Geodesic
Uniqueness of the Solution of the Inverse Problem for a Model of the Dynamics of an Age-Structured Population
Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 125-133.

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For the McKendrick model of the dynamics of an age-structured population, we consider the inverse problem of reconstructing two coefficients of the model: in the equation and in the nonlocal boundary condition of integral form. The values of the solution on a part of the boundary are used as the additional information in the inverse problem. We obtain conditions for the sought coefficients to be uniquely determined. The derived integral formulas can be used to solve the inverse problem numerically by the iteration method, taking into account the fact that the inverse problem is ill posed.
Keywords: inverse problem, population dynamics model, age-structured model. 
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A. Yu. Shcheglov. Uniqueness of the Solution of the Inverse Problem for a Model of the Dynamics of an Age-Structured Population. Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 125-133. http://geodesic.mathdoc.fr/item/MZM_2022_111_1_a11/

[1] W. O. Kermack, A. G. McKendrick, “Contributions to the mathematical theory of epidemics. I”, J. Washington Acad. Sci., 27:7 (1937), 299–303

[2] A. J. Lotka, “Population analysis: a theorem regarding the stable age distribution”, Proc. Royal Soc., 115A (1927), 700–721

[3] A. N. Kolmogorov, “Kachestvennoe izuchenie matematicheskikh modelei dinamiki populyatsii”, Problemy kibernetiki, 1972, no. 5, 100–106

[4] H. Inaba, “Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model”, Math. Biol., 54:1 (2007), 101–146 | DOI | Zbl

[5] M. Iannelli, F. Milner, The Basic Approach to Age-Structured Population Dynamics. Models, Methods and Numerics, Springer, Cham, 2017 | DOI | Zbl

[6] D. M. Ediev, “O suschestvovanii i edinstvennosti otsenki ozhidaemoi prodolzhitelnosti zhizni v modeli stabilnogo naseleniya”, Matem. modelirovanie, 33:3 (2021), 73–84 | DOI | Zbl

[7] A. M. Denisov, A. S. Makeev, “Iteratsionnye metody resheniya obratnoi zadachi dlya odnoi modeli populyatsii”, Zh. vychisl. matem. i matem. fiz., 44:8 (2004), 1480–1489 | MR | Zbl

[8] D. V. Churbanov, “Uniqueness of finding the coefficient of the derivative in a first order nonlinear equation”, Moscow Univ. Comput. Math. Cybernet., 37:1 (2013), 8–13 | DOI | Zbl

[9] S. G. Golovina, A. G. Razborov, “Reconstruction of the discontinuity line of a piecewise-constant coefficient in the two-dimensional internal initial?boundary value problem for the homogeneous heat equation”, J. Comput. Math. Model., 25:1 (2014), 49–56 | DOI | Zbl

[10] S. I. Solov'eva, S. R. Tuikina, “Simulating the heart's electric activity: numerical methods for inverse problems”, Moscow Univ. Comput. Math. Cybernet., 41:2 (2017), 51–57 | DOI

[11] S. G. Golovina, E. V. Zakharov, “A Numerical way of determining the boundaries of a system of bodies in a three-dimensional medium by means of integral equations”, Moscow Univ. Comput. Math. Cybernet., 42:3 (2018), 100–104 | DOI

[12] A. V. Baev, “Ob odnoi obratnoi zadache dlya uravneniya KdV s peremennym koeffitsientom”, Matem. zametki, 106:5 (2019), 788–792 | DOI | Zbl

[13] A. M. Denisov, A. A. Efimov, “The inverse problem for an integro-differential equation and its solution method”, J. Comput. Math. Model., 30:4 (2019), 403–412 | DOI | Zbl

[14] I. V. Tikhonov, Vu Nguyen Son Tung, “Solvability of a nonlocal problem for an evolution equation with a super-stable semigroup”, Differential Equations, 56:4 (2020), 478–498 | DOI | Zbl

[15] S. Gavrilov, “A numerical method for determining the inhomogeneity boundary in the electrical impedance tomography problem in the case of piecewise-constant conductivity”, Math. Models Comput. Simulations, 13:4 (2021), 579–585 | DOI