Mathematical Modeling and Forecasting of COVID-19 in Moscow and Novosibirsk Region

Abstract

We investigate inverse problems of finding unknown parameters of mathematical models SEIR-HCD and SEIR-D of COVID-19 spread with additional information about the number of detected cases, mortality, self-isolation coefficient, and tests performed for the city of Moscow and Novosibirsk region since 23.03.2020. In SEIR-HCD the population is divided into seven groups, and in SEIR-D into five groups with similar characteristics and transition probabilities depending on the specific region of interest. An identifiability analysis of SEIR-HCD is made to reveal the least sensitive unknown parameters as related to the additional information. The parameters are corrected by minimizing some objective functionals which is made by stochastic methods (simulated annealing, differential evolution, and genetic algorithm). Prognostic scenarios for COVID-19 spread in Moscow and in Novosibirsk region are developed, and the applicability of the models is analyzed.

Mean field game for modeling of COVID-19 spread

“…Since models of the SIR type are poorly applied for long-term prediction, here, to approximate the epidemiological situation, two curves with different epidemiological parameters were Mean field game for modeling of COVID-19 spread glued together. The epidemiological parameters of the model were restored according to statistical data and the optimization method presented in the work [21] for two time intervals: from May 1 to June 30 and from June 30 to August 8, 2020. The obtained parameters are presented in table 1.…”

Iteratively regularized Gauss–Newton type methods for approximating quasi–solutions of irregular nonlinear operator equations in Hilbert space with an application to COVID–19 epidemic dynamics

“…In [18] the approach was used to find a time–dependent coefficient in an epidemiological model similar to (3.1) describing the spread of Spanish flu in 1918 and Ebola in West Africa in 2014–2015. An alternative approach based on stochastic methods is developed in a recent paper [20] .…”

Differential evolution and particle swarm optimization against COVID-19

“…Various modified versions of SIR/SEIR models are also being optimized with DE/PSO algorithms. Such modified SIR/SEIR variants often include more kinds of compartments with various additional classes of human population, like those who are hospitalized (H, Ames et al 2020 ; Oliveira et al 2021 ), deceased (D, Ames et al 2020 ; Oliveira et al 2021 ; Paggi 2020 b; Fanelli and Piazza 2020 ; Giudici et al 2020 ; Godreev et al 2020 ; Lobato et al 2020 ; Quaranta et al 2020 ), quarantined (Q, Cordelli et al 2020 ), confined (C, the term is loosely related to quarantined, de Camino Beck 2020 ), asymptomatic (A, Qaranta et al 2020 ; Paggi 2020 a), unrecognized recovered (U, Oliveira et al 2021 ; Paggi 2020 a), in critical conditions (Z, Krivorot’ko et al 2020 ), as well as the effects of lockdown (L, Paggi 2020 a) or migration (M, Zhan et al 2020 ). Such extended variants of SIR/SEIR models often have more parameters for calibration.…”