SIR-based model with multiple imperfect vaccines
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Abstract
Since the introduction of vaccination in the current COVID-19 outbreak, many countries have approved and implemented vaccination campaigns to mitigate and ultimately curtail the pandemic. Several types of vaccines have been proposed and many of them have finally been approved and used in different countries. The different types of vaccines have different vaccine parameters, and therefore, this situation induces the necessity of modeling mathematically the scenario of multiple imperfect vaccines. In this paper, we introduce a SIR-based model considering different vaccines, and study the basic properties of the model, including the stability of the Disease-Free Equilibrium (DFE), which is locally asymptotically stable if the reproduction number is less than 1. A sequence of further results aims to enumerate the conditions where the reproduction number can be decreased (or increased). Two important mathematical propositions indicate that in general vaccination might not be enough to contain an outbreak and that the addition of new vaccines could be counterproductive if the leakiness parameter is greater than a threshold η . This model, despite its simplicity, was validated with data of the COVID-19 pandemic in five countries: Israel, Chile, Germany, Lithuania, and Czech Republic, observing that improvements for the vaccine campaigns can be suggested by the developed theory.
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SciScore for 10.1101/2021.05.07.21256860: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
Ethics not detected. Sex as a biological variable not detected. Randomization not detected. Blinding not detected. Power Analysis not detected. Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:Similar cases can be found in the literature, and therefore, it is important to consider that the compartmental model usually presents limitations for long-term prediction (even more than two months). Despite it, parameter estimation with the data is needed …
SciScore for 10.1101/2021.05.07.21256860: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
Ethics not detected. Sex as a biological variable not detected. Randomization not detected. Blinding not detected. Power Analysis not detected. Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:Similar cases can be found in the literature, and therefore, it is important to consider that the compartmental model usually presents limitations for long-term prediction (even more than two months). Despite it, parameter estimation with the data is needed to validate this model, even when further considerations will be added to improve the quality of the fittings. COVID-19 motivates the generalization of the VSIR model with multiple vaccines, but instead of only focusing on this disease, we provided a more general preliminary model, but excluding the compartments of the extended models such as SEIR and SIRD. In this manner, our model attempts to use only the necessary compartments to extend the SIR model with multiple types of vaccines. However, the addition of E, D and other compartments, time-dependent parameters, and specific compartments for one and two doses would improve the model for the sole study of the COVID-19 pandemic. Theoretical analysis showed two important results. Could the vaccination itself manage to eliminate the outbreak? Proposition 4 and its general version 5 provide a negative answer for this question: if the reproduction number and the leakiness of the vaccine are high enough it is impossible to reach ℛc < 1, even with a very high vaccination rate. At the beginning of the pandemic, Billah, Mamun Mian, and Nuruzzaman Khan [5] estimated a summary for the reproductive number, which was 2.87. In this manner, vaccines with εL higher than 0.34843 might re...
Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
Results from rtransparent:- Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
- No funding statement was detected.
- No protocol registration statement was detected.
Results from scite Reference Check: We found no unreliable references.
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