Saturated incidence rates and treatment responses are essential in epidemiology and clinical research. They signify peak event occurrences in a population, aiding in disease understanding and intervention planning. This study proposes a mathematical model of COVID-19, focusing on the impact of saturated incidence rates and treatment responses on its dynamical transmission. Via qualitative analysis, the existence and uniqueness of the model’s solution are verified, a positive invariant region is established, and the local stability analysis highlights the model’s resilience to minor perturbations. The model solution is obtained utilizing the homotopy perturbation method, and simulations with Maple 18 software reveal that increasing treatment intensity might not result in significant additional decrease in the number of infections, particularly in situations where the spread of infection is uncontrolled. Thus, the finding underscores the need to refine treatment strategies through a tailored approach and to optimize preventive measures.

饱和发病率和治疗反应对于流行病学和临床研究至关重要。它们标志着人群中事件发生的高峰，有助于疾病理解和干预计划。本研究提出了 COVID-19 的数学模型，重点关注饱和发病率和治疗反应对其动态传播的影响。通过定性分析，验证了模型解的存在性和唯一性，建立了正不变区域，局部稳定性分析强调了模型对微小扰动的恢复能力。模型解是利用同伦摄动方法获得的，并且使用Maple 18软件进行的模拟表明，增加治疗强度可能不会导致感染数量的显着额外减少，特别是在感染传播不受控制的情况下。因此，这一发现强调需要通过量身定制的方法来完善治疗策略并优化预防措施。