Cure rate models are mostly used to study data arising from cancer clinical trials. Its use in the context of infectious diseases has not been explored well. In 2008, Tournoud and Ecochard first proposed a mechanistic formulation of cure rate model in the context of infectious diseases with multiple exposures to infection. However, they assumed a simple Poisson distribution to capture the unobserved pathogens at each exposure time. In this paper, we propose a new cure rate model to study infectious diseases with discrete multiple exposures to infection. Our formulation captures both over-dispersion and under-dispersion with respect to the count on pathogens at each time of exposure. We also propose a new estimation method based on the expectation maximization algorithm to calculate the maximum likelihood estimates of the model parameters. We carry out a detailed Monte Carlo simulation study to demonstrate the performance of the proposed model and estimation algorithm. The flexibility of our proposed model also allows us to carry out a model discrimination. For this purpose, we use both likelihood ratio test and information-based criteria. Finally, we illustrate our proposed model using a recently collected data on COVID-19.

翻译：治愈率模型主要用于研究癌症临床试验数据，其在传染病领域的应用尚未得到充分探索。2008年，Tournoud与Ecochard首次提出了一种针对多次感染暴露的传染病情境下治愈率模型的机制化表述。然而，他们采用简单的泊松分布来刻画每次暴露时未观测到的病原体数量。本文提出了一种新型治愈率模型，用于研究具有离散多次感染暴露的传染病。我们的模型能够同时捕捉每次暴露时病原体计数的过离散与欠离散特性。我们还基于期望最大化算法提出了一种新的估计方法，用于计算模型参数的最大似然估计值。通过详细的蒙特卡洛模拟研究，我们验证了所提模型与估计算法的性能。所提模型的灵活性还允许我们进行模型判别，为此采用了似然比检验与基于信息准则的方法。最后，我们利用近期收集的COVID-19数据对所提模型进行了实例验证。