Mathematical models not only forecast the possible future but also is used to find hidden parameters of the COVID-19 pandemic. Numerical estimates can inform us of both goals. Still, the interdependencies of parameters stay obscure. Many numerical solutions have been proposed so far; however, the analytical relationship between the outbreak growth, decay and equilibrium are much less studied. In this study, we have employed both an equivalent agent-based model and a Susceptible-Exposed-Infected-Recovered (SEIR)-like model to prove that the growth rate can be determined analytically in terms of other model parameters, including contact tracing rate. We identify the most sensitive parameters as undocumented transmission rate and documentation ratio. Unfortunately, these are the parameters we have the least knowledge. We derived an identity that predicts the effectiveness of contact tracing in a country from observable parameters. We underline an unavoidable dilemma: that even in the case of high contact tracing, we cannot bring the outbreak to stalemate without applying substantial quarantine; however, some countries are benefiting from contact tracing. Besides, we have shown that the seemingly same parameters of the SEIR models and agent-based models are not equivalent. We propose a correction to bridge both models.
Background. Human behavior, economic activity, vaccination, and social distancing are inseparably entangled in epidemic management. This study aims to investigate the effects of various parameters such as stay-at-home restrictions, work hours, vaccination and social distance on the containment of pandemics such as COVID-19. Methods. To achieve this, we developed an agent-based model based on a time-dynamic graph with stochastic transmission events. The graph is constructed from a real-world social network. The graph's edges have been categorized into three categories: home, workplaces, and social environment. The conditions needed to mitigate the spread of wild-type (WT) COVID-19 and the delta variant have been analyzed. Our purposeful agent-based model has carefully executed tens of thousands of individual-based simulations. We propose simple relationships for the trade-offs between effective reproduction number (Re), transmission rate, work hours, vaccination, and stay at home restrictions. Results. For the WT, it has been found that a 13% increase in vaccination impacts the reproduction number, like the magnitude of decreasing nine hours of work to four and a single day of stay-at-home order. For the delta, 16% vaccination has the same effect. Also, since we can keep track of household and non-household infections, we observed that the change in household transmission rate does not significantly alter the Re. Household infections are not limited by transmission rate due to the high frequency of connections. For COVID-19's specifications, the Re depends on the non-household transmissions rate. Conclusions. Vaccination and transmission reduction are almost interchangeable. Without vaccination or teaching people how to lower their transmission probability significantly, changing work hours or weekend restrictions will only make people more frustrated
Background Human behaviour, economic activity, vaccination, and social distancing are inseparably entangled in epidemic management. This study aims to investigate the effects of various parameters such as stay-at-home restrictions, work hours, vaccination, and social distance on the containment of pandemics such as COVID-19. Methods To achieve this, we have developed an agent based model based on a time-dynamic graph with stochastic transmission events. The graph is constructed from a real-world social network. The edges of graph have been categorized into three categories: home, workplaces, and social environment. The conditions needed to mitigate the spread of wild-type COVID-19 and the delta variant have been analyzed. Our purposeful agent based model has carefully executed tens of thousands of individual-based simulations. We propose simple relationships for the trade-offs between effective reproduction number (Re), transmission rate, working hours, vaccination, and stay-at-home restrictions. Results We have found that the effect of a 13.6% increase in vaccination for wild-type (WT) COVID-19 is equivalent to reducing four hours of work or a one-day stay-at-home restriction. For the delta, 20.2% vaccination has the same effect. Also, since we can keep track of household and non-household infections, we observed that the change in household transmission rate does not significantly alter the Re. Household infections are not limited by transmission rate due to the high frequency of connections. For the specifications of COVID-19, the Re depends on the non-household transmissions rate. Conclusions Our findings highlight that decreasing working hours is the least effective among the non-pharmaceutical interventions. Our results suggest that policymakers decrease work-related activities as a last resort and should probably not do so when the effects are minimal, as shown. Furthermore, the enforcement of stay-at-home restrictions is moderately effective and can be used in conjunction with other measures if absolutely necessary.
The rapid spread of antibiotic-resistant pathogens has prompted drug combinations to maintain clinical efficacy and combat the development of resistance. Drugs interact to increase (synergistic) or decrease (antagonistic) the effect of the combined therapy. Furthermore, the interactions of the two drugs can change as the bacteria evolves from the wild type (WT) to the mutant type (MT). Experimental studies have shown that the evolution of resistance is impeded if drugs interact antagonistically in the WT. In contrast, other studies have shown that antagonistic interactions in the MT speed up the resistance's emergence. Theoretical works investigated the effect of WT drug interactions on resistance. A fundamental question is how the different combination of drug interactions in WT and the MT influences antimicrobial resistance. Here we analyze a mathematical model that captures any combination of drug interactions in WT and the MT. The novelty of this work is to examine the association between synergistic and antagonistic interaction of antibiotics for wild-type (sensitive bacteria) and mutants (resistant bacteria) on the growth rate of resistant strains. The most important contribution is to clarify that antagonistic interaction against the wild type has a more critical role in slowing the growth rate of resistant bacteria. The antagonistic interaction in the MT speeds up evolution but minimally. Our results suggest that it would be more appropriate to consider the nature of the drug interactions for the WT when designing combination therapy.
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