Abstract
Countries affected by the coronavirus epidemic have reported many infected cases and deaths based on world health statistics. The crowding factor, which we named "crowding effects," plays a significant role in spreading the diseases. However, the introduction of vaccines marks a turning point in the rate of spread of coronavirus infections. Modeling both effects is vastly essential as it directly impacts the overall population of the studied region. To determine the peak of the infection curve by considering the third strain, we develop a mathematical model (susceptible–infected–vaccinated–recovered) with reported cases from August 01, 2021, till August 29, 2021. The nonlinear incidence rate with the inclusion of both effects is the best approach to analyze the dynamics. The model's positivity, boundedness, existence, uniqueness, and stability (local and global) are addressed with the help of a reproduction number. In addition, the strength number and second derivative Lyapunov analysis are examined, and the model was found to be asymptotically stable. The suggested parameters efficiently control the active cases of the third strain in Pakistan. It was shown that a systematic vaccination program regulates the infection rate. However, the crowding effect reduces the impact of vaccination. The present results show that the model can be applied to other countries' data to predict the infection rate.
Highlights
The acronym SARS stands for severe acute respiratory syndrome
Pfizer vaccines are for people aged 12 and up, while Johnson & Johnson, and Dynamical analysis of coronavirus disease with crowding effect, and vaccination
Rajagopal et al investigated the fractional-order model to predict the dynamics of coronavirus outbreaks [29]
Summary
The acronym SARS stands for severe acute respiratory syndrome. Initially, it was discovered in Asia in 2003. The virus was previously found in a wild animal, most likely a bat, and it was discovered in humans via tests conducted during a pneumonia outbreak in Wuhan It traveled all over the world, eventually reaching the USA on January 20, 2020. On COVID -19 vaccination, the spike proteins on the virus hold on to ACE2 and force the RNA into our cells, causing more COVID -19 virus to be produced. This process causes other cells to be infected. The immuned people can prevent the virus from spreading [21]
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