlide30

Modeling vaccine efficacy against JD

X

1

(1-p)(

-)

(1-p)





d

X

2

Resistant



d

Tr

Transient



d



()

H

Latent



d



Y

1

Low



d



Y

2

High



d





Susceptible

VX

1

Susceptible

p

(-)

p





d

VX

2

Resistant



d

VTr

Transient



d



e

20

()

VH

Latent



d

e

3



VY

1

Low



d

e

4



VY

2

High



d

e

5



Slide31

Estimating vaccine efficacy against JD with field dataKnown information:birth datedeath date annual test dates and resultsvaccination statusMissing information:Date of infectionOnset of low-sheddingOnset of high-sheddingTrue infection status (if all tests results were negative)

To estimate vaccine efficacy,

missing information must also be estimatedSlide32

Estimating vaccine efficacy with Markov Chain Monte Carlo modelsMCMC models are Bayesian statistical models, useful for disease modeling because theyCan account for nonlinear systemsparameters may be inter-relatedCan account for time-dependence i.e. infectious pressureHave a mechanism for missing-data problems:Missing information can be estimated probabilistically, given a set of parameters drawn from a prior distributionThe full dataset can then be used to determine the relative likelihood of a different set of parameters drawn from the prior

The new set of parameters may be accepted or rejected, based on its relative likelihood

This process is iterated until it converges on a posterior distribution for all parametersSlide33

Validating MCMC modelsIn order to test that an MCMC model predicts the true parameter distribution, we feed it data simulated with known parametersIn the case of the JD model, the full model requires individual animal data:Infection statusVaccination statusDates of birth, compartment transitions, deathWe need an individual-animal stochastic modelSlide34

Optimal control of Johne’s disease using an individual-based (agent-based) modeling approachControls: test-based culling, farm management, JD vaccinesAdvantages of individual-based modeling (IBM)Providing a general framework to model infectious disease transmission in a dairy herd;Integrating all individual information together to predict the dynamics on farms;Adding controls on farm level and/or individual animals easily.

Economic analysis based on IBM would be more accurate.

Disadvantages of IBM

Individual information collection: a detailed profile for each animal in a herd.

(also an advantage)

Simulations: efficient algorithm and powerful computers are necessary.Slide35

Project 3: “Develop, evaluate and improve food animal systems-based mathematical models of antimicrobial resistance among commensal bacteria”Cristina Lanzas, DVM, PhD, Research AssociateSlide36

Bergstrom and Feldgarden, 2008 At least 200,000 people suffer from hospital acquired infection every year, and at least 90,000 die in US. Economical burden of antimicrobial resistance in clinical settings in US is estimated to be as high as $ 80 billion annually.

Pathogens outside the hospital are also becoming progressively resistant to common antimicrobials.

Antimicrobial resistance is also considered a food safety issue because infections with drug resistant foodborne pathogens (e.g.

Salmonella

) can be particularly serious.

Slide37
Slide38

Reservoirs of resistant genes are found in commensal bacteria in the human and animal gastrointestinal tracts (small intestine supports ~ 1010 bacterial cells/g) . Commensal bacteria can transfer mobile genes coding antimicrobial resistance among themselves and to pathogen bacteria (e.g. plasmid transfer between Salmonella and E. coli)

Molecular mechanisms involved in the spread of antimicrobial resistance. Inter-cellular movement (horizontal spread) is the main cause of acquisition of resistance genes.

Boerlin, 2008

Salyers et al., 2004Slide39

WITHIN HOST

R

S

Population dynamics of antibiotic-sensitive and –resistant bacteria

Linked to antibiotic exposure

Emergence of resistance during antibiotic treatment

Fitness cost linked to microbial growth

BETWEEN HOSTS

Transmission of resistant clones

Individuals colonized with either susceptible or resistant strains

The host population is divided according its epidemiological status (e.g. susceptible, infectious)

“Binary response”: Animal carries the bacteria carrying the resistance or not

S

I

-

+Slide40

Within host dynamics of antimicrobial resistance disseminationMicrobial growth for sensitive and resistant strains with horizontal gene transfer

Logistic Growth

Antibiotic effect

Plasmid loss during segregation

Plasmid transfer

Percentage of resistant bacteria 24 h after the end of the antimicrobial treatmentSlide41

Between host dynamics of antimicrobial resistance dissemination

S

I

S

I

R

I

SR

S

susceptible

I

infectious

W

environment

γ

πη

λSlide42

Integrating within and between host antimicrobial resistance dynamics Interventions to minimize the dissemination of antimicrobial resistance can be applied at different organizational levels (e.g. within host/between hosts and environment):Optimize antimicrobial dosage regimes to mitigate the dissemination of antimicrobial resistance within enteric commensal bacteria.Reduce the exposure of animals to antimicrobial resistant bacteria. Mathematical approaches that integrate within and between host dynamics are necessary to optimize mitigation strategies acting at different hierarchical scales:

Agent-based/Individual-based models

Dynamic nested models

Slide43

Modeling On-farm Escherichia coli O157:H7 population dynamics Metapopulation models has allowed us to investigate the potential role of non-bovine habitats (i.e., water troughs, feedbunks, and the surrounding pen environment) on the persistence and loads of E. coli O157:H7 in feedlots.O157:H7 survive and reproduce in water troughs, feed, slurry, pen floors.

Ayscue et al.,

Foodborne

Pathog

Dis

, 6:461-470 (2009)Slide44

Monogastric calfGrowing ruminant heifer

Lactating cow

Bred ruminant heifer

Dry cow

Cull cow

Dairy beef

S, R

S, R

S, R

S, R

Animal patches

Selective

pressures

Environment

(S, R)

Water

(S,R)

This metapopulation approach is suitable for modeling the dynamics of antimicrobial resistance dissemination. Pharmacokinetics and pharmacodynamics and biological fitness of antimicrobial resistance can be integrated.Slide45

Assuming three types of ecological patches (water, environment and n animals) and assuming indirect transmission (bacteria are transmitted to animals through water and environment):

For the

j

animal:

Water patch:

Environmental patch:Slide46

Potential students projects Application of optimal control to evaluate strategies in metapopulation models Development of agent based models to address antimicrobial resistance dissemination. Optimization in agent based models Optimization in hierarchical models