Exploring Discrete-Time Epidemic Behavior Based on Saturated Incidence Rate and Multiple Transmission Pathways

• Preeti Deolia ^[1] ; Vijay Shankar Sharma ^[2] ; Anuraj Singh ^[1]
  1. [1] ABV-Indian Institute of Information Technology and Managemen
  2. [2] Madhav Institute of Technology & Science (MITS)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 3, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • The viral shedding is crucial for understanding the transmission of infectious diseases via contaminated surfaces. In this work, a discrete-time SIR-type mathematical model incorporating pathogen shedding is investigated. The basic reproduction number (R0) is used to determine the conditions for the local stability of the fixed points of the discrete-time model. The existence of co-dimension one bifurcations particularly, transcritical (BP) and period-doubling (PD) bifurcations, along with co-dimension two bifurcations namely, generalized period doubling (GPD), and limit point period doubling (LPPD) bifurcations are discussed. The presence of these bifurcations is detected using algebraic criterion methods. These methods are based on the properties of the coefficients of the characteristic polynomial instead of the eigenvalues of the Jacobian matrix. The sensitivity indices of R0 are calculated via the normalized forward sensitivity method with respect to significant parameters. The performed numerical simulation supports the analytical findings of the model. The existence of several bifurcations in the discrete-time epidemic model reflects a situation where a slight adjustment in some specific parameters can significantly impact the model outcomes.

• Referencias bibliográficas
  • 1. Bentout, S., Chekroun, A., Kuniya, T.: Parameter estimation and prediction for coronavirus disease outbreak 2019 (covid-19) in algeria....
  • 2. Ganegoda, N., Götz, T., Wijaya, K.P.: An age-dependent model for dengue transmission: Analysis and comparison to field data. Applied Mathematics...
  • 3. Wang, Q., Jiang, Q., Yang, Y., Pan, J.: The burden of travel for care and its influencing factors in china: An inpatient-based study of...
  • 4. Li, B., Wang, W., Zhao, L., Li, M., Yan, D., Li, X., Zhang, J., Gao, Q., Feng, Y., Zheng, J., et al.: Aggregation-induced emission-based...
  • 5. Zhao, Y., Hu, M., Jin, Y., Chen, F., Wang, X., Wang, B., Yue, J., Ren, H.: Predicting the transmission trend of respiratory viruses in...
  • 6. Hu, F., Ma, Q., Hu, H., Zhou, K.H., Wei, S.: A study of the spatial network structure of ethnic regions in northwest china based on multiple...
  • 7. Bentout, S.: Analysis of global behavior in an age-structured epidemic model with nonlocal dispersal and distributed delay. Mathematical...
  • 8. Soufiane, B., Touaoula, T.M.: Global analysis of an infection age model with a class of nonlinear incidence rates. Journal of Mathematical...
  • 9. Kim, S., Aurelio, A., Jung, E.: Mathematical model and intervention strategies for mitigating tuberculosis in the philippines. Journal...
  • 10. Saha, S., Samanta, G.P.: Dynamics of an epidemic model with impact of toxins. Physica A: Statistical Mechanics and its Applications 527,...
  • 11. Saha, S., Samanta, G.: Dynamics of an epidemic model under the influence of environmental stress. Mathematical biology and bioinformatics...
  • 12. Deolia, P., Singh, A.: Analysing the probable insights of ade in dengue vaccination embodying sequential zika infection and waning immunity....
  • 13. Dutta, P., Samanta, G., Nieto, J.J.: Periodic transmission and vaccination effects in epidemic dynamics: a study using the SIVIS model....
  • 14. Yakubu, A.-A., Franke, J.E.: Discrete-time SIS epidemicmodel in a seasonal environment. SIAM Journal on Applied Mathematics 66(5), 1563–1587...
  • 15. Zhou, Y., Ma, Z.: Global stability of a class of discrete age-structured sis models with immigration. Math. Biosci. Eng 6, 409–425 (2009)
  • 16. Parsamanesh, M., Erfanian, M., Mehrshad, S.: Stability and bifurcations in a discrete-time epidemic model with vaccination and vital dynamics....
  • 17. Xiang, L., Zhang, Y., Huang, J.: Stability analysis of a discrete sirs epidemic model with vaccination. Journal of Difference Equations...
  • 18. Van den Driessche, P., Yakubu, A.-A.: Disease extinction versus persistence in discrete-time epidemic models. Bulletin of mathematical...
  • 19. Parsamanesh, M., Erfanian, M.: Stability and bifurcations in a discrete-time sivs model with saturated incidence rate. Chaos, Solitons...
  • 20. Yu, X., Liu, M., Zheng, Z., Hu, D.: Complex dynamics of a discrete-time sir model with nonlinear incidence and recovery rates. International...
  • 21. Brauer, F., Feng, Z., Castillo-Chavez, C.: Discrete epidemic models. Mathematical Biosciences & Engineering 7(1), 1–15 (2009)
  • 22. Hu, Z., Teng, Z., Jiang, H.: Stability analysis in a class of discrete sirs epidemic models. Nonlinear Analysis: Real World Applications...
  • 23. Hu, Z., Teng, Z., Zhang, L.: Stability and bifurcation analysis in a discrete sir epidemic model. Mathematics and computers in Simulation...
  • 24. Wang, X., Wang, Z., Shen, H.: Dynamical analysis of a discrete-time sis epidemic model on complex networks. Applied Mathematics Letters...
  • 25. Eskandari, Z., Khoshsiar Ghaziani, R., Avazzadeh, Z.: Bifurcations of a discrete-time sir epidemic model with logistic growth of the susceptible...
  • 26. Asamoah, J.K.K., Owusu, M.A., Jin, Z., Oduro, F., Abidemi, A., Gyasi, E.O.: Global stability and cost-effectiveness analysis of covid-19...
  • 27. Bentout, S., Tridane, A., Djilali, S., Touaoula, T.M.: Age-structured modeling of covid-19 epidemic in the usa, uae and algeria. Alexandria...
  • 28. Asamoah, J.K.K., Okyere, E., Abidemi, A., Moore, S.E., Sun, G.-Q., Jin, Z., Acheampong, E., Gordon, J.F.: Optimal control and comprehensive...
  • 29. Asamoah, J.K.K., Jin, Z., Sun, G.-Q., Seidu, B., Yankson, E., Abidemi, A., Oduro, F., Moore, S.E., Okyere, E.: Sensitivity assessment...
  • 30. Asamoah, J.K.K., Bornaa, C., Seidu, B., Jin, Z.: Mathematical analysis of the effects of controls on transmission dynamics of sars-cov-2....
  • 31. Acheampong, E., Okyere, E., Iddi, S., Bonney, J.H., Asamoah, J.K.K., Wattis, J.A., Gomes, R.L.: Mathematical modelling of earlier stages...
  • 32. Van Doremalen, N., Bushmaker, T., Morris, D.H., Holbrook, M.G., Gamble, A., Williamson, B.N., Tamin, A., Harcourt, J.L., Thornburg, N.J.,...
  • 33. Li, J., Li, J., Verbeek, F.J., Schultz, T., Liu, H.: Outlier detection using iterative adaptive mini-minimum spanning tree generation...
  • 34. Kassa, S.M., Njagarah, J.B., Terefe, Y.A.: Analysis of the mitigation strategies for covid-19: from mathematical modelling perspective....
  • 35. Eisenberg, M.C., Robertson, S.L., Tien, J.H.: Identifiability and estimation of multiple transmission pathways in cholera and waterborne...
  • 36. Weber, D.J., Rutala, W.A.: Understanding and preventing transmission of healthcare-associated pathogens due to the contaminated hospital...
  • 37. Peace, A., O’Regan, S.M., Spatz, J.A., Reilly, P.N., Hill, R.D., Carter, E.D., Wilkes, R.P., Waltzek, T.B., Miller, D.L., Gray, M.J.:...
  • 38. Chen, Z., Zhu, W., Feng, H., Luo, H.: Changes in corporate social responsibility efficiency in chinese food industry brought by covid-19...
  • 39. Mahroug, F., Bentout, S.: Dynamics of a diffusion dispersal viral epidemic model with age infection in a spatially heterogeneous environment...
  • 40. Tien, J.H., Earn, D.J.: Multiple transmission pathways and disease dynamics in a waterborne pathogen model. Bulletin of mathematical biology...
  • 41. Rwezaura, H., Tchoumi, S., Tchuenche, J.: Impact of environmental transmission and contact rates on covid-19 dynamics: A simulation study....
  • 42. Singh, A., Deolia, P.: Covid-19 outbreak: a predictive mathematical study incorporating shedding effect. Journal of Applied Mathematics...