MGSurvE: Mosquito Gene SurveillancE
Proof of Concept

Héctor M. Sánchez C.

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Structure

I. Mosquito Landscape Analysis
II. Migration Model Description
III. Trap Placement Optimization
IV. Current Status and Future Work

I. Mosquito Landscape Analysis

1) Mosquito-Borne Diseases

2) Gene Drives' Surveillance

3) Heterogeneity in Spatial Resources

4) Research Question

1) Mosquito-Borne Diseases

2) Mosquito Gene Drives' Surveillance

3) Heterogeneity in Spatial Resources

4) Research Question

Given a heterogeneous environment and a limited number of traps, where should we place them?

II. Migration Model Description

1) Objectives and Assumptions

2) Migration Network

3) Migration Network with Traps

4) Fitness Function

5) Ok, so why is useful?

1) Objective and Assumptions

O: To define a metric that allows us to optimize traps' locations in complex environments.
A: Mosquitos are Markov walkers in a network-based landscape.
A: The landscape is static over time.
A: Traps are fully absorbing.

2) Migration Network

Given a function that transforms distances into migration probabilities
$$\alpha(s_i\to s_j)= \kappa(D(s_i\to s_j), \rho_{bio}) * \lambda(\hat{s}_i, \hat{s}_j)$$

we can calculate the migration matrix of the whole landscape
$$ \overline{\overline{\tau_{[s_n,s_n]}}} = \begin{bmatrix} p_{s_1\to s_1} & p_{s_1\to s_2} & ... & p_{s_1\to s_{n-1}} & p_{s_1\to s_n} \\ p_{s_2\to s_1} & p_{s_2\to s_2} & ... & p_{s_2\to s_{n-1}} & p_{s_2\to s_n} \\ \vdots & & \ddots & & \vdots \\ p_{s_{n-1}\to s_1} & p_{s_{n-1}\to s_2} & ... & p_{s_{n-1}\to s_{n-1}} & p_{s_{n-1}\to s_n} \\ p_{s_n\to s_1} & p_{s_n\to s_2} & ... & p_{s_n\to s_{n-1}} & p_{s_n\to s_n} \end{bmatrix} = \begin{Vmatrix} \alpha({s_1\to s_1}) & \alpha({s_1\to s_2}) & ... & \alpha({s_1\to s_{n-1}}) & \alpha({s_1\to s_n}) \\ \alpha({s_2\to s_1}) & \alpha({s_2\to s_2}) & ... & \alpha({s_2\to s_{n-1}}) & \alpha({s_2\to s_n}) \\ \vdots & & \ddots & & \vdots \\ \alpha({s_{n-1}\to s_1}) & \alpha({s_{n-1}\to s_2}) & ... & \alpha({s_{n-1}\to s_{n-1}}) & \alpha({s_{n-1}\to s_n}) \\ \alpha({s_n\to s_1}) & \alpha({s_n\to s_2}) & ... & \alpha({s_n\to s_{n-1}}) & \alpha({s_n\to s_n}) \end{Vmatrix} $$

3) Migration Network with Traps

To incorporate the traps' effects we can follow a similar process but split in three parts
$$ \begin{align*} \delta(s_i\to t_j) &= \hat{\eta}(D(s_a\to t_b), \hat{\rho}_{trap}) &\Rightarrow \overline{\overline{\alpha_{[s_n,t_n]}}} & & \text{Distance-based trapping efficacy}\\ \delta(t_i\to s_j || t_i\to t_j |_{i\neq j}) &= 0 &\Rightarrow \overline{\overline{0_{[t_n,s_n]}}}& & \text{No migration out of the traps}\\ \delta(t_i\to t_i) &= 1 &\Rightarrow \overline{\overline{I_{[t_n,t_n]}}}& & \text{Stay traped!} \end{align*} $$
With this in hand, we assemble the traps' migration matrix
$$ \overline{\overline{\chi_{[s_n+t_n, s_n+t_n]}}} = \begin{bmatrix} \overline{\overline{\tau_{[s_n,s_n]}}} & \overline{\overline{\alpha_{[s_n,t_n]}}} \\ \overline{\overline{0_{[t_n,s_n]}}} & \overline{\overline{I_{[t_n,t_n]}}} \end{bmatrix} = \begin{bmatrix} \overline{\overline{B}} & \overline{\overline{A}} \\ \overline{\overline{0}} & \overline{\overline{I}} \end{bmatrix} $$

4) Fitness (or cost) Function

This allows is to get the Markov fundamental matrix
$$\overline{\overline{F_{[s_n,s_n]}}}=(I-B)^{-1}$$
which tells us how much time we spend in any site, given that we started in any other site, before we fall into a trap.
Finally, we can calculate the average maximum time it would take for us to trap a mosquito from anywhere in the landscape
$$ \begin{align*} \overline{\varphi_{[s_n]}} &=Max^{j}(\overline{\overline{F(i, j)}})\\ \phi &= Mean(\overline{\varphi_{[s_n]}}) \end{align*} $$

5) Ok, so why is this useful?

5) More complexity, please?

III. Trap Placement Optimization

1) Fitness Function

2) Genetic Algorithm

3) Optimization Cycle

4) Demo Results

1) Fitness Function

Average maximum time it takes for mosquitoes to fall into traps from anywhere in the landscape (G).

2) Genetic Algorithm

3) Optimization Cycle

4) Benchmark Results

4) Demo Results

IV. Current Status and Future Work

1) Project's Status

2) Extensions and Neat Properties

3) The Future

1) Project's Status

Proof of concept is working and pypi package is under development!
(base code ~70%, docs ~50%, unit tests ~20%)

1) Example Code


# Sites information ------------------------------------------------------------
pts = (
	(0.0, 0.0, 0), 
	(2.0, 0.5, 0), 
	(2.5, 1.5, 0),
)
points = pd.DataFrame(pts, columns=('x', 'y', 't'))
# Traps settings ---------------------------------------------------------------
trp = (
	(2.5, 0.75, 0, 0),
	(0.0, 0.50, 0, 0)
)
traps = pd.DataFrame(trp, columns=('x', 'y', 't', 'f'))
tKernels = {0: {'kernel': srv.exponentialDecay, 'params': {'A': 0.5, 'b': 3}}}
# Generating and using landscape -----------------------------------------------
lnd = srv.Landscape(points, traps=traps, trapsKernels=tKernels)
lnd.calcFundamentalMatrix()
fitness = lnd.getDaysTillTrapped()


(fig, ax) = plt.subplots(figsize=(15, 15))
lnd.plotSites(fig, ax)
lnd.plotMigrationNetwork(fig, ax)
lnd.plotTraps(fig, ax)
lnd.plotTrapsNetwork(fig, ax)
fig.show()

2) Neat Properties and Extensions