Dynamic Simulation Modeling of
Mosquito Populations with Climate Data
Andrew Comrie & Cory Morin
University of Arizona
Why Model Mosquitoes & Climate?
http://upload.wikimedia.org/wikipedia/commons/4/48/Aedes_aegypti_biting_human.jpg
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Disease impacts of climate change are poorly
understood, oversimplified
Mosquito vectors responsible for a huge disease burden
Few empirical/statistical mosquito models, poor
mosquito data series, no dynamic models
Climate Change Impacts are Underway
Bryan Christie/Scientific American August 2000 (in Epstein PR & Mills E, 2005)
Disease: Coupled Natural & Social Systems
National Research Council, 2001
Epidemiologic Triangle of Disease
Host
(eg, Human)
Vector
Agent
(eg, Pathogen)
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Start with coupling
between climate
and mosquito
populations
Environment
(eg, Climate)
A multi-factorial relationship between hosts,
agents, vectors and environment
Modeling Malaria & Climate Change
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2ºF simple
increase vs.
more complex
empirical
model
http://www.exploratorium.edu/climate/global-effects/data/risk6-3.jpg
AZ
Hatched = current
Rogers & Randolph Science 2000
Abrupt Climate Change & Dengue
1990
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Increased
dengue risk
based on
projected
humidity
changes
Oversimplified?
2085
Hales et al. Lancet 2002
Mosquitoes: Aedes Aegypti
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Characteristics
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Urban, Container Breeding
Mosquito
Tropical Habitat
Dengue Fever Vector
Dengue Fever
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Picture taken from http://www.interetgeneral.info/IMG/Aedes-Aegypti-2.jpg
100 Million Cases a Year
Worldwide
4 Serotypes without Cross
Immunity
Dengue Hemorrhagic Fever
from Multiple Infections
Picture from http://www.cdc.gov/ncidod/dvbid/
dengue/map-distribution-2005.htm
West Nile
Virus
2006
http://www.cdc.gov/ncidod/EID/vol11no08/images/05-0289a_1b.gif
http://diseasemaps.usgs.gov/wnv_us_human.html
Mosquitoes: Culex Quinquefasciatus
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Characteristics
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Urban Mosquito
Feeds on Humans and
Animals
West Nile Virus Vector
West Nile Virus
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Arrived in Arizona in
2003
150 Cases with 10
Deaths in 2005
Symptoms: Mild FeverEncephalitis
Image taken from http://www.lahey.org/Medical/
InfectiousDiseases/WestNileVirus.asp
Dynamic Modeling of Mosquitoes
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Create climate-driven model based on ‘first principles’
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Inputs
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Temperature, Precipitation, Daylight (Monthly)
Evaporation Derived (Hamon’s Equation)
Irrigation/Land Cover
Governing Processes
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Development Rates (Rueda 1990, Sharpe 1977)
Death Rates (Conway 1974, Kasule 1996)
Reproductive Rates (Christophers 1960)
Larval/Pupa Capacity (Christophers 1960)
Water Flux (sources and sinks)
Conceptual Model
Dynamic Mosquito Simulation Model
(DyMSiM)
Model Base
Sub-Model Detail
Implemented in Stella® software
DyMSiM: Sample Equations/Code
Days_with_No_Water(t) = Days_with_No_Water(t - dt) + (No_Water - Water_Day) * dtINIT Days_with_No_Water = 0
INFLOWS:
No_Water = if Total_Water=0 then 1 else 0
OUTFLOWS:
Water_Day = if Total_Water>0 then Days_with_No_Water else 0
Water(t) = Water(t - dt) + (Rain + Irrigation1 - Evaporation - Infiltration) * dtINIT Water = 0
INFLOWS:
Rain = Prec*Area:_Permiable
Irrigation1 = Irrigation*Area:_Permiable
OUTFLOWS:
Evaporation = ((2.1*Day_Light^2*(.6108*EXP((17.27*ATemp)/(237.3+ATemp))))/(ATemp+273.2)/10)*Area:_Permiable
Infiltration = Area:_Permiable*PermiabilityRate
Water1(t) = Water1(t - dt) + (Rain_in_Containers + Irrigation2 - Evaporation1 - Spill) * dtINIT Water1 = 0
INFLOWS:
Rain_in_Containers = Prec*Area:_Containters
Irrigation2 = Irrigation*Area:_Containters
OUTFLOWS:
Evaporation1 = ((2.1*Day_Light^2*(.6108*EXP((17.27*ATemp)/(237.3+ATemp))))/(ATemp+273.2)/10)*Area:_Containters
Spill = if Water1> Area:_Containters*Hight_Container then Water1-(Area:_Containters*Hight_Container) else 0
AdltDeath = if Mos>AdltMinPop then if ATemp<AdltTempMin or ATemp>AdltTempMax then 1 else AdltDeathRate else 0
AdltDeathRate = .14
AdltMinPop = 2
AdltSize = -0.0147*History(ATemp, Time-10)+ 2.1127
AdltTempMax = 40
AdltTempMin = 5
Area = 40468564
Area:_Containters = Percent_Contain*Area
Area:_Permiable = Percent_Perm*Area
Area_Perminant = Area*Percent_Permanant
ATemp = Temp+TempDifference
Day_Light = If TIME>0 and TIME<32 then 10.083 else if TIME>31 and TIME<61 then 10.6 else if TIME>60 and TIME<92 then 11.52 else if TIME>91 and
TIME<122 then 12.52 else if TIME>121 and TIME<153 then 13.45 else if TIME>152 and TIME<183 then 14.12 else if TIME>182 and TIME<214 then 14.22
else if TIME>213 and TIME<245 then 13.73 else if TIME>244 and TIME<275 then 12.82 else if TIME>274 and TIME<306 then 11.85 else if TIME>305 and
TIME<336 then 10.88 else 10.2
Dept = 5
EggsLaid = (46.5*AdltSize)
Food = 1
Food_or_ecological_rating = .5
Genotrophic_cycle = if Food =1 and ATemp> 20 then (.00898*((ATemp+273.15)/(298.15))*EXP(15725.23/(1.987)*(1/(298.15)1/(ATemp+273.15))))/(1+EXP(1756481.07/(1.987)*(1/(447.17)-1/(ATemp+273.15))))*24 else 0
Hight_Container = 20
Irrigation = if IR_Index=1 then IR_1 else if IR_Index=2 then IR_2 else 0
IR_1 = if ATemp>Temp_Thresh then IR_Ammount else 0
IR_2 = if TIME>Julian_Start and TIME<Julian_Stop then IR_Ammount else 0
IR_Ammount = .1
IR Index = 0
DyMSiM Dynamics
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Development
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Degree Day Model: Members of each cohort proceed
through development stages at a rate governed by
temperature
Death
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Immature mosquitoes: Based on temperature and
water availability
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When population exceeds capacity, youngest die first
Adults: Daily survival rates from mark-releaserecapture studies and temperature
Reproduction
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Adult mosquitoes will feed and mate at certain
temperatures, water is required for egg laying
Experiments
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Three runs for a “typical” one-acre area
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Aedes Aegypti
Urban vs Non-Urban Runs
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Tucson daily data, 1950-2005
Climate = same for both runs
Urban = 2 x amount of impermeable land +
small areas of permanent water
Urban Areas with/without Heat Island Effect
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Land cover settings held constant
Simulate a 3°C rise in temperature over last 55 years
(+0.27°C every 5 years)
Also a proxy for climate change
Urban vs Non-Urban
• Urban areas >> non-urban (more impermeable sfc, standing water)
• Population explosions in particular years
A Closer Look at Non-Urban
1955
1964
1983
Non-urban population responds often, but with small numbers relative to
urban population explosions
1954 vs
1955
Temps = similar
Precip totals =
similar
Precip timing =
priceless
Urban Mosquitoes in 1983
1983 summer = unremarkable; TS in October = major flooding
and mosquito population explosion in urban areas
Urban vs Non-Urban by Month
In semi-arid (water-limited) Tucson, moist urban environments
increase the number of mosquitoes and extend the survival season
Urban with/without Heat Island
3°C linear increase leads to slightly reduced population
Urban with/without Heat Island by Month
The heat island effect:
(i) reduces mosquitoes during Summer (evaporation), but
(ii) increases numbers in Spring and early Winter (temperature)
Model Limitations
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“All Models are Wrong, Some are Useful”
-George Box
The model only accounts for climate and land
use factors. The following variables are not
considered
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Predation, Pesticides, Food Availability, Human
Behaviors, Migration
Assumptions
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All mosquitoes will react similarly to stressors
All female mosquitoes are fertile
All female mosquitoes take a blood meal
What Do These Results Tell Us?
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Precipitation timing, and not necessarily
seasonal amount, accounts for major
urban mosquito population explosions
Urban areas are key to enabling mosquito
breeding in semi-arid locations
Warming temperatures (urban or climate
change) are projected to extend the
season when mosquitoes can survive