A Discrete SIS Model of Epidemic for a Heterogeneous Population without Discretization of its Continuous Counterpart

• Autorzy: Choiński Marcin

Identyfikatory

DOI

10.12913/22998624/174335

• Języki publikacji: EN

Abstrakty

EN

In this paper we propose a model of an infectious disease transmission in a heterogeneous population consisting of two different subpopulations: individuals with accordingly low and high susceptibility to an infection. This is a discrete model which was built without discretization of its continuous counterpart. It is not a typical approach. We assume that parameters describing particular processes in each subpopulation have different values. This assumption makes model analysis more complicated comparing to models without this assumption. We investigate conditions for existence and local stability of stationary states. The novelty of this paper lies in presenting the explicit condition concerning stationary states, including stability. We compute the basic reproduction number R0 of the given system, which determines the local stability of the disease-free stationary state. Additionally, we consider a situation when there is no illness transmission in the subpopulation with the low susceptibility. Theoretical result are complemented with numerical simulations in which we fit the model to epidemic data from the Warmian–Masurian province of Poland. These data reflect the case of the tuberculosis epidemic for which the homeless people were treated as a group with the high susceptibility.

Słowa kluczowe

EN

SIS epidemic model; local stability; discrete modeling

• Wydawca: Lublin University of Technology ; Polish Society of Ecological Engineering (PTIE), Branch of PTIE in Lublin
• Czasopismo: Advances in Science and Technology. Research Journal
• Rocznik: 2023
• Tom: Vol. 17, no 6
• Strony: 288--300
• Opis fizyczny: Bibliogr. 13 poz., fig., tab.

Twórcy

autor

Choiński Marcin

• Institute of Information Technology, Warsaw University of Life Sciences

• https://orcid.org/0000-0001-6157-8963

Bibliografia

• 1. Choiński M. A discrete SIS–model built on the strictly positive scheme. Applicable Algebra in Engineering, Communication and Computing 2023.
• 2. Choiński M., Bodzioch M., Foryś U. A non-standard discretized SIS model of epidemics. Mathematical Biosciences and Engineering 2022; 19(1): 115–133.
• 3. Choiński M., Bodzioch M., Foryś U. Simple discrete SIS criss-cross model of tuberculosis in heterogeneous population of homeless and non-homeless people. Mathematica Applicanda 2019; 47(1): 103–115.
• 4. Castillo–Chavez D., Yakubu A.-A. Discrete-time S-I-S models with complex dynamics. Proceedings of the Third World Congress of Nonlinear Analysts, Part 7 2001; 47, 4753–4762.
• 5. Martcheva M. An Introduction to Mathematical Epidemiology. Springer, 2015.
• 6. Franke J.E., Yakubu A.-A. Discrete-time SIS epidemic model in a seasonal environment. SIAM Journal on Applied Mathematics 2006;, 66(5): 1563–1587.
• 7. Bravo de la Parra R., Sanz-Lorenzo L. Discrete epidemic models with two time scales. Advances in Difference Equations 2021; 478(2021).
• 8. Bravo de la Parra R. Reduction of discrete-time infectious disease models. Mathematical Methods in the Applied Sciences 2023; 2021(478): 1–19.
• 9. Driessche P., Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 2002; 180(1–2): 29–48.
• 10. Romaszko J., Siemaszko A., Bodzioch M., Buciński A., Doboszyńska A. Active case finding among homeless people as a mean of reducing the incidence of pulmonary tuberculosis in general population. Advances in Experimental Medicine and Biology – Neuroscience and Respiration 2016; 911: 67–76.
• 11. Murray J.D. Mathematical Biology: I. An Introduction, Springer, 2002.
• 12. Rozkrut D. et al. Statistical yearbooks. Central Statistical Office of Poland, 2017.
• 13. Lai W.H., Kek S.L., Gaik T.K. Solving nonlinear least squares problem using Gauss-Newton method. International Journal of Innovative Science 2015; Engineering and Technology, 4(1): 258–262.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).