Centre for International Health, University of Bergen, Bergen, Norway

Bjerknes Centre for Climate Research, University of Bergen/Uni Research, Bergen, Norway

Hawassa University, Hawassa, Ethiopia

National Meteorological Agency of Ethiopia, Addis Ababa, Ethiopia

Geophysical Institute, University of Bergen, Bergen, Norway

Abstract

Background

Most of the current biophysical models designed to address the large-scale distribution of malaria assume that transmission of the disease is independent of the vector involved. Another common assumption in these type of model is that the mortality rate of mosquitoes is constant over their life span and that their dispersion is negligible. Mosquito models are important in the prediction of malaria and hence there is a need for a realistic representation of the vectors involved.

Results

We construct a biophysical model including two competing species,

Conclusions

This study highlights some of the assumptions commonly used when constructing mosquito-malaria models and presents a realistic model of

Background

This is the first of two papers describing a dynamic model (Open Malaria Warning; OMaWa) of

In this paper, we describe a model of the dynamics of the two species and then show how parameters can influence the success of the two species, and how temperature, humidity and mosquito size can influence malaria transmission.

Climate and malaria

Most of the 149-274 million cases and 537,000-907,000 deaths from malaria occur in sub-Saharan Africa

Malaria and mosquito models

At the turn of the 20th century the work of several researchers, including Battista Grassi and Ronald Ross, resulted in the discovery that mosquitoes of the

In 2011, The malERA Consultative Group on Modeling

Many traditional models rely on a threshold principle. The idea has been to find thresholds for longevity, number of bites or days to recovery that must be reduced to interrupt the transmission. With increased computational power it is now possible to make more complex models and hence explore a wider range for the dynamics of malaria and mosquito survival. By integrating the knowledge from simpler models into a complex system, it is possible to test if the assumptions are true over a wider geographical range. In addition, these complex models can make quantitative predictions about strategies for control

Model summary and motivation

A model is mental copy that describes one possible representation of a system. We present an alternative formulation of the dynamics of

The ODEs parametrize daily mortality rates, which are size-dependent for adult mosquitoes; development rates in the aquatic stages; biting rates; fecundity; the probability of finding a blood meal; and mortality related to flushing of eggs, larva and pupa out of oviposition sites. These parametrization schemes are driven by air temperature, relative humidity, relative soil moisture, water temperature, and runoff. As already mentioned, the model can be applied in a spatial domain. In this case, temperature and other environmental data are taken from a regional climate model, the Weather Research and Forecasting Model (WRF)

At this spatial resolution, the model should potentially be able to define larger foci of mosquito productivity, while the ability to identify hotspots will be limited

The mosquito model described here is designed to capture the spatial distribution and the time-dependent density of

We have chosen to represent the non-exponential mortality of

We do not claim that the additional complexity adds any value. Stating this before the model has been fully evaluated and compared to simpler models would be dangerous. The model is thus one possible way of describing the dynamics of

To highlight some of the components that contribute to the dynamics of

Material and methods: model description

Summary of the model

Figure

Overview of the mosquito model

**Overview of the mosquito model.** A (regional) climate model is used to force the mosquito model. In addition, static and semi-static fields are used as part of the parametrization schemes. Human and bovine densities limit the availability of blood meals.

As mentioned above, the model comprises a system of ODEs for eggs, first to fourth instar larvae, and pupae; an age-structured formulation for adult mosquitoes; and size prediction for adult mosquitoes (measured as wing length in mm). The first limitation in the aquatic stage is the availability of ovipositing sites, which is parametrized in terms of relative soil moisture and the potential for puddle formation in a specific location. Once ovipositing sites have been formed, adult female mosquitoes are allowed to deposit eggs until the site is full, defined as the biomass relative to the carrying capacity for the location. To account for density-dependent mortality, first instar larvae can be preyed on by fourth instar larvae

We adopt these general ideas for two species,

In addition to time, the model can include two (three, since space is two-dimensional) additional dimensions, namely age and space. The space dimension allows dispersion of mosquitoes, meaning that (re)establishment through migration to areas that were previously free of

The ODEs were solved using the ODE solver lsoda ^{-6}). The model can be run either as a spatial model (with or without mosquito dispersion) or evaluated at a single point at which movement is neglected. A detailed overview of the possible model parameters can be found in Table

**Variable**

**Description**

**Equation(s)/reference**

Description of model components.

_{
indoor
}

Indoor temperature

36

_{
air
}

Near surfacetemperature (2 m)

25, 26, 30, 36

Potential number ofnew eggs

13

_{
n
}

Number of mosquitoes ineach age group

8

Daily probability of gettinga blood meal

41

_{
water
}

Water temperature

14, 16, 18

_{
soil
}

0-10 cm soil temperature

_{
N,L
}(_{
water})

Natural mortiality rate,eggs, larva, and pupa

14, 1, 2, 3, 4, 5, 6

_{
g
a
m
b
}

20

_{
arab
}

22

_{
E
}

_{
P
}

_{
arab
}

Aquatic development rate modification

_{
g
a
m
b
}

Aquatic development rate modification

_{
n
}

Number of larvae

21, 19

_{
arab
}

Mortality rate modification

_{
g
a
m
b
}

Mortality rate modification

_{
f
}

scaling factor for winddispersion

39

_{
m
}

Flight range

41

Number of eggs

1

Biting rate/gonotrophiccycle

26

time

_{
L
}

Larva biomass

1

_{
I,x
}

Induced mortalityin aquatic and adult stages

1, 2, 3, 4, 5, 6,7, 8

_{
r
}

Dimensionless time varying water constant, or rate at which ovipositing sites are found

24

Carrying capacity

24

_{1}

Number of 1^{st }instar larva

2

_{2}

Number of 2^{nd }instar larva

3

_{3}

Number of 3^{rd }instar larva

4

_{4}

Number of 4^{th }instar larva

5

Number of pupa

6

_{
pred}

Predation constant.Currently set to 0

2

_{
g
o
n
o
t
}

part of gonotrophic cycle formulation

26

_{d}

Degree days

_{c}

Critical temperature

26

_{h,m}

Adult mortality related to feeding

42

Number of humans

_{
ı,ȷ
}

flux

39

Dimension in age grid

_{
size
}

Size of newly emerged mosquitoes

9

Size of mosquitoes in age group

12

_{
size
}

Prediction of larva size

10

_{
s
p
p
}

Size constant

_{
s
p
p
}

Size constant

_{
p
}

Potential river length in km

23

Equally spaced riverdataset resolution indegrees

23

Earth radius inkm (6371.22)

23

latitude in radians

23

Diffusion coefficient

39

Local time

37

Diurnal modification fortransport of mosquitoes

37

Human blood index

41, 42

Size dependent mortality

28

_{
N,m
}

Natural mortality of adultmosquitoes

32, 7, 8

_{
N,m
}(

Survival curve for adultmosquitoes

35, 31

Shape parameter for adult survival

3330

_{
mod
}

Sub-function forequation 33

34

_{
bovine/cattle}

Probability of finding cattle

41

_{human}

Probability of findinghumans

41

Differential equations for the aquatic compartment

The aquatic compartment consists of six stages: eggs (_{1},_{2},_{3},_{4}), and pupae (

New eggs added to the population depend on the number of adult mosquitoes (_{
size}), the inverse length of the gonotrophic cycle (_{
r
}, dimensionless) and the larval biomass already present in puddles (_{
L
}):

where _{
r }is a function of the relative soil moisture and the potential puddle formation area, _{
N,E
}(_{
I,E }is the induced mortality rate for eggs (not specified) and _{
E }is the inverse of development time from eggs to first instar larvae.

The term 1-_{
L}/

First instar larvae (_{1}) are added as eggs develop into larvae. Additional mortality is added in the transition stage in relation to how much biomass there already is in a given location _{L}/

Shoukry looked at how fourth instar larvae of _{
pred }is tunable to both limit the predation on _{1 }and make it more specific to species in the future. At most temperatures, this constant does not influence the density of mosquitoes (Additional file

**Density of mosquitoes under different predation regimes and temperatures.**

Click here for file

The number of first instar larva is given by:

Second (_{2}), third (_{3}) and fourth instar larvae (_{4}) and pupae (

where

Differential equations for adult mosquitoes

The life history and mortality rate vary over the lifespan of a mosquito population. We formulated a model to account for this variation. Adult mosquitoes are denoted by _{
n
}, where _{1 }=[0,1], _{2 }= (2,4], _{3 }= (5,8], _{4 }= (9,13], _{5 }= (14,19], _{6 }= (20,26], _{7 }= (27,34], _{8 }= (35,43] and _{9 }= (44,_{
n }of 1.000, 0.500, 0.333, 0.250, 0.200, 0.167, 0.143, 0.125 and 0.067 for _{
n
}, where

Although there is no ageing from age group 9, the term _{9 }is included to limit the concentration of old mosquitoes. This is a user-specified variable and in the model results shown here we set this to

When _{
n,ı,ȷ
}.

Again, _{
n
}) of the mosquitoes.

The number of adult mosquitoes of a specific age in a grid point is controlled by new mosquitoes from _{
n-1}, as well as the flux to and from the point of interest _{
n+1}, and mortality due to lack of food (

This results in the following equation for the first age group:

The equations for age groups

Differential equations predicting mosquito size

Mosquito size (_{
size}) is important for the efficiency of mosquito multiplication. There are also some indications that increased body size is a strategy for survival in arid environments

Since the size of

For size prediction we use the symbol

The size (wing length in mm)of newly emerged mosquitoes is approximated according to the linear relationship

where larva size _{
size }(in mg) is approximated as:

The constants _{
s
p
p }and _{
s
p
p }are 0.45 and 0.12 for

The size of mosquitoes in the first age group at any time is given by

Therefore, the size of newly emerged mosquitoes (

For the remaining age groups, size

Therefore, the size in age groups 2-9 only depends on the number of mosquitoes surviving from one age group to the next (_{
n-1}) and the size of mosquitoes in the younger age group (

Model forcing

To drive a dynamic malaria model it is necessary to have boundary conditions that are consistent over time and space. Temperature, relative humidity, and rainfall data from weather stations are point measures. Hence, they might not be representative of larger areas over shorter time scales. This is especially true in areas with varying topography or where convective rainfall is dominant

The problems of point measurements are described later, and represent one of the reasons why OMaWa is tightly linked to a climate model. As shown in sensitivity experiments, the model can also be run with constant forcing (e.g. temperature) or with data from weather stations.

Where we present results for Africa as a whole, OMaWa is driven by data from WRF 3.3.1. This realization (TC50), described in part two of this paper, has a tropical channel set-up in which set-up, the domain consists of boundaries above and below a certain latitude and no side boundaries. The model was run at 50-km resolution from January 1, 1989 to January 1, 2009. At the northern (45°N) and southern (-45°N) boundaries the model was driven by Era Interim. The Kain Frisch cumulus parametrization scheme was used

Climate and weather models

Currently, our best guess of (future) climate at multidecadal time scales comes from general circulation models (GCMs). These models are designed to close the energy budget of the Earth and include an interactive representation of the atmosphere, ocean, land, and sea ice. A set of scenarios with different emissions describes how sensitive the climate is to atmospheric constituents (greenhouse gasses)

Both climate and weather models are mostly structured on a grid, with coordinates from west to east (^{2}, operational weather models such as the European Centre for Medium-Range Weather Forecast (ECMWF) model are run at approximately 160 ^{2}. If the state of the atmosphere is observed correctly, higher resolution can lead to better local skill in predicting the weather. A hybrid between a weather model and a climate model is a limited-area model (LAM), which relies on initial and boundary conditions from a weather or climate model. Given these conditions (weather), the LAM can be run at a higher resolution over a limited area, which potentially improves the spatial accuracy of the coarse model

In tropical regions, most rainfall comes from convective clouds. This type of rainfall is generally intense and of short duration. The geographical extent of such rainfall episodes may be limited. Therefore, rainfall measurements in regions where convective rainfall is dominant should be handled with care

Parametrization schemes in the aquatic stages

To relate a variable such as mortality to the physical environment, we need simplified equations that describe this relationship. An equation in which temperature influences mortality only states that there is a relationship between the two, but does not explain why temperature modifies mortality. In this paper we use parametrization schemes to represent the influence of the environment on mosquitoes. This section describes the aquatic parametrization schemes used, excluding water availability, which is discussed later.

The aquatic stages comprise eggs, four instar stages, and pupae. The number of eggs in a location at any time is controlled by the number of potential new eggs laid (_{
N/I,E/L/P
}) and movement from the _{1 }compartment. In addition, 20% instant mortality is introduced when rainfall exceeds the infiltration rate. This is in line with observations by Paaijmans et al.

where _{
n
} is the number of mosquitoes in age group

Estimation of water temperature

Using the 0-10-cm soil temperature (_{
soil }) from the NOAH land surface model _{
water }) in larval habitats, we assume that evaporative cooling and heat fluxes at the water boundaries are negligible. Hence, the water temperature is equal to the top soil temperature. Paaijmans et al. showed that the 5-cm soil temperature represents the water temperature in small ponds reasonably well ^{2}, this effect should be negligible, although we do not have data to support this. We hope to improve the prediction of water temperature in the future, either by modelling this explicitly or using a parametrized version based on data from Huang et al.

Parametrization of mortality

We used two approaches to calculate mortality in the aquatic stages. In the simpler approach, we assume that mortality and development time in the aquatic stages are independent of the species. We also assume that the relationship between the mortality rate and temperature is the same for eggs, instars and pupae. In this method we do not consider competition effects as described by Paaijmans et al.

Species-independent mortality (BLL)

Data provided by Bayoh and Lindsay ^{2 }= 0.81). We call this the BLL method. Mortality rate data are plotted in Figure

Water temperature and mortality rates (^{-1}) in the aquatic compartments

**Water temperature and mortality rates (**^{-1}**) in the aquatic compartments.** Blue points show data used to estimate the mortality curves. Blue lines indicate mortality without competition, while light blue to red shows mortality as competition increases. For reference, red points show data from Holstein

where _{
N,L
}(_{
water
}) = _{
N,E
}(_{
water
}) = _{
N,P
}(_{
water
}) is the aquatic mortality rate per day and _{
water }is the water temperature (°C). The constants _{
n }are given in Table

**Constant**

**Value**

**Equation**

_{1}

700000

14

_{2}

8.4

14

_{3}

.126

14

_{4}

10.8

14

_{5}

150

14

_{6}

-.08

14

_{7}

.1

14

_{8}

-.61

14

_{9}

33

14

_{1}

0.1675256

33

_{2}

0.0121402

33

_{3}

0.1686

33

_{4}

1.991

33

_{5}

1.881

33

_{6}

4.641589

33

_{7}

250

33

_{8}

23

33

_{9}

12

33

_{10}

100

33

_{11}

3

33

Species-dependent mortality (KBLL)

Kirby et al. reported that the mortality rate of _{
N,L }is given by

and

_{gamb }and _{arab }are the ratio of _{size }is estimated as a function of _{
L }and

Parametrization of the development rate

The rate of development between the different aquatic stages follows the corrected version of Bayoh and Lindsay

Water temperature according to development time in days from first instar to adult

**Water temperature according to development time in days from first instar to adult.** Left panel: ratio of

The two previous studies also suggest that the development rate

for

for _{
arab } and _{
gamb }is the fraction of

Parametrization of breeding sites

The formation of puddles can be described as a balance of runoff, infiltration, evaporation, and rainfall entering the puddle. The formulation of an idealized puddle can be found in Additional file

**Idealized puddle model**

Click here for file

Modelling of every single breeding site requires high enough resolution to resolve the puddle. In practice this is not possible and the problem has to be simplified.

Mushinzimana et al. described typical breeding sites in a Kenyan highland area

If we assume that breeding mainly occurs in the vicinity of potential rivers and lakes, the availability of breeding sites can be expressed as a function of potential river length and soil saturation. At high resolution this might not always be true

The Hydrological Data and Maps based on SHuttle Elevation Derivatives at Multiple Scales (HydroSHEDS) 15s river data set from the US Geological Survey (USGS)

Here we divide rivers into three different classes: perennial, intermittent and ephemeral streams. For each class, potential river length (_{
p
}, km) within a grid is defined as

where Ξ is the equally spaced river data-set resolution in degrees, where

In a simplified model we estimate puddle volume as a function of river length and relative soil moisture. Although this is a very crude estimate, we compared this simple model with data from Mushinzimana et al.

where _{
r }is the relative soil moisture content (fraction).

In the current implementation we do not distinguish between fast- and slow-flowing rivers. It should be noted that this way of approximating breeding sites has limited validity in areas with irrigation or around rivers where breeding sites could form as rivers recede

Parametrization of the gonotrophic cycle

The gonotrophic cycle depends on temperature and is important for the vectorial capacity of mosquitoes. Lardeux et al. studied the gonotrophic cycle for ^{-1}) and data used to develop the formula are shown in Figure

Inverse of the duration of the gonotropic cycle according to the mean daily temperature (in °C)

**Inverse of the duration of the gonotropic cycle according to the mean daily temperature (in °C).** The solid black line shows Eq. 26 and the dashed line shows the formula given by Hoshen and Morse

where _{
air }is the air temperature (°C), _{
d }is degree days, and _{
c }is the critical temperature from Hoshen and Morse _{
d }= 37, and _{c }= 7.7.

Parametrization of the age-dependent mortality of adult mosquitoes

The mortality of adult anophelines differs according to age and species

Proportion of

**Proportion of ****surviving at 60% relative humidity and mean temperature of 0, 10, 20, 30, and 40°C (selected for clarity) according to time (in days).** Dashed vertical lines indicate the different age groups in the model. The Survival curve panel shows Eq. 31, while the Numerical solution panel shows survival in the model when the age groups are split into nine classes. For reference we also show survival according to the Marten equation (27) and Eq. 7 from Ermert et al. (Bayoh scheme)

Our new survival curves are based on unpublished data from Bayoh and Lindsay ^{-1} and 1^{-1}, independent of age group. However, there are uncertainties at relative humidity below 40%. The lack of studies in this range is a limitation of this survival model, and could make the model less accurate for _{
air }and relative humidity). In Figure

Size affects the survival of adult mosquitoes _{
size}). _{
air }may be completely or partly replaced by indoor temperature (_{
indoor }, described later), depending on the proportion of mosquitoes indoors. In experiments covering the African domain, we assumed that 80% of

where

If we assume that differences in adult mortality for

AL adult mortality

A similar approach can be used for

Constants _{1,…,11} are listed in Table

The corresponding curve is shown in Figure

Proportion of

**Proportion of ****surviving at daily maximum temperatures.** Estimated from Afrane et al.

Parametrization of air temperature

Paaijmans et al. discussed the importance of using indoor rather than outdoor temperature, to describe the environment for mosquitoes and parasites ^{2 }= 0.89). It is clear that temperatures inside a house are more stable than outdoor temperatures. House type greatly influences daily temperature fluctuations

Since the data are based on maximum and minimum temperatures, the timing of the indoor temperature might be offset by a couple of hours. This is evident in a study by Makaka and Meyer

Relationship between outdoor and indoor temperatures

**Relationship between outdoor and indoor temperatures.** Numbers denote the study from which data were taken: 1, Afrane et al. ^{2 }= 0.89.

Hence, _{
air }can be partly or fully replaced by _{
indoor }, depending on the proportion of mosquitoes indoors.

It should be noted that we still do not include temperatures in resting places described by Holstein, such as holes in rocks and cracks in soil, covered pigsties, rabbit hutches, hen coops and dry wells

Approximation of mosquito movement

The role of diffusion and advection in vector borne diseases have been explored in several papers

Transport of mosquitoes is defined by fluxes (^{-1}) at the grid boundaries. In the model we allow fluxes from the eight neighboring grid points. A special case is implemented when a neighbouring cell is water. In this case, fluxes to water are reduced to 0.1

Since the movement of mosquitoes has a high computational cost, the spatial fluxes do not change the size calculations. This will introduce some minor errors when the movement of mosquitoes is low compared to their density, with larger errors if many mosquitoes are moved relative to their density. When a cell free of mosquitoes is colonized, the size is set to 3.05 mm.

The possible flight range of anophelines varies with food availability ^{-1 }independent of age group. Anophelinae also travel with humans ^{-1}). This can be understood by considering the following example. For a constant ^{-1} and _{
f
}, which is equal to the distance travelled at 20^{-1} to the east. For example, with _{
f }= 750^{-1}, the eastward distance traveled will be _{
f }are unknown tunable constants.

Since the species considered here are most active at night

where

Transport of mosquitoes and mosquito sizes inside and outside a grid are defined by

More specifically, during a time ^{-1}, and the flux at a boundary is defined as

and transport _{
ı,ȷ
}
_{
n }is then equal to

In the presence of wind, we obtain additional transport as a function of zonal and meridional wind components.

Mortality related to feeding

One factor that is often overlooked in malaria (mosquito) models is survival related to food availability (_{
m }= 0.5^{2}
^{-1}, the daily probability of finding a blood meal can be calculated as

where _{
human }and _{
bovine }is the probability of finding a human and bovine source, respectively. _{
humans }is defined as the human population density per ^{2 }multiplied by 0.1 (since a smaller area on a human is accessible) and _{
bovine }is defined as the bovine density per ^{2}, each with a user-defined threshold at which the density is so low that

Since blood meals, besides sugar meals, are important for the mobility

In the model, mortality caused by food limitations is a function of how many humans or cattle are available per mosquito and the human blood index. We assume that

The functional form of of equation 42 can be seen in Additional file

**The functional form of of equation 42.**

Click here for file

Figure

Probability of finding a blood meal for

**Probability of finding a blood meal for **
**
An. arabiensis
**

Results and discussion

Sensitivity experiments

Sensitivity experiments are useful in understanding which parameters are important for the success of

Settings

To demonstrate some of the capabilities of the model, we set up a series of experiments. Some aspects are best visualized as a one-dimensional model (time and age), while other features are shown using a spatial domain (time, age, and space). For the one-dimensional experiments, the water temperature is set to the air temperature, except for temperature greater than 33°C, for which we set temperature to 33°C. This modification is required since pupae and fourth instar larvae will not develop below 18°C or above 34°C

The age-dependent mortality is influenced by temperature, relative humidity and mosquito size [Eq. (32)]. This experiment explores how the dynamics of malaria is sensitive to temperature, relative humidity and mosquito size (measured as mm). We assume that no births occur to isolate the effect of the transmission process, and consequently constant mosquito body size in the course of integration, but include mortality and the biting rate. In this experiment we assume that only one species is present (since the main competition occurs in the aquatic stages). This sensitivity test is designed to observe how the proportion of mosquitoes becomes infected as a function of temperature, relative humidity and mosquito size, given that we start with 1000 newly emerged mosquitoes, with _{1 }= 1000 and _{2-9 }= 0 as the initial conditions. In this experiment, 1% of the human population is infectious for

The rate of sporozoite development within mosquitoes is expressed as

where a = 9.5907,

The gonotrophic cycle and biting rate are defined in Eq. (26).

The integrations are repeated with different combinations of temperature and relative humidity. This is a simple representation of gametocyte transmission to mosquitoes and is an idealized approach for exploring the proportion of mosquitoes (of the original 1000) that would become infected under different temperature, RH and mosquito size. Figure

Percentage of 1000 mosquitoes that are infectious after

**Percentage of 1000 mosquitoes that are infectious after ****days. **The

These results should be viewed in light of recent findings by Paaijmans et al. that optimal transmission occurs at lower temperatures

The aim of this sensitivity test was to investigate how carrying capacity and temperature determine the relative proportion of ^{-2}.

Carrying capacity in the aquatic stages influences larval growth and adult survival. While

As observed in Figure

Fraction of

**Fraction of **** as a function of air temperature and carrying capacity.** The water temperature is set to the same value as the air temperature unless the temperature is greater than 33°C (at which most pupae would not develop into adults

This experiment shows how the model responds to changes in the probability of finding a blood meal, which influences the rate at which mosquitoes can oviposit and increases energy consumption if hosts are hard to locate. If, for example, cattle are easier to find compared to humans,

We set the probability of finding blood to one for

Figure

Fraction of

**Fraction of ****as a function of air temperature and probability of finding a blood meal.** The fraction of

Sensitivity to the probability of finding blood in a spatial domain (pBlood2D)

This experiment is similar to pBlood1D, but this time we integrate the model for 5 years over the African domain. The experiment consists of two runs, for which the first has ^{2 }(remember that the number of mosquitoes is limited by the number of hosts). Thus, the only limitation in this experiment is the physical environment (air and water temperatures, relative humidity, wind and run-off), which is updated every 3 h. The initial conditions for the mosquito populations were the same for the two runs.

Even though we have stated that the probability of finding blood

Under the scenario of equal probability of finding blood for the two species,

Square root of number of ^{2 }in the two pBlood2D experiments

**Square root of number of**** per**^{2 }**in the two pBlood2D experiments.** In P0 we used realistic values of the probability of finding blood,

Square root of the number of ^{2 }in the two pBlood2D experiments

**Square root of the number of **** per**^{2 }**in the two pBlood2D experiments.** In P0 we used realistic values of the probability of finding blood,

It is also worth mentioning that the density of

Figures

Mosquito transport (mosqTran)

The purpose of this experiment was to demonstrate how the initial conditions and competition influence the distribution of

The purpose of this demonstration was to show the importance of mosquito movement and how new areas can or cannot be colonized. In a model in which movement is restricted, the vector range would also be restricted by the initial model conditions. For example, if only one point was specified for mosquitoes at the beginning of the integration, only the same point would have mosquitoes after 100 years. With dynamic movement the mosquitoes could colonize new areas if the environmental conditions, or the probability of finding blood, change over time.

Figure

Relative change in dispersal (mean over 5 years) for

**Relative change in dispersal (mean over 5 years) for ****with (mosqTran(a)) and without (mosqTran(b)) ****.** The black solid circle and triangle indicate the initial position of

**A note on how initial conditions can influence the spatial distribution of****
An. gambiae s.l.
**

Click here for file

Figure ^{2}. It is interesting to note that dispersal occurs in pulses. The dispersal of

Number of months required to reach a density of ^{2}

**Number of months required to reach a density of **^{2}**.** Panel 1 (left to right) represents

Conclusions

We developed a model to predict the presence and abundance of

Sensitivity tests showed that as well as temperature, relative humidity and mosquito size are important factors in malaria transmission. The result for body size is in line with several studies

We show that relative humidity can be important for malaria transmission. Several models have neglected the role of (relative) humidity

Assumption of exponential mortality has several advantages (see Figure

Experiment pBlood2D showed how the model responds to the parameter

Finally, experiment mosqTran showed how the initial conditions influence the dispersal of

The strong influence of initial conditions on dispersal of the

The availability of mosquito models allows researchers to build on and improve our understanding of the role of the

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

The work presented here was carried out as a collaboration between all the authors. BL and AS defined the research theme. TML designed methods and mosquito experiments, performed the model runs, analysed the data, interpreted the results and wrote the paper. DK, AS and TML designed and evaluated the regional climate simulations. EL provided input with respect to the malaria situation in Ethiopia, which in turn was used in the model formulation. All the authors have contributed to, seen and approved the manuscript.

Acknowledgements

We are grateful to the National Center for Atmospheric Research (NCAR) for making their WRF model available in the public domain. We also thank the Bergen Centre for Computational Science for computational and other resources provided during this study. This work was made possible by grants from The Norwegian Programme for Development, Research and Education (NUFU) and the University of Bergen. We thank Steve Lindsay for providing data on the survival of