A Heterogeneous Branching Process with Immigration Modeling for COVID-19 Spreading in Local Communities in China

The COVID-19 pandemic spread catastrophically over the world since the spring of 2020. In this paper, a heterogeneous branching process with immigration is established to quantify the human-to-human transmission of COVID-19 in local communities, based on the temporal and structural transmission patterns extracted from public case disclosures by four provincial Health Commissions in China. With proper parameter settings, our branching model matches the actual transmission chains satisfactorily and, therefore, sheds light on the underlying COVID-19 spreading mechanism. Moreover, based on our branching model, the efficacy of home quarantine and social distancing are explored, providing a reference for the effective prevention of COVID-19 worldwide.

Spatial analysis of COVID-19 spread in Iran: Insights into geographical and structural transmission determinants at a province level

ABSTRACTThe Islamic Republic of Iran reported its first COVID-19 cases by 19th February 2020, since then it has become one of the most affected countries, with more than 73,000 cases and 4,585 deaths at the date. Spatial modeling could be used to approach an understanding of structural and sociodemographic factors that have impacted COVID-19 spread at a province-level in Iran. In the present paper, we developed a spatial statistical approach to describe how COVID-19 cases are spatially distributed and to identify significant spatial clusters of cases and how the socioeconomic features of Iranian provinces might predict the number of cases. We identified a cluster of provinces with significantly higher rates of COVID-19 cases around Tehran, which indicated that the spread of COVID-19 within Iran was spatially correlated. Urbanized, highly connected provinces with older population structures and higher average temperatures were the most susceptible to present a higher number of COVID-19 cases. Interestingly, literacy is a protective factor that might be directly related to health literacy and compliance with public health measures. These features indicate that policies related to social distancing, protecting older adults, and vulnerable populations, as well as promoting health literacy, might be targeted to reduce SARS-CoV2 spread in Iran. Our approach could be applied to model COVID-19 outbreaks in other countries with similar characteristics or in case of an upturn in COVID-19 within Iran.

Permeability of multi-layer structures

In this paper we show that ‘permeability’ of a heterogeneous structure with mass transport and thermodynamic properties varying across its thickness is a misleading concept leading to incorrect results and design decisions while two structural transmission rate equations are recommended for practical applications. The notion of structural identity of multi-layer films is introduced to explain the apparent failure of the ‘permeability’ concept. Structural identity of two or more films means the same material sequence in the structure relative to separated environments with constant relative thickness of each corresponding layer. Structurally identical films indeed have the same ‘permeability’, however the notion of identity is shown to contradict the practical goals of multi-layer film design. Engineering examples are provided to demonstrate potential misuses of the ‘permeability’ concept in practical multi-layer design decisions. Correct problem statements and calculation procedures are included. Some general limitations of transmission rate equations are also discussed. These include the role of boundary conditions, temperature and concentration dependence of permeant diffusivity and solubility in a polymer matrix, the presence of co-permeants, surface sorption effects, film thickness, homogeneity of polymer matrix for permeation purposes and correct utilization of available data for predicting gas transport properties of multilayer films.