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<p>Since the coronavirus COVID-19 is among the serious contagious diseases such as HIV and Influenza etc. That has lay down a huge encumbrance on economy, education and medical fields all over the world due to which countries with weak economy are facing severe economic problems. So in order to cope with this problem we have mathematically examined the generalized S (Susceptible) I (Infected) R (Recovered or Removed) (GSIR) non-linear COVID-19 epidemic model which is modified form of SIR model for the dynamical behavior of the infectious disease a novel coronavirus (COVID-19). In addition, the main hallmarks of the work are a novel signal flow graph to describe transmission of virus among the population, the calculation of equilibrium points and stability of the model shows that the model is stable. In this work, the (GSIR) nonlinear COVID-19 epidemic model’s dynamical behavior is based on a semi-analytical technique: variational iteration method (VIM). Our mathematical analyses and numerical solutions assist us that the feast of the virus may be controlled by maintaining social distance between infected and healthy individuals which is only possible by decreasing contact number between them. In this work the analytical solutions of GSIR model, numerical solutions and the practical scenario developed by coronavirus COVID-19 are totally converge to each other which facilitates the researchers to find some treatment and cure by using our mathematical formulations and predictions which shows the novelty of the work. Also, the analytical solution of the aforesaid mathematical model has been calculated with the help of computational software Maple code. At last, our numerical results comparison shows that initially the recovered or removed population is zero but the susceptible population is the greatest and the infected population exponentially rises. After some time, the susceptible population decreases and the infected, the recovered or removed population raises due to the increasing contact number between susceptible and infected population.</p>

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Mathematical Analysis of Generalized SIR Nonlinear Epidemic Model Using an Analytical Method

  • 期刊论文

  • 发表日期：

    2025年8月13日

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  • Jamshad Ahmad,
  • Umer Ghani,
  • Ehsan Ul Haq,
  • Qazi Mahmood Ul Hassan

摘要

Since the coronavirus COVID-19 is among the serious contagious diseases such as HIV and Influenza etc. That has lay down a huge encumbrance on economy, education and medical fields all over the world due to which countries with weak economy are facing severe economic problems. So in order to cope with this problem we have mathematically examined the generalized S (Susceptible) I (Infected) R (Recovered or Removed) (GSIR) non-linear COVID-19 epidemic model which is modified form of SIR model for the dynamical behavior of the infectious disease a novel coronavirus (COVID-19). In addition, the main hallmarks of the work are a novel signal flow graph to describe transmission of virus among the population, the calculation of equilibrium points and stability of the model shows that the model is stable. In this work, the (GSIR) nonlinear COVID-19 epidemic model’s dynamical behavior is based on a semi-analytical technique: variational iteration method (VIM). Our mathematical analyses and numerical solutions assist us that the feast of the virus may be controlled by maintaining social distance between infected and healthy individuals which is only possible by decreasing contact number between them. In this work the analytical solutions of GSIR model, numerical solutions and the practical scenario developed by coronavirus COVID-19 are totally converge to each other which facilitates the researchers to find some treatment and cure by using our mathematical formulations and predictions which shows the novelty of the work. Also, the analytical solution of the aforesaid mathematical model has been calculated with the help of computational software Maple code. At last, our numerical results comparison shows that initially the recovered or removed population is zero but the susceptible population is the greatest and the infected population exponentially rises. After some time, the susceptible population decreases and the infected, the recovered or removed population raises due to the increasing contact number between susceptible and infected population.