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How to strategically allocate the available vaccines is a crucial issue for pandemic control. In this work, we propose a mathematical framework for optimal stabilizing vaccine allocation, where our goal is to send the infections to zero as soon as possible with a fixed number of vaccine doses. This framework allows us to efficiently compute the optimal vaccine allocation policy for general epidemic spread models including SIS/SIR/SEIR and a new model of COVID-19 transmissions. By fitting the real data in New York State to our framework, we found that the optimal stabilizing vaccine allocation policy suggests offering vaccines priority to locations where there are more susceptible people and where the residents spend longer time outside the home. Besides, we found that offering vaccines priority to young adults (20-29) and middle-age adults (20-44) can minimize the cumulative infected cases and the death cases. Moreover, we compared our method with five age-stratified strategies in cite{bubar2021model} based on their epidemics model. We also found its better to offer vaccine priorities to young people to curb the disease and minimize the deaths when the basic reproduction number $R_0$ is moderately above one, which describes the most world during COVID-19. Such phenomenon has been ignored in cite{bubar2021model}.
As a common strategy of contagious disease containment, lockdown will inevitably weaken the economy. The ongoing COVID-19 pandemic underscores the trade-off arising from public health and economic cost. An optimal lockdown policy to resolve this trad
We apply optimal control theory to a generalized SEIR-type model. The proposed system has three controls, representing social distancing, preventive means, and treatment measures to combat the spread of the COVID-19 pandemic. We analyze such optimal
The recent global surge in COVID-19 infections has been fueled by new SARS-CoV-2 variants, namely Alpha, Beta, Gamma, Delta, etc. The molecular mechanism underlying such surge is elusive due to 4,653 non-degenerate mutations on the spike protein, whi
We propose and study a new mathematical model of the human immunodeficiency virus (HIV). The main novelty is to consider that the antibody growth depends not only on the virus and on the antibodies concentration but also on the uninfected cells conce
The pandemic of COVID-19 has caused severe public health consequences around the world. Many interventions of COVID-19 have been implemented. It is of great public health and societal importance to evaluate the effects of interventions in the pandemi