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.
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.
ABSTRACT
This study presents a structure preserving nonstandard finite difference scheme to analyze a susceptible-infected-treatment-recovered (SITR) dynamical model of coronavirus 2019 (covid-19) with bimodal virus transmission in susceptible population. The underlying model incorporates the possible treatment measures as the emerging scenario of covid-19 vaccines. Keeping in view the fact that the real time data for covid-19 is updated at discrete time steps, we propose a new structure preserving numerical scheme for the proposed model. The proposed numerical scheme produces realistic solutions of the complex bi-modal SITR nonlinear model, converges unconditionally to steady states and reflects dynamical consistency with continuous sense of the model. The analysis of the model reveals that the model remains stable at the steady state points. The basic reproduction number Rcovid falls less than 1 when treatment rate is increased and disease will die out. On the other hand, it predicts that human population may face devastating effects of pandemic if the treatment measures are not strictly implemented.