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 $R_0$ is obtained such that $R_0\le 1$ indicates the possibility of dysentery eradication in the community while $R_0>1$ 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 $R_0>1$. 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.

在本文中，使用微分方程的稳定性理论从理论上研究了带控制的痢疾动力学模型。该系统被认为是具有处理和卫生条件的 SIRSB 确定性隔室模型。阈值数$R_0$获得这样的$R_0\le \mathrm{1个}$表明在社区内根除痢疾的可能性，同时$R_0>\mathrm{1个}$表示疾病的均匀持续性。Lyapunov-LaSalle 方法用于证明无病平衡的全局稳定性。此外，使用几何逼近方法获得了独特地方性平衡的全局稳定性的充分条件$R_0>\mathrm{1个}$. 进行数值模拟以验证分析结果。图形结果被呈现和定量讨论。发现通过持续控制治疗和卫生可以减少疾病的恶化。