The Impact of Household Capital
Models on Targeted Epidemiological
Control Strategies for Diseases with
Age-Based Etiologies
Nina H. Fefferman
EENR/DIMACS
Rutgers University
& InForMID
Tufts Univ. School of Medicine
Integrating economics into epidemiology has
led to targeted recommendations for
treatment to combat epidemics
Decisions using cost-benefit analyses or optimization
techniques are based on trying to achieve particular goal:
• Minimize deaths
• Minimize economic loss (to community or individuals)
• Minimize interruption of society/service
• Minimize numbers ill (per unit time or overall)
• etc.
However, most of these have looked either at individual
health choices (made only for yourself), or total
communities
For total communities:
Normal assumption: limited resources are a “community
level problem”
• Individuals don’t make decisions, public health
officials recommend strategies
− Vaccinate children first
− Treat elderly first
− etc.
• Targeted treatment/prophylaxis recommendations
are then followed or not, leading to sensitivity
studies for “coverage”, “compliance” or
“adherence”
For individuals:
Normal assumption is behavior is “selfish”, maximizing
personal health outcome at a minimum of personal cost
• Individuals are usually assumed to be willing to
cause public hardship in favor of personal benefit
− Tragedy of the Commons
− Lemon Paradox
− even Prisoner’s Dilemma type things
• Investigation then usually examines how the
individual behaviors predicted by the models will
cause community-level effects (e.g. herd immunity)
But do the same recommendations hold for
“household economic” decisions?
In practice, economic resources are shared within a family
If recommendations involve “elderly” or “children”, the
also involve all the other members of the family
(a little different for nursing homes and orphanages, but still…)
Also, while community-level recommendations can be
made, individuals are still potentially paying the costs
If this is done via a tax or community fund, then we’re just
fine, but if this is voluntary participation in a public health
recommendation, there may be different trade-offs
(especially if not mediated by a community physician)
What happens when households themselves
have limited economic resources?
We know that, independent of disease, access to health care
and monetary resources themselves increase individual
health
If illness compromises an individual’s ability to earn money,
their future health, independent of the particular illness
could also be jeopardized.
If the same individual is responsible for supporting
dependents, the health of those dependents could also be
compromised
Does this “dependents” perspective alter our
analysis of how best to mitigate risks?
For ease, let’s say that the dynamics of these things are a bit
simple:
1.
Lack of resources instantly decreases health, and thereby
increases susceptibility to disease
2.
There are only two types of people: producers and consumers
a. Consumers rely on producers for resources
b. Producers produce resources for themselves and others
c. For simplicity, we’ll assume Consumers are children and
Producers are adults (e.g. dependent elderly are treated
economically AND etiologically like children)
Simple daily model of economics
Each day starts with “left over” resources, saved from
previous days
In each household, an average number of Producers gain an
average amount of resources for the household
In each household, if there are sick people, the household
pays up to what they have to treat them according to a
public health recommendation (we’ll vary these to see
what happens)
If there is money left over, then they buy food (shared
evenly among all, though maybe not enough)
Mostly simple daily SIR disease process:
Basic household:
S
p , I p , R p , S c , I c , Rc 
I

p
, I c

Average size of household: h
Rates of transmission within household:  p and  c
Rates of transmission within community:  p and c
When there isn’t enough food, these increase to: ˆ ,ˆ
Natural rates of recovery:
p
and
Treatment based rates of recovery:
~ ~ ~

S
,I ,R
Basic community:
.
p
Total population size: N
p
c


 p , c
~ ~ ~
S
p , c , I c , Rc

So the picture: Lots of “average” households,
which together are a community
Transmission comes both from within the
family and from the community
 p and  c
 p and c
We assume that each house really is every house, so
there are no differences in either econ or epi
between houses
 p and  c
 p and c
Mathy details happen! (details available upon
request, but they are somewhat involved)
dS p
if M h   0, A

dt if M h   0, Aˆ
dS c
if M h   0, B

dt if M h   0, Bˆ
dI p
if

dt if












    
    
    
    
 
 
 
 
~
~
A   p S p I p  I p   p S p I c  I c   p S p I p   p S p I c
~
~
B   c S c I p  I p   c S c I c  I c   c S c I p   c S c I c
~
~
Aˆ  ˆ p S p I p  I p  ˆ p S p I c  I c  ˆp S p I p  ˆp S p I c
~
~
Bˆ  ˆc S c I p  I p  ˆc S c I c  I c  ˆc S c I p  ˆc S c I c
M h   0,  A1  T p    p I p
 Aˆ   p I p
M h   0,
S c N  h 
~
Sc 
h
 
   S I  I     
dt
~
~
dS
   S I  I    S I  I    S I    S I 
dt
dI
~
~
  S I  I    S I  I    S I    S I 1  T   
dt
~
~
dI
  S I  I    S I  I    S I    S I 1  T    I
dt
dS p
  p S p I p  I
c
dI

p
c
dI c
c
c
c

c
c
p
p

p
p
p
c

c
p
dRc
c

p
p
c
c
c
  
   S I

c
c
c
p
p
c
c
p
p
c c
p
c
p c
p
c c
c
    
   S I~    S I~ T   
p
c c
~
~
  p S p I p  I p   p S p I c  I c   p S p I p   p S p I c T p    p I p
c
dR p
c

p
  
  S I
dt
dt
p
c
p
 I p
dt
  p I p   p I p
dt
  c I c   c I c
c
c
c
 I c
c
c
p
c
c c
c
 
c c
I




I p  I p N  h 
~
Ip 
h
~
~
 p S p I p  p S p Ic
p
p
c
p

c
c
c
p

p
S p N  h 
~
Sp 
h
Ip
I c  I c N  h 
~
Ic 
h
R p N  h 
~
Rp 
h
and
Rc N  h 
~
Rc 
h
We then model the epidemiological outcome
and compare results
First, we choose public health strategies: treat everyone
uniformly, treat only consumers, treat only producers
Next, we model the disease spread without any economic
limitation (so no ˆ ,ˆ ), and we treat everyone our
strategy says we should
Lastly, include household economic limitation and try all our
strategies again this time using ˆ ,ˆ
We pick some parameter values (don’t really
matter because we hold them constant across
models)
Epidemiological Parameters
Economic
Parameters
% Producers in Population
50%
% Consumers in Population
50%
p
0.3
c
0.5
̂ p
0.4
̂ c
0.7
p
0.1
c
0.1


p
1
 c
1
p
0.03
c
0.05
ˆp
0.04
ˆc
0.07
Daily Producer Contribution
Daily Producer Consumption
Daily Consumer Consumption
Cost of Treatment
5
3
2
7
Epidemic curves when treatment costs don’t
impact household health maintenance or
susceptibility.
Epidemic curves when treatment costs do impact
household health maintenance and
susceptibility
Comparison of Outcomes:
Without Econ
Constraint
With Econ
Constraint
Comparison of Outcomes: The numbers
No Economic
Limitation on
Household Healthcare
Expenditure
With Economic
Limitation on
Household Healthcare
Expenditure
Goal Levels of
Treatment
Total %
Infected
% of
Consumers
Infected
% of
Producers
Infected
100% Treatment
8
9
8
100% Consumers Only
84
90
77
100% Producers Only
88
95
82
50% Treatment
86
93
80
0% Treatment
98
100
97
100% Treatment
95
99
92
100% Consumers Only
99
100
98
100% Producers Only
89
95
83
50% Treatment
98
100
96
0% Treatment
99
100
98
Comparison of Outcomes: The numbers
No Economic
Limitation on
Household Healthcare
Expenditure
With Economic
Limitation on
Household Healthcare
Expenditure
Goal Levels of
Treatment
Total %
Infected
% of
Consumers
Infected
% of
Producers
Infected
100% Treatment
8
9
8
100% Consumers Only
84
90
77
100% Producers Only
88
95
82
50% Treatment
86
93
80
0% Treatment
98
100
97
100% Treatment
95
99
92
100% Consumers Only
99
100
98
100% Producers Only
89
95
83
50% Treatment
98
100
96
0% Treatment
99
100
98
Model agrees with previous studies: recommends most effective
control for whole population is children
Comparison of Outcomes: The numbers
No Economic
Limitation on
Household Healthcare
Expenditure
With Economic
Limitation on
Household Healthcare
Expenditure
Goal Levels of
Treatment
Total %
Infected
% of
Consumers
Infected
% of
Producers
Infected
100% Treatment
8
9
8
100% Consumers Only
84
90
77
100% Producers Only
88
95
82
50% Treatment
86
93
80
0% Treatment
98
100
97
100% Treatment
95
95
99
99
99
92
100
98
100% Consumers Only
95
83
50% Treatment
89
89
98
98
100
96
0% Treatment
99
99
100
98
100% Producers Only
Model demonstrates economics matter! Recommends most
effective control for whole population is producers!
But what if we want to prevent most severe
outcomes? Maybe we should still treat
consumers first?
No Economic
Limitation on
Household Healthcare
Expenditure
With Economic
Limitation on
Household Healthcare
Expenditure
Goal Levels of
Treatment
Total %
Infected
% of
Consumers
Infected
% of
Producers
Infected
100% Treatment
8
9
8
100% Consumers Only
84
90
77
100% Producers Only
88
95
82
50% Treatment
86
93
80
0% Treatment
98
100
97
100% Treatment
95
99
92
100% Consumers Only
99
100
100
98
100% Producers Only
89
95
95
83
50% Treatment
98
96
0% Treatment
99
100
100
100
100
98
Nope! Still better to target producers for treatment – allowing
them to continue supporting consumers helps consumers more!
But what if we want to prevent most severe
outcomes? Maybe we should still treat
consumers first?
No Economic
Limitation on
Household Healthcare
Expenditure
With Economic
Limitation on
Household Healthcare
Expenditure
Goal Levels of
Treatment
Total %
Infected
% of
Consumers
Infected
% of
Producers
Infected
100% Treatment
8
9
8
100% Consumers Only
84
90
77
100% Producers Only
88
95
82
50% Treatment
86
93
80
0% Treatment
98
100
97
100% Treatment
95
99
92
100% Consumers Only
99
100
98
100% Producers Only
89
95
83
50% Treatment
98
100
96
0% Treatment
99
100
98
That’s not true in the model without economic constraint.
Moral of the story:
Economic constraints on families lead to different
population-level optimal strategies for both limiting
overall incidence AND limiting incidence in high-risk
populations
Model agrees that, without economic constraints, preventing
disease in “reservoir” populations helps curtail risks to
total population, but shifts recommendation once
household production constraints are included
Policy needs to be based on understanding productivity
Optimal strategies in non-resource-limited areas may be
wrong for resource-limited communities
Thanks to:
Jacques Kibambe Ngoie (an economist
who worked on this with me)
DIMACS
Prof. Mugisha
Makerere University
All of you for your time