A significant proportion of malaria infections in humans exhibit no symptoms, but it is a reservoir for maintaining malaria transmission. A time periodic reaction-diffusion model for malaria spread is introduced in this paper, incorporating spatial heterogeneity, incubation periods, symptomatic and asymptomatic carriers. This paper introduces the concept of the basic reproduction number \(\mathcal {R}_{0}\), which is defined as the spectral radius of the next generation operator, and we present some preliminary results by elementary analysis. The threshold dynamic behavior analysis shows that when \(\mathcal {R}_{0}<1\), the disease is extinct, and when \(\mathcal {R}_{0}>1\), the disease is persistent. We investigate the case of constant system parameters, focusing on the global asymptotic stability of the disease-free steady state when \(\mathcal {R}_{0}=1\). In the numerical simulation section, we validate the theoretical results obtained, and then use elasticity analysis methods to explore the influence of parameters on the output solution. In addition, sensitivity analysis of the basic reproduction number under homogeneous conditions indicates direction of controlling malaria transmission. And several control measures are evaluated in the following steps.

人类中很大一部分疟疾感染没有症状，但它是维持疟疾传播的储存库。本文介绍了疟疾传播的时间周期反应扩散模型，其中考虑了空间异质性、潜伏期、有症状和无症状携带者。本文介绍了基本再生数\(\mathcal {R}_{0}\)的概念，定义为下一代算子的谱半径，并通过初等分析给出了一些初步结果。阈值动态行为分析表明，当\(\mathcal {R}_{0}<1\)时，疾病灭绝，当\(\mathcal {R}_{0}>1\)时，疾病消失执着的。我们研究恒定系统参数的情况，重点关注\(\mathcal {R}_{0}=1\)时无病稳态的全局渐近稳定性。在数值模拟部分，我们验证了获得的理论结果，然后利用弹性分析方法探讨了参数对输出解的影响。此外，均质条件下基本再生数的敏感性分析表明了控制疟疾传播的方向。并按以下步骤评估几种控制措施。