Berhe Hailay Weldegiorgis, Makinde Oluwole Daniel, Theuri David Mwangi
Pan African University Institute of Basic Sciences Technology and Innovation, Nairobi, Kenya.
Faculty of Military Science, Stellenbosch University, Cape Town, South Africa.
J Biol Dyn. 2019 Dec;13(1):192-217. doi: 10.1080/17513758.2019.1588400.
In this paper, the dysentery dynamics model with controls is theoretically investigated using the stability theory of differential equations. The system is considered as SIRSB deterministic compartmental model with treatment and sanitation. A threshold number is obtained such that indicates the possibility of dysentery eradication in the community while represents uniform persistence of the disease. The Lyapunov-LaSalle method is used to prove the global stability of the disease-free equilibrium. Moreover, the geometric approach method is used to obtain the sufficient condition for the global stability of the unique endemic equilibrium for . Numerical simulation is performed to justify the analytical results. Graphical results are presented and discussed quantitatively. It is found out that the aggravation of the disease can be decreased by using the constant controls treatment and sanitation.
本文利用微分方程稳定性理论对具有控制措施的痢疾动力学模型进行了理论研究。该系统被视为具有治疗和卫生措施的SIRSB确定性 compartmental模型。得到了一个阈值数，使得 表示社区中痢疾根除的可能性，而 表示疾病的一致持续存在。利用Lyapunov-LaSalle方法证明了无病平衡点的全局稳定性。此外，采用几何方法得到了 时唯一地方病平衡点全局稳定性的充分条件。进行了数值模拟以验证分析结果。给出了图形结果并进行了定量讨论。结果发现，通过采用恒定的控制措施（治疗和卫生措施）可以降低疾病的严重程度。
