Geodesic
Mathematical model of the spread of a pandemic like COVID-19
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 83 (2022) no. 1, pp. 63-75.

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Using the example of the infectious disease called COVID-19, a mathematical model of the spread of a pandemic is considered. The virus that causes this disease emerged at the end of 2019 and spread to most countries around the world over the next year. A mathematical model of the emerging pandemic, called the SEIR-model (from the English words susceptible, exposed, infected, recovered), is described by a system of four ordinary dynamical equations given in §1. The indicated system is reduced to a nonlinear integral equation of Hammerstein–Volterra type with an operator that does not have the property of monotonicity. In §3, we prove a theorem on the existence and uniqueness of a non-negative, bounded and summable solution of this system. Based on real data on the COVID-19 disease in France and Italy, given in §2, numerical calculations are performed showing the absence of a second wave for the obtained solution. 
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A. G. Sergeev; A. Kh. Khachatryan; Kh. A. Khachatryan. Mathematical model of the spread of a pandemic like COVID-19. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 83 (2022) no. 1, pp. 63-75. http://geodesic.mathdoc.fr/item/MMO_2022_83_1_a3/

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