Space, the final frontier

Mosquito Movement and Vector Control

[MASH + MAP] Malaria Retreat 2019
Héctor M. Sánchez C. [sanchez.hmsc@berkeley.edu]

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Agenda

1. Gene-Drives
2. Vector Control
3. MoNeT

1. Gene-Drives

A. Background
B. MGDrivE
C. Spatial Heterogeneity

1A. Background

1B. MGDrivE

1B. Tensor Equations

1) Genetic Inheritance

$$ \begin{align*} \overline{O(T_x)} = & \sum_{j=1}^{n} \Bigg( \bigg( (\beta*\overline{s} * \overline{ \overline{Af_{[t-T_x]}}}) * \overline{\overline{\overline{Ih}}} \bigg) * \Lambda \Bigg)^{\top}_{ij}\\ \end{align*}$$

2) Migration

$$ \begin{align*} \overline{Am_{(t)}^{i}}= &\sum{\overline{A_{m}^j} \otimes \overline{\overline{\tau m_{[t-1]}}}} \\ \overline{\overline{Af_{(t)}^{i}}}= &\sum{\overline{\overline{A_{f}^j}} \otimes \overline{\overline{\tau f_{[t-1]}}}} \end{align*} $$

3) Life History

$$ \begin{align*} \overline{L_{[t]}}= &\overline{L_{[t-1]}} * (1-\mu_{l}) * F(\overline{L_{[t-1]})} +\overline{O(T_e)}* \theta_{e} - \overline{O(T_e+T_l)} * \theta_{e} * D(\theta_l,0)\\ \overline{E^{'}}=& \overline{O(T_e+T_l+T_p)} * \bigg(\overline{\xi_m} * (\theta_{e} * \theta_{p}) * (1-\mu_{ad}) * D(\theta_l,T_p) \bigg)\\ \overline{Am_{[t]}}=& \overline{Am_{[t-1]}} * (1-\mu_{ad})*\overline{\omega_m} + (1-\overline{\phi}) * \overline{E^{'}} + \overline{\nu m_{[t-1]}}\\ \overline{\overline{Af_{[t]}}}=& \overline{\overline{Af_{[t-1]}}} * (1-\mu_{ad}) * \overline{\omega_f} + \bigg( \overline{\phi} * \overline{E^{'}}+\overline{\nu f_{[t-1]}}\bigg)^{\top} * \bigg( \frac{\overline{\eta}*\overline{Am_{[t-1]}}}{\sum{\overline{Am_{[t-1]}}}} \bigg)\\ \end{align*} $$