*Article* **An Epidemic Model with Time Delay Determined by the Disease Duration**

**Samiran Ghosh 1,†, Vitaly Volpert 2,3,\*,† and Malay Banerjee 1,†**


**Abstract:** Immuno-epidemiological models with distributed recovery and death rates can describe the epidemic progression more precisely than conventional compartmental models. However, the required immunological data to estimate the distributed recovery and death rates are not easily available. An epidemic model with time delay is derived from the previously developed model with distributed recovery and death rates, which does not require precise immunological data. The resulting generic model describes epidemic progression using two parameters, disease transmission rate and disease duration. The disease duration is incorporated as a delay parameter. Various epidemic characteristics of the delay model, namely the basic reproduction number, the maximal number of infected, and the final size of the epidemic are derived. The estimation of disease duration is studied with the help of real data for COVID-19. The delay model gives a good approximation of the COVID-19 data and of the more detailed model with distributed parameters.

**Keywords:** epidemic model; disease duration; time delay; COVID-19

**MSC:** 34K60; 92D30
