Stability Analysis of a Deterministic Epidemic Model in Metapopulation Setting

We present in this article an epidemic model with saturated in metapopulation setting. We develop the mathematical modelling of HIV transmission among adults in Metapopulation setting. We discussed the positivity of the system. We calculated the reproduction number, If ?for , then each infectious individual in Sub-Population j infects on average less than one other person and the disease is likely to die out. Otherwise, if ?for , then each infectious individual in Sub-Population j infects on average more than one other person;the infection could therefore establish itself in the population and become endemic. An epidemic model, where the presence or absence of an epidemic wave is characterized by the value of ?both ideas of the inner equilibrium point of stability properties are discussed.

Stability Analysis and Stochastic SI Modelling of Endemic Diseases

In this paper, we study a stochastic epidemic model in Meta-population setting. The stochastic model is obtained from the deterministic model by set up random perturbations about the endemic equilibrium state. The outcome of random perturbations on the stability actions of endemic equilibrium is discussed. Stability of the two equilibriums is studied using the Lyapunov function.

TransCode:Uncovering COVID-19 transmission patterns via deep learning

Background The heterogeneity of COVID-19 spread dynamics is determined by complex spatiotemporal transmission patterns at a fine scale,especially in densely populated regions.In this study,we aim to discover such fine-scale transmission patterns via deep learning.Methods We introduce the notion of TransCode to characterize fine-scale spatiotemporal transmission patterns of COVID-19 caused by metapopulation mobility and contact behaviors.First,in Hong Kong,China,we construct the mobility trajectories of confirmed cases using their visiting records.Then we estimate the transmissibility of individual cases in different locations based on their temporal infectiousness distribution.Integrating the spatial and temporal information,we represent the TransCode via spatiotemporal transmission networks.Further,we propose a deep transfer learning model to adapt the TransCode of Hong Kong,China to achieve fine-scale transmission characterization and risk prediction in six densely populated metropolises:New York City,San Francisco,Toronto,London,Berlin,and Tokyo,where fine-scale data are limited.All the data used in this study are publicly available.Results The TransCode of Hong Kong,China derived from the spatial transmission information and temporal infectiousness distribution of individual cases reveals the transmission patterns(e.g.,the imported and exported transmission intensities)at the district and constituency levels during different COVID-19 outbreaks waves.By adapting the TransCode of Hong Kong,China to other data-limited densely populated metropolises,the proposed method outperforms other representative methods by more than 10%in terms of the prediction accuracy of the disease dynamics(i.e.,the trend of case numbers),and the fine-scale spatiotemporal transmission patterns in these metropolises could also be well captured due to some shared intrinsically common patterns of human mobility and contact behaviors at the metapopulation level.Conclusions The fine-scale transmission patterns due to the metapopulation level mobility(e.g.,travel across different districts)and contact behaviors(e.g.,gathering in social-economic centers)are one of the main contributors to the rapid spread of the virus.Characterization of the fine-scale transmission patterns using the TransCode will facilitate the development of tailor-made intervention strategies to effectively contain disease transmission in the targeted regions.