Parameters values.

This study presents a reliable mathematical model to explain the spread of typhoid fever, covering stages of susceptibility, infection, carrying, and recovery, specifically in the Sheno town community. A detailed analysis is done to ensure the solutions are positive, stay within certain limits, and are stable for both situations where the disease is absent and where it is consistently present. The Routh-Hurwitz stability criterion has been used and applied for the purpose of stability analysis. Using the next-generation matrix, we determined the intrinsic potential for disease transmission. It showing that typhoid fever is spreading actively in Sheno town, with cases above a critical level. Our findings reveal the instability of the disease-free equilibrium point alongside the stability of the endemic equilibrium point. We identified two pivotal factors for transmission of the disease: the infectious rate, representing the speed of disease transmission, and the recruitment rate, indicating the rate at which new individuals enter the susceptible population. These parameters are indispensable for devising effective control measures. It is imperative to keep these parameters below specific thresholds to maintain a basic reproduction number favorable for disease control. Additionally, the study carefully examines how different factors affect the spread of typhoid fever, giving a detailed understanding of its dynamics. At the end, this study provides valuable insights and specific strategies for managing the disease in the Sheno town community.本研究构建了一套可靠的数学模型，用以阐释伤寒（typhoid fever）的传播规律，模型涵盖易感、感染、带菌及康复四个阶段，研究场景聚焦于舍诺镇社区。为保证解的合法性与合理性，研究开展了详尽的分析，确保解为正值且限定于特定区间内，同时针对疾病绝迹与持续流行两种场景，均验证了解的稳定性。本研究采用劳斯-赫尔维茨稳定性判据（Routh-Hurwitz stability criterion）完成稳定性分析，并借助下一代矩阵（next-generation matrix）测算得到疾病传播的内在潜能。研究结果显示，舍诺镇当前伤寒疫情正处于活跃传播阶段，实际病例数高于临界阈值。本研究发现，无病平衡点（disease-free equilibrium point）呈现不稳定性，而地方病平衡点（endemic equilibrium point）则保持稳定。我们识别出两类影响疾病传播的核心因素：其一为感染率，代表疾病的传播速率；其二为招募率，反映易感人群的新增个体流入速率。上述参数对于制定高效的疾病防控策略不可或缺。为使基本再生数（basic reproduction number）处于利于疾病防控的区间，必须将这些参数控制在特定阈值范围内。此外，本研究系统考察了各类因素对伤寒传播的影响，深入解析了其传播动力学机制。本研究最终为舍诺镇社区的伤寒防控工作提供了极具价值的理论见解与具体可行的防控策略。