A continuous mathematical model referred to as the susceptible infected tested quarantined recovered (SITQR) model is developed. Positivity depends on performance parameters such as false positive rates. Positive test results lead to quarantining. Using the model, two categories of tests are available. One test which is high-performance, but which is also more expensive and time-consuming (analogous to the RT-PCR tests) and the other which is relatively less performing, less expensive and rapid (analogous to the rapid antibody or rapid-antigen tests).