A compartmental epidemic model incorporating probable cases to model COVID-19 outbreak in regions with limited testing capacity.

We propose a new compartmental epidemic model taking into account people who have symptoms with no confirmatory laboratory testing (probable cases). We prove well-posedness of the model and provide an explicit expression for the basic reproduction number (R). We use the model together with an extended Kalman filter (EKF) to estimate the time-varying effective reproduction number (R) of COVID-19 in West Java province in Indonesia and the state of Michigan in the USA, where laboratory testing capacities are limited. Based on our estimation, the value of R is higher when the probable cases are taken into account. This correction can be used by decision and policy makers when considering re-opening policy and evaluation of public measures.