Abstract
Since the beginning of the COVID-19 pandemic, vaccination has been the main strategy to contain the spread of the coronavirus. However, with the administration of many types of vaccines and the constant mutation of viruses, the issue of how effective these vaccines are in protecting the population is raised. This work aimed to present a mathematical model that investigates the imperfect vaccine and finds the additional measures needed to help reduce the burden of disease. We determine the R0 threshold of disease spread and use stability analysis to determine the condition that will result in disease eradication. We also fitted our model to COVID-19 data from Morocco to estimate the parameters of the model. The sensitivity analysis of the basic reproduction number, with respect to the parameters of the model, is simulated for the four possible scenarios of the disease progress. Finally, we investigate the optimal containment measures that could be implemented with vaccination. To illustrate our results, we perform the numerical simulations of optimal control.
Highlights
Since the beginning of the ongoing COVID-19 pandemic, the world has been racing to develop a vaccination that helps protect the populations around the world and bring human life to a normal status
The basic reproduction number R0 is the average number of persons in a susceptible population that one person infected with COVID-19 is expected to infect, and it is calculated using the generation matrix approach [26]
When imperfect vaccination is administered to a population, there is a need to find the optimal approach to use it in order to reduce the burden of the disease in the population
Summary
Since the beginning of the ongoing COVID-19 pandemic, the world has been racing to develop a vaccination that helps protect the populations around the world and bring human life to a normal status. These facts make the question of the efficacy of vaccines legitimate and need to be investigated This problem was investigated using mathematical modeling to study the possible measure that needed to be implemented to reduce the impact of an imperfect vaccine. In the case of imperfect vaccination, the authors showed that a critical proportion of the population needed vaccination Another delay model with distributed delay [7] and the delay model with a generalized incidence function were studied in [8]. The aim was to study the dynamics of this model and present the possible control measures that need to be implemented in order to reduce the impact of the vaccine’s imperfection.
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