Statistical Inference of COVID‑۱۹ Outbreak: Delay Distribution Effect in EQIR Modeling of Epidemic

Background: The world is experiencing another pandemic called COVID‑۱۹. Several mathematical models have been proposed to examine the impact of health interventions in controlling pandemic growth. Method: In this study, we propose a fractional order distributed delay dynamic system, namely, EQIR model. In order to predict the outbreak, the proposed model incorporates changes in transmission rate, isolation rate, and identification of infected people through time varying deterministic and stochastic parameters. Furthermore, proposed stochastic model considers fluctuations in population behavior and simulates different scenarios of outbreak at the same time. Main novelty of this model is its ability to incorporate changes in transmission rate, latent periods, and rate of quarantine through time varying deterministic and stochastic assumptions. This model can exactly follow the disease trend from its beginning to current situation and predict outbreak future for various situations. Results: Parameters of this model were identified during fitting process to real data of Iran, USA, and South Korea. We calculated the reproduction number using a Laplace transform‑based method. Results of numerical simulation verify the effectiveness and accuracy of proposed deterministic and stochastic models in current outbreak. Conclusion: Justifying of parameters of the model emphasizes that, although stricter deterrent interventions can prevent another peak and control the current outbreak, the consecutive screening schemes of COVID‑۱۹ plays more important role. This means that the more diagnostic tests performed on people, the faster the disease will be controlled.