Kifle Zenebe Shiferaw, Obsu Legesse Lemecha
Department of Mathematics, Adama Science and Technology University, Adama, Ethiopia.
Heliyon. 2023 Jul 31;9(8):e18726. doi: 10.1016/j.heliyon.2023.e18726. eCollection 2023 Aug.
This study proposes a mathematical model for examining the COVID-19 and tuberculosis (TB) co-dynamics thoroughly. First, the single infection dynamics: COVID-19 infection and TB infection models are taken into consideration and examined. Following that, the co-dynamics with TB and COVID-19 is also investigated. In order to comprehend the developed model dynamics, the basic system attributes including the region of definition, theory of nonnegativity and boundedness of solution are investigated. Further, a qualitative analysis of the equilibria of the formulated model equations is performed. The equilibria of both infection models are globally asymptotically stable if their respective basic reproductive number is smaller than one. As the associated reproductive number reaches unity, they experience the forward bifurcation phenomenon. Additionally, it is demonstrated that the formulated co-dynamics model would not experience backward bifurcation by applying the center manifold theory. Moreover, model fitting is done by using daily reported COVID-19 cumulative data in Ethiopia between March 13, 2020, and May 31, 2022. For instance, the non-linear least squares approach of fitting a function to data was performed in the fitting process using from the Python. Finally, to corroborate the analytical findings of the model equation, numerical simulations were conducted.
本研究提出了一个数学模型，用于全面研究新冠病毒（COVID-19）和结核病（TB）的共同动态。首先，考虑并研究单一感染动态：即COVID-19感染模型和TB感染模型。在此之后，还研究了TB和COVID-19的共同动态。为了理解所建立模型的动态，研究了包括定义区域、解的非负性和有界性理论在内的基本系统属性。此外，对所制定模型方程的平衡点进行了定性分析。如果各自的基本再生数小于1，则两个感染模型的平衡点都是全局渐近稳定的。当相关再生数达到1时，它们会经历前向分岔现象。此外，通过应用中心流形理论证明，所制定的共同动态模型不会经历后向分岔。此外，使用2020年3月13日至2022年5月31日埃塞俄比亚每日报告的COVID-19累计数据进行模型拟合。例如，在拟合过程中使用Python中的 执行将函数拟合到数据的非线性最小二乘法。最后，为了证实模型方程的分析结果，进行了数值模拟。
