Yaagoub Zakaria, Danane Jaouad, Allali Karam
Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, Mohammedia, Morocco.
Laboratory of Systems Modelization and Analysis for Decision Support, National School of Applied Sciences, Hassan First University, Berrechid, Morocco.
Comput Methods Biomech Biomed Engin. 2024 Apr;27(5):632-650. doi: 10.1080/10255842.2023.2197542. Epub 2023 Apr 5.
In this paper, we study mathematically a two strains epidemic model taking into account non-monotonic incidence rates and vaccination strategy. The model contains seven ordinary differential equations that illustrate the interaction between the susceptible, the vaccinated, the exposed, the infected and the removed individuals. The model has four equilibrium points, namely, disease free equilibrium, endemic equilibrium with respect to the first strain, endemic equilibrium with respect to the second strain and the endemic equilibrium with respect to both strains. The global stability of the equilibria has been demonstrated using some suitable Lyapunov functions. The basic reproduction number is found depending on the first strain reproduction number and the second reproduction number We have shown that the disease dies out when the basic reproduction number is less than unity. It was remarked that the global stability of the endemic equilibria depends, on the strain basic reproduction number and on the strain inhibitory effect reproduction number. We have also observed that the strain with high basic reproduction number will dominate the other strain. Finally, the numerical simulations are presented in the last part of this work to support our theoretical results. We notice that our suggested model has some limitations and does not predicting the long-term dynamics for some reproduction numbers cases.
在本文中，我们从数学角度研究了一个考虑非单调发病率和疫苗接种策略的两菌株流行病模型。该模型包含七个常微分方程，描述了易感者、接种者、暴露者、感染者和康复者之间的相互作用。该模型有四个平衡点，即无病平衡点、关于第一种菌株的地方病平衡点、关于第二种菌株的地方病平衡点以及关于两种菌株的地方病平衡点。利用一些合适的李雅普诺夫函数证明了平衡点的全局稳定性。基本再生数取决于第一种菌株的再生数和第二种菌株的再生数。我们已经表明，当基本再生数小于1时，疾病会消亡。有人指出，地方病平衡点的全局稳定性取决于菌株基本再生数和菌株抑制效应再生数。我们还观察到，具有高基本再生数的菌株将主导另一种菌株。最后，在这项工作的最后部分给出了数值模拟，以支持我们的理论结果。我们注意到，我们提出的模型有一些局限性，并且对于某些再生数情况无法预测长期动态。
