PModel (Aedes Albopictus)

Model Overview

How to run the model?

Locate the file src/heiplanet_models/global_settings.yaml.
Modify the path where you have the data, for instance:

ingestion:
    path_root_datasets: "data/in/"

Run the Python script src/heiplanet_models/Pmodel/run_model.py

python run_model.py

Architecture

Inputs

Dataset	Description	Format
ERA5Land Temperature	Gridded temperature data	NetCDF4
ERA5Land Precipitation	Gridded precipitation	NetCDF4
Human population	Population distribution	NetCDF4
Initial conditions (opt)	Starting model state	NetCDF4

Outputs

Dataset	Description	Format
Mosquito Abundance	Gridded mosquito abundance for the Aedes Albopictus specie	NetCDF4

Model Structure

Equations

Workflow

Examples

References:

Barman, S., Semenza, J.C., Singh, P. et al. A climate and population dependent diffusion model forecasts the spread of Aedes Albopictus mosquitoes in Europe. Commun Earth Environ 6, 276 (2025). https://doi.org/10.1038/s43247-025-02199-z
List of equations
Supplementary material

Authors & Contact

[deprecated] How the original Octave/Matlab code works

Entry point name: `aedes_albopictus_model.m`

Create variables to assign the prefix of each dataset that will be used matlab tmean_prefix = 'ERA5land_global_t2m_daily_0.5_'; pr_prefix = 'ERA5land_global_tp_daily_0.5_'; dens_prefix = 'pop_dens_';
Create a for loop to iterate over years. The following operations are done in each loop:

a. The name for each dataset is completed with the year and extension: matlab tmean = [tmean_prefix, num2str(years), '.nc']; pr = [pr_prefix, num2str(years), '.nc']; dens = [dens_prefix, num2str(years), '_global_0.5.nc'];

b. Log the year that is being processed: matlab year = years; % change years according to file name disp(['Year in Process: ', num2str(years)]);

c. Run the model that calculates the differential equations. This model receives the following datasets and variable:
- dataset tmean: mean temperature dataset
- dataset pr: precipitation dataset
- dataset dens: population density dataset
- variable year: year of the dataset
matlab %model_run(tmax,tmin,tmean, pr,dens,year); model_run(tmean, pr,dens,year); % for tmean only with NO DTR (Tmax or Tmin is not present) disp(['Year done: ', num2str(years)]);
3. End the program

Name: `model_run.m`

Create a variable name for the output file.

outfile = strcat('Mosquito_abundance_Global_', num2str(year), '.nc')      % change the output file name as required

if exist(outfile) == 2
    delete(outfile)
end

Copy the dataset that contains the precipitation (one of the ERA5*.nc) and store this copy using the variable name for the output file.

copyfile(pr, outfile);   % overwriting the file gives us advantage that we can loose the ;latitude and longitude information of Tmax,
% Tmin file and only work with time varible in 3rd dimension and then rewrite this over same nc file

Rename the internal variable (pr) of this copy with the name adults. It means, we have a new .nc file that contains longitude, latitude and the variable name adults. With this we can just overwrite the variable adult with the calculations we intend to do.

ncid = netcdf.open(outfile,'NC_WRITE');
netcdf.reDef(ncid)
netcdf.renameVar(ncid,3,'adults');
netcdf.endDef(ncid);
netcdf.close(ncid);

Defines a delta time step that will be important for solving the system of differential equations.

step_t = 10;

Load variables from each dataset involved (tmean, pr, dens)

a. Load temperature variables and applies some preprocessing steps with load_temp2(tmean, step_t) function matlab [Temp, Tmean] = load_temp2(tmean, step_t); % Without DTR if Tmean is only available, no Tmax or Tmin

b. Load population density variables and applies some preprocessing steps with load_hdp(dens) matlab DENS = load_hpd(dens);

c. Load Precipitation variable with load_rainfall(pr) function matlab PR = load_rainfall(pr);

d. Load Latitude variable from the tmean dataset with the function load_latitude(tmean) matlab LAT = load_latitude(tmean);
Calculate Juvenile Carrying Capacity: $K_{L}(W,P)$
- $W$: Rainfall accumulation, this the information we get from PR
- $P$: Human density, this is the information we get from DENS
matlab CC = capacity(PR, DENS);
- file associated: capacity.m
- Equation in Supplement Information: 14
Calculate Hatching fraction depending in human density and rainfall: $Q(W,P)$ $$ Q(W,P) = (1 - E_{rat}) \left( \frac{(1+E_{0})e^{\left(-E_{var}(W(t)-E_{opt})\right)^2}}{e^{\left( -E_{var} (W(t)-E_{opt})^2 \right)}} \right) + E_{rat} \left( \frac{E_{dens}}{E_{dens} + e^{-E_{fac}P}} \right) $$

Where:
- $W$: Precipitation, we get this information from PR
- $P$: Human density, we get this information from DENS
- $E_{opt}$ = 8;
- $E_{var}$ = 0.05;
- $E_{0}$ = 1.5;
- $E_{rat}$= 0.2;
- $E_{dens}$ = 0.01;
- $E_{fac}$ = 0.01;
matlab egg_active = water_hatch(PR, DENS); - file associated: water_hatch.m - Equation in Supplementary Information: 13
Create a Vector Initial population: $V_{0}$ matlab previous = 'no_previous'; v0 = load_initial(previous, size(Temp));
- File associated: load_initial.m
- TODO: Ask about the name and meaning of this variable.
Calculate the parameters for each time step and run ODEs matlab v = call_func(v0, Temp, Tmean, LAT, CC, egg_active, step_t);

Input variables:
- initial vector: v0
- temperature: Temp
- mean temperature: Tmean
- latitude: LAT
- juvenile carrying capacity: CC
- hatching fraction depending in human density and rainfall: egg_active
- time step: step_time
- File associated: call_func.m
Once all the variables are calculated, write to the output file.

ncwrite(outfile,'adults', permute(v(:,:,5,:),[1,2,4,3]));

Name: `call_func.m`

Description: This file the main file that contains the ODEs to calculate the 6 differential equations proposed in the paper.

Input Variables:

v
Temp
Tmean
LAT
CC
egg_activate
step_t

Process:

Calculate the Diapause Lay
- File associated: mosquito_dia_lay.m
- TODO: ask about the equation.
Calculate the Diapause Hatch
- File associated: msoquito_dia_hatch.m
- TODO: ask about the equation
Calculate Diapausing egg mortality rate : $m_{Ed}(T)$ $$ m_{Ed}(T) = -\ln\left( 0.955 \left(-0.5 \left(\frac{T-18.8}{21.53}\right)^6 \right) \right) $$
- Input Variables:
  - Temp
  - step_t
- File associated: mosq_surv_ed.m
- Comments: hardcoded values do not correspond to the values in the paper.
Create a n-dimensional matrix v_out full of zeros.
Create a for loop that iterates over the time:

5.1. Creates a temperatures vector

octave T = Temp(:,:,t);

5.2. Calculates the Mosquito Birth

$$ mos $$
- Inputs:
  - T
- File associated: mosq_birth.m
- Comments:
  - TODO: This equation is not present in the supplementary material.
octave T = Temp(:,:,t);

5.3. Calculates the Mosquito development j
- Inputs:
  - T
- File associated: mosq_dev_j.m
- Comments:
  - TODO: This equation is not present in the suplement material.
octave dev_j = mosq_dev_j(T);

5.4. Calculates the Mosquito development i
- Inputs:
  - T
- File associated: mosq_dev_i.m
- Comments:
  - TODO: This equation is not present in the suplement material.
octave dev_j = mosq_dev_i(T);

5.4. Other calculations I do not understand ```octave dev_e = 1./7.1; %original function of the model dia_lay = diapause_lay(:,:,ceil(t/step_t)); dia_hatch = diapause_hatch(:,:,ceil(t/step_t)); ed_surv = ed_survival(:,:,t); water_hatch = egg_activate(:,:,ceil(t/step_t)); mort_e = mosq_mort_e(T); mort_j = mosq_mort_j(T);

T = Tmean(:,:,ceil(t/step_t)); mort_a = mosq_mort_a(T); ```

5.5. ODE octave vars = {ceil(t/step_t), step_t, Temp, CC, birth, dia_lay, dia_hatch, mort_e, mort_j, mort_a, ed_surv, dev_j, dev_i, dev_e, water_hatch}; v = RK4(@eqsys, @eqsys_log, v, vars, step_t); % Runge-Kutta 4 method % v = FE(@eqsys, @eqsys_log, v, vars, step_t); % Forward Euler method

5.6. Additional calculations ```octave if mod(t/step_t,365) == 200 v(:,:,2) = 0; end

if mod(t,step_t) == 0 if mod(ceil(t/step_t),30) == 0 disp(['MOY: ', num2str(t/step_t/30)]); end for j = 1:5 %v_out(:,:,j,t/step_t) = v(:,:,j); v_out(:,:,j,t/step_t) = max(v(:,:,j), 0); % if any abundance is negative it will make it zero end end

```

Table 1. Mapping Equations from Octave/Matlab code to Python code

!!! note

Numbers in brackets refer to the corresponding row numbers in [Table S11 from the Supplementary Material](https://static-content.springer.com/esm/art%3A10.1038%2Fs43247-025-02199-z/MediaObjects/43247_2025_2199_MOESM2_ESM.pdf).

Octave Function	Python Function	Equation Number in Paper
`mosq_dev_j.m`	`mosq_dev_j`	[5]
`mosq_dev_i.m`	`mosq_dev_i`	[6]
`mosq_dev_e.m`	`mosq_dev_e`	`[NR 1]`
`capacity.m`	`carrying_capacity`	[14]
`mosq_mort_e.m`	`mosq_mort_e`	[9]
`mosq_mort_j.m`	`mosq_mort_j`	[10]
`mosq_mort_a.m`	`mosq_mort_a`	[11]
`mosq_surv_ed.m`	`mosq_surv_ed`	`[NR 2]`

Table 2. Climate sensitive parameter description and functions (inspired on Table S11 in Supplementary information)

!!! warning

Put special attention to the Not Reported (`[NR <number>]`) equations and the Not Reported units (`[NA]`).

Number	Description	Symbol	Unit
[5]	Juvenile development rate		$\frac{1}{day}$
[6]	Emerging adult development		$\frac{1}{day}$
`[NR 1]`	(tentative) Emerging adult development Briere model.		`[NR 1]`
[14]	Juvenile carrying capacity		`NA`
[9]	Egg mortality rate	$m_{E}(T)$	$\frac{1}{day}$
[10]	Juvenile mortality rate	$m_{J}(T)$	$\frac{1}{day}$
[11]	Adult mortality rate	$m_{A}(Tmean)$	$\frac{1}{day}$
`[NR 2]`	(tentative) Diapausing egg mortality rate	$m_{Ed}(T)$	$\frac{1}{day}$

List of equations

[5] Juvenile development rate: $\delta_{J}(T)$ $$ \delta_{J}(T) = \frac{1}{0.08T^{2} - 4.89T + 83.85} $$

Parameter Description

$T$ Temperature (°C)
[6] Emerging adult development rate: $$ \delta_{Aem}(T) = \frac{1}{0.069T^{2} - 3.574T + 50.1} $$

Parameter Description

$T$ Temperature (°C)
[NR 1] (tentative) Emerging adult development Briere model $$ BM = q \cdot T \cdot (T - T_0) \cdot \sqrt{T_m - T} $$

Parameter Description

$q$ Empirical coefficient for development rate

$T$ Temperature (°C)

$T_0$ Minimum threshold temperature (°C)

$T_m$ Maximum threshold temperature (°C)

[14] Juvenile carrying capacity: $$ K_{L}(W,P) = \lambda\,\frac{0.1}{1 - 0.9^{t}}\sum_{x=1}^{t} 0.9^{(t-x)}\left(\alpha_{\text{rain}}W(x) + \alpha_{\text{dens}}P(x)\right) $$

Parameter	Description
$\lambda$	Scaling coefficient
$t$	---
$x$	---
$\alpha_{\text{rain}}$	Weight for rainfall contribution
$W(x)$	Rainfall at time step $x$
$\alpha_{\text{dens}}$	Weight for population contribution
$P(x)$	Population at time step $x$

[9] Egg mortality rate:

!!! warning

Equation in paper do not show the exponential function $exp()$. However, the exponential function is used in the Octave code.

$$ m_{E}(T) = -\ln\left( 0.955\, \exp\left[ -0.5 \left( \frac{T - 18.8}{21.53} \right)^{6} \right] \right) $$

Parameter	Description
$T$	Temperature (°C)

[10] Juvenile mortality rate:

!!! warning

Equation in paper do not show the exponential function $exp()$. However, the exponential function is used in the Octave code.

$$ m_{J}(T) = -\ln\left[\,0.977\, \exp\left(-0.5 \left(\frac{T - 21.8}{16.6}\right)^{6}\right)\,\right] $$

Parameter	Description
$T$	Temperature (°C)

[11] Adult mortality rate:

!!! warning

The equation reported on paper do not show the exponential $exp()$ found in the Octave/Matlab code. Additionally the equation in Octave should look like this.

$$
m_{A}(T) = 
\begin{cases}
-\ln\left[\,0.677\, \exp\left(-0.5 \left(\frac{T - 20.9}{13.2}\right)^{6}\right)\, T^{0.1}\,\right], & \text{if } T > 0 \\[1.5ex]
-\ln\left[\,0.677\, \exp\left(-0.5 \left(\frac{T - 20.9}{13.2}\right)^{6}\right)\,\right], & \text{if } T \leq 0
\end{cases}
$$

$$ m_{A}(T_{\text{mean}}) = -\ln\left[\,0.677\, \exp\left(-0.5 \left(\frac{T_{\text{mean}} - 20.9}{13.2}\right)^{6}\right)\, (T_{\text{mean}})^{0.1}\,\right] $$

Parameter	Description
$T_{\text{mean}}$	Temperature (°C)

[NR 2] (tentative) Diapausing egg mortality rate: !!! warning The constants in the code are different than constants reported on the paper.

$$ m_{Ed}(T) = m_{E}(T) = -\ln\left( 0.955\, \exp\left[ -0.5 \left( \frac{T - 18.8}{21.53} \right)^{6} \right] \right) $$

Parameter	Description
$T$	Temperature (°C)

Parameter	Description
$q$	Empirical coefficient for development rate
$T$	Temperature (°C)
$T_0$	Minimum threshold temperature (°C)
$T_m$	Maximum threshold temperature (°C)

PModel (Aedes Albopictus)

Model Overview

How to run the model?

Architecture

Inputs

Outputs

Model Structure

Equations

Workflow

Examples

References:

Authors & Contact

[deprecated] How the original Octave/Matlab code works

Entry point name: aedes_albopictus_model.m

Name: model_run.m

Name: call_func.m

```

Table 1. Mapping Equations from Octave/Matlab code to Python code

Table 2. Climate sensitive parameter description and functions (inspired on Table S11 in Supplementary information)

List of equations

Entry point name: `aedes_albopictus_model.m`

Name: `model_run.m`

Name: `call_func.m`