Maya Mueller Applying the Optimal Presenter Interpolation Data Assimilation Method to an S-E-I-R-D Model to a Simulated Ebola Epidemic and to Forecast the Coronavirus Dr. Bedrich (COVID-19) Pandemic in Nigeria Sousedik Advisor Maya Mueller (Advised By: Bedrich Sousedik and Ashok Krishnamurthy of Mount Royal University) Dr. Ashok Krishnamurthy Advisor
Overview: 1.The Compartmental Model of an Infectious Disease: SEIRD 2.Running the SEIRD Model Simulation: Nigeria 3.Optimal Interpolation Data Assimilation 4.Insights and Challenges of Forecasting COVID-19 in Nigeria
The Compartmental Epidemic Model of an Infectious Disease: SEIRD S number of subjects who are susceptible Susceptible but not yet infected; base pool of persons number of subjects who are infected but E Exposed not yet infectious; in an incubatory stage where they cannot yet transmit the disease I number that are infected and can transmit Infectious the disease number that have received immunization, R Recovered are fully recovered, or quarantined; cannot transmit the disease D number confirmed to have died from the Dead disease 3
The Compartmental Epidemic Model of an Infectious Disease: SEIRD Parameter Description Daily fraction that move out of the susceptible β compartment into the exposed compartment Daily fraction that move out of the exposed γ compartment into the infectious compartment Daily fraction that move out of the infectious σ compartment into the recovered compartment Daily fraction that move out of the recovered δ compartment into the dead compartment 4
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sha1_base64="1p0SjlIOxpbS/6keCJHzLWAYHRk=">AB+3icbVBNSwMxEM36WevXWo9egkXwVHaLoMeiF29WsR/QXUs2nW1Dk+ySZMVS+le8eFDEq3/Em/GtN2Dtj4YeLw3w8y8KOVMG8/7dlZW19Y3Ngtbxe2d3b196DU1EmKDRowhPVjogGziQ0DMc2qkCIiIOrWh4NfVbj6A0S+S9GaUQCtKXLGaUGCt13VJwI6BPcKCzSIPBdw/Vrlv2Kt4MeJn4OSmjHPWu+xX0EpoJkIZyonXH91ITjokyjHKYFINMQ0rokPShY6kAnQ4nt0+wSdW6eE4UbakwTP198SYCK1HIrKdgpiBXvSm4n9eJzPxRThmMs0MSDpfFGcmwRPg8A9poAaPrKEUMXsrZgOiCLU2LiKNgR/8eVl0qxWfK/i356Va5d5HAV0hI7RKfLROaqha1RHDUTRE3pGr+jNmTgvzrvzMW9dcfKZQ/QHzucP9CmTuA=</latexit> The Compartmental Epidemic Model of an Infectious Disease: SEIRD SEIRD Model: Epidemic Dynamics in Continuous Time: a system of five PDEs to describe spatio-temporal evolution over connected planar domain Ω ⊂ R 2 weight function The function for each SEIRD variable describes the density of the population for each compartment at spatial coordinate (x,y) and time t. For example, E(x,y,t) describes the density of the exposed population at spatial point (x,y) and time t.
The Compartmental Epidemic Model of an Infectious Disease: SEIRD Weight Function: weight function measures influence of infectives at (u,v) on exposure of susceptibles at (x,y) expresses idea that influence of nearby infectives drops as an exponential function of Euclidean distance The more mobile the society, the higher the λ value (constant characteristic of the distance the disease spreads) This distance parameter is adequate for capturing local dynamics, thereby allowing us to learn about spatial transmission of the disease across neighboring cells 6
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