Simulation of COVID-19 Incubation Period and the Effect of Probability Distribution Function on Model Training Using MIMANSA

Coronavirus disease 2019 (COVID-19) has infected people all over the world. While scientists are busy finding a vaccine and medicine, it becomes difficult to control the spread and manage patients. Mathematical models help one get a better feel for the challenges in patient management. With this in mind, our team developed a model called Multilevel Integrated Model with a Novel Systems Approach (MIMANSA) Welling et. al (2020). MIMANSA is a multi-parametric model. One of the challenges in the design of MIMANSA was to simulate the incubation period of coronavirus. The incubation period decides when virus-infected patients would show symptoms. The probability distribution function (PDF), when applied to the number of virus-infected cases, gives a good representation of the process of the incubation period. The probability distribution functions can take various forms. In this paper, we explore a variety of PDFs and their impact on parameter estimation in the MIMANSA model. For our experiments, we used Weibull, Gaussian, uniform, and Gamma distribution. To ensure a fair comparison of Weibull, Gaussian, and Gamma distribution, we matched the peak value of the distribution. Our results show that the Weibull distribution with shape 7.7 and scale 7 for 14 days gives a better training model and predictions.