In this paper, we propose a continuous-time stochastic intensity model, namely, two-phase dynamic contagion process (2P-DCP), for modelling the epidemic contagion of COVID-19 and investigating the lockdown effect based on the dynamic contagion model introduced by Dassios and Zhao (2011). It allows randomness to the infectivity of individuals rather than a constant reproduction number as assumed by standard models. Key epidemiological quantities, such as the distribution of final epidemic size and expected epidemic duration, are derived and estimated based on real data for various regions and countries. The associated time lag of the effect of intervention in each country or region is estimated. Our results are consistent with the incubation time of COVID-19 found by recent medical study. We demonstrate that our model could potentially be a valuable tool in the modeling of COVID-19. More importantly, the proposed model of 2P-DCP could also be used as an important tool in epidemiological modelling as this type of contagion models with very simple structures is adequate to describe the evolution of regional epidemic and worldwide pandemic.

In this paper, we propose a continuous-time stochastic intensity model, namely, two-phase dynamic contagion process (2P-DCP), for modelling the epidemic contagion of COVID-19 and investigating the lockdown effect based on the dynamic contagion model introduced by Dassios and Zhao [24] . It allows randomness to the infectivity of individuals rather than a constant reproduction number as assumed by standard models. Key epidemiological quantities, such as the distribution of final epidemic size and expected epidemic duration, are derived and estimated based on real data for various regions and countries. The associated time lag of the effect of intervention in each country or region is estimated. Our results are consistent with the incubation time of COVID-19 found by recent medical study. We demonstrate that our model could potentially be a valuable tool in the modeling of COVID-19. More importantly, the proposed model of 2P-DCP could also be used as an important tool in epidemiological modelling as this type of contagion models with very simple structures is adequate to describe the evolution of regional epidemic and worldwide pandemic.

In this paper, we present a novel family of multivariate mixed Poisson-Generalized Inverse Gaussian INAR(1), MMPGIG-INAR(1), regression models for modelling time series of overdispersed count response variables in a versatile manner. The statistical properties associated with the proposed family of models are discussed and we derive the joint distribution of innovations across all the sequences. Finally, for illustrative purposes different members of the MMPGIG-INAR(1) class are fitted to Local Government Property Insurance Fund data from the state of Wisconsin via maximum likelihood estimation.

Motivated by the extended Poisson INAR(1), which allows innovations to be serially dependent, we develop a new family of binomial-mixed Poisson INAR(1) (BMP INAR(1)) processes by adding a mixed Poisson component to the innovations of the classical Poisson INAR(1) process. Due to the flexibility of the mixed Poisson component, the model includes a large class of INAR(1) processes with different transition probabilities. Moreover, it can capture some overdispersion features coming from the data while keeping the innovations serially dependent. We discuss its statistical properties, stationarity conditions and transition probabilities for different mixing densities (Exponential, Lindley). Then, we derive the maximum likelihood estimation method and its asymptotic properties for this model. Finally, we demonstrate our approach using a real data example of iceberg count data from a financial system.

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