Malaria is a life-threatening mosquito-borne disease. It is transmitted through the bite of an infected Anopheles mosquito. Malaria may be fatal if not treated promptly. Malaria is a major public health problem in India. Here we propose an SIRS model to study the transmission dynamics of malaria with saturated treatment. We assume that the mosquito population is growing logistically in the environment. Here we include a saturated type treatment function which is more suitable for the regions with limited resources. We discuss the existence and stability of different equilibria of the proposed model. We also compute the basic reproduction number \(R_0\) which plays an important role in existence and stability of equilibria of the model. For \(R_0 < 1\), backward bifurcation occurs, which suggests that lowering \(R_0\) below one is not enough to eliminate the disease from the population. We estimate the key parameter corresponding to transmission of malaria using real data from different states of India by least square method. We also perform sensitivity analysis using PRCC to identify the key parameters which influence the infection prevalence of the disease and the basic reproduction number. Numerical simulations are presented to illustrate the analytic findings. Our numerical results suggest that infected population should get proper treatment and increase in the death rate of mosquito can also help to eradicate the malaria disease from the population.

疟疾是威胁生命的蚊媒疾病。它通过被感染的按蚊的叮咬传播。如果不及时治疗，疟疾可能是致命的。疟疾是印度的主要公共卫生问题。在这里，我们提出一个SIRS模型来研究饱和治疗下疟疾的传播动态。我们假设环境中蚊子的数量呈逻辑增长。这里我们包括一个饱和型处理函数，它更适合于资源有限的地区。我们讨论了所提出模型不同平衡点的存在性和稳定性。我们还计算了基本复制数\（R_0 \），它对模型的存在和稳定性起着重要作用。对于\（R_0 <1 \），发生向后分叉，这表明将\（R_0 \）降低到1以下不足以从人群中消除该疾病。我们通过最小二乘法使用来自印度不同州的真实数据估算与疟疾传播相对应的关键参数。我们还使用PRCC进行敏感性分析，以确定影响该疾病的感染率和基本繁殖数量的关键参数。数值模拟表明了分析结果。我们的数值结果表明，受感染的人群应该得到适当的治疗，增加蚊子的死亡率也可以帮助从人群中消除疟疾。