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The main objective of this paper is to address the following question are the containment measures imposed by most of the world governments effective and sufficient to stop the epidemic of COVID-19 beyond the lock-down period? In this paper, we propose a mathematical model which allows us to investigate and analyse this problem. We show by means of the reproductive number, $\cal R_0$ that the containment measures appear to have slowed the growth of the outbreak. Nevertheless, these measures remain only effective as long as a very large