Time delay and nonlinear incidence effectson the stochastic SIRC epidemic model
| dc.citation.epage | 95 | |
| dc.citation.issue | 11 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 84 | |
| dc.citation.volume | 1 | |
| dc.contributor.affiliation | Університет Мохаммеда V у Рабаті | |
| dc.contributor.affiliation | Mohammed V University in Rabat | |
| dc.contributor.author | Бен Лахбіб, А. | |
| dc.contributor.author | Азрар, Л. | |
| dc.contributor.author | Ben Lahbib, A. | |
| dc.contributor.author | Azrar, L. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-10-20T07:44:29Z | |
| dc.date.created | 2024-02-24 | |
| dc.date.issued | 2024-02-24 | |
| dc.description.abstract | У цій статті подано теоретичні та чисельні дослідження стохастичної моделі епідемії SIRC із затримкою в часі та нелінійною захворюваністю. Доведено існування та єдиність глобального позитивного розв'язку. Метод аналізу Ляпунова використовується для отримання достатніх умов існування стаціонарного розподілу та зникнення захворювання за певних припущень. Також розроблено числове моделювання для розглянутої стохастичної моделі з метою підтвердження теоретичних висновків. | |
| dc.description.abstract | This paper presents theoretical and numerical study of a stochastic SIRC epidemic model with time delay and nonlinear incidence. The existence and uniqueness of a global positive solution is proved. The Lyapunov analysis method is used to obtain sufficient conditions for the existence of a stationary distribution and the disease extinction under certain assumptions. Numerical simulations are also elaborated for the considered stochastic model in order to corroborate the theoretical findings. | |
| dc.format.extent | 84-95 | |
| dc.format.pages | 12 | |
| dc.identifier.citation | Ben Lahbib A. Time delay and nonlinear incidence effectson the stochastic SIRC epidemic model / A. Ben Lahbib, L. Azrar // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 84–95. | |
| dc.identifier.citationen | Ben Lahbib A. Time delay and nonlinear incidence effectson the stochastic SIRC epidemic model / A. Ben Lahbib, L. Azrar // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 84–95. | |
| dc.identifier.doi | 10.23939/mmc2024.01.084 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/113800 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 11 (1), 2024 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 11 (1), 2024 | |
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| dc.relation.references | [14] Khan M. A., Badshah Q., Islam S., Khan I., Shafie S., Khan S. A. Global dynamics of SEIRS epidemic model with nonlinear generalized incidences and preventive vaccination. Advances in Difference Equations. 2015, 88 (2015). | |
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| dc.relation.referencesen | [1] Niu Y., Li Z., Meng L., Wang S., Zhao Z., Song T., Lu J., Chen T., Li Q., Zou X. The collaboration be- tween infectious disease modeling and public health decision-making based on the COVID-19. Journal of Safety Science and Resilience. 2 (2), 69–76 (2021). | |
| dc.relation.referencesen | [2] Ivorra B., Ferr´andez M. R., Vela-P´erez M., Ramos A. M. Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections: The case of China. Communications in Nonlinear Science and Numerical Simulation. 88, 105303 (2020). | |
| dc.relation.referencesen | [3] Casagrandi R., Bolzoni L., Levin S. A., Andreasen V. The SIRC model and influenza A. Mathematical Biosciences. 200 (2), 152–169 (2006). | |
| dc.relation.referencesen | [4] Ruan S., Wang W. Dynamical behavior of an epidemic model with a nonlinear incidence rate. Journal of Differential Equations. 188 (1), 135–163 (2003). | |
| dc.relation.referencesen | [5] Brauer F. Mathematical epidemiology: Past, present, and future. Infectious Disease Modelling. 2 (2), 113–127 (2017). | |
| dc.relation.referencesen | [6] Khan M. A., Ullah S., Ullah S., Farhan M. Fractional order SEIR model with generalized incidence rate. AIMS Mathematics. 5 (4), 2843–2857 (2020). | |
| dc.relation.referencesen | [7] Iacoviello D., Stasio N. Optimal control for SIRC epidemic outbreak. Computer Methods and Programs in Biomedicine. 110 (3), 333–342 (2013). | |
| dc.relation.referencesen | [8] Wei F., Xue R. Stability and extinction of SEIR epidemic models with generalized nonlinear incidence. Mathematics and Computers in Simulation. 170, 1–15 (2020). | |
| dc.relation.referencesen | [9] Champagne C., Cazelles B. Comparison of stochastic and deterministic frameworks in dengue modelling. Mathematical Biosciences. 310, 1–12 (2019). | |
| dc.relation.referencesen | [10] Yan C., Jia J. Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. Abstract and Applied Analysis. 2014, 109372 (2014). | |
| dc.relation.referencesen | [11] Zhang J., Ma Z. Global dynamics of an SEIR epidemic model with saturating contact rate. Mathematical Biosciences. 185 (1), 15–32 (2003). | |
| dc.relation.referencesen | [12] Beretta E., Breda D. An SEIR epidemic model with constant latency time and infectious period. Mathematical Biosciences and Engineering. 8 (4), 931–952 (2011). | |
| dc.relation.referencesen | [13] Liu L. A delayed SIR model with general nonlinear incidence rate. Advances in Difference Equations. 2015, 329 (2015). | |
| dc.relation.referencesen | [14] Khan M. A., Badshah Q., Islam S., Khan I., Shafie S., Khan S. A. Global dynamics of SEIRS epidemic model with nonlinear generalized incidences and preventive vaccination. Advances in Difference Equations. 2015, 88 (2015). | |
| dc.relation.referencesen | [15] Adi-Kusumo F. The Dynamics of a SEIR–SIRC Antigenic Drift Influenza Model. Bulletin of Mathematical Biology. 79, 1412–1425 (2017). | |
| dc.relation.referencesen | [16] Rihan F. A., Alsakaji H. J., Rajivganthi C. Stochastic SIRC epidemic model with time-delay for COVID-19. Advances in Difference Equations. 2020, 502 (2020). | |
| dc.relation.referencesen | [17] Mao X. Stochastic Differential Equations and Applications. Woodhead Publishing (2011). | |
| dc.relation.referencesen | [18] Khasminskii R. Stochastic stability of differential equations. Springer Berlin, Heidelberg (1980). | |
| dc.relation.referencesen | [19] Higham D., Kloeden P. An Introduction to the Numerical Simulation of Stochastic Differential Equations. Journal of Differential Equations. 188, 135–163 (2003). | |
| dc.relation.referencesen | [20] Imran A., Rohul A. Numerical solution of a class of delay differential and delay partial differential equations via Haar wavelet. Applied Mathematical Modelling. 40 (23–24), 10286–10299 (2016). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2024 | |
| dc.subject | модель SIRC | |
| dc.subject | стохастичний | |
| dc.subject | часова затримка | |
| dc.subject | функція Ляпунова | |
| dc.subject | нелінійна захворюваність | |
| dc.subject | стаціонарний розподіл | |
| dc.subject | SIRC model | |
| dc.subject | stochastic | |
| dc.subject | time delay | |
| dc.subject | Lyapunov function | |
| dc.subject | nonlinear incidence | |
| dc.subject | stationary distribution | |
| dc.title | Time delay and nonlinear incidence effectson the stochastic SIRC epidemic model | |
| dc.title.alternative | Вплив часової затримки та нелінійної захворюваності на стохастичну модель епідемії SIRC | |
| dc.type | Article |
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