Formulation of the SVEIR Model for COVID-19 by incorporating Control Intervention in Pakistan

• Main Author: Kainat, Laghari
• Format: Thesis
• Language: English; English; English
• Published: UNIMAS 2025
• Subjects: QA75 Electronic computers. Computer science
• Online Access: http://ir.unimas.my/id/eprint/49886/

Like other countries around the world, Pakistan experienced a COVID-19 outbreak, starting from February 26, 2020, when the first two cases of COVID-19 were reported. To save the nation from this disease, the government of Pakistan took different strict measures. Along with the various aspects of the disease, including its epidemiology, transmission, clinical features, diagnosis, treatment, and prevention, it is widely accepted that mathematical models can be helpful to predict the occurrence of infectious diseases. However, the control interventions incorporating the Non-pharmaceutical interventions (NPI) measure for the current scenario in Pakistan, which include vaccination compartments, have not yet been identified for COVID-19. Therefore, the main objective of this study was to propose a new COVID-19 model by incorporating the vaccine factor to analyze the COVID-19 trends in Pakistan. In order to achieve the objective of research, a systematic process was followed, and an analogous existing model called STEQIR (Gill et al., 2020) was evaluated. Then, by using some modifications such as transitioning individuals from the susceptible population to a vaccinated population and by compartmental analysis, including the control intervention of the vaccine, a new model, namely the SVEIR (Susceptible, Vaccinated, Exposed, Infected, and Recovered) model, was derived. The proposed model is based on the assumption that Vaccination reduces the effective susceptible group, lowering the force of infection. The possibility of the analytical solution of the proposed SVEIR model was investigated. However, the analytical solution for the SVEIR model is quite tricky and impractical due to high non-linearity and the implicit nature of the governing equations. Therefore, the numerical solution of the proposed SVEIR model was computed using a higher-order Runge-Kutta method, which yields a stable solution of the SVEIR model. The numerical simulation of all five variables can project the outbreak well over the next few months. It was established that despite the large population of Pakistan, the measured maximum percentage error (MAPE) was in an acceptable range for all five variables that fell between 9.72 and 15.42, and the results were statistically significant at 90% and 95% confidence levels. The validation of the proposed SVEIR model was also done by comparing a benchmarking method (Gill, 2020), and it was shown that the SVEIR model performs better for the Pakistan COVID-19 data. To assess the variations caused by the working parameters involved in the SVEIR model, a sensitivity analysis was conducted, and the impact of all parameters involved in the SVEIR model was analyzed. From the analysis, it was revealed that among all the parameters, the transmission rate, death rate ε, and the average number of contacts per day per case are sensitive as they produce more variations in almost all population classes. Finally, the simulation of the basic reproduction number R0 regarding sensitive parameters and values was obtained. It was pointed out that the R0 remains more dominant for the probability of susceptibility β, becoming infectious per contact, and death rate; for other parameters, it remains less than 1. The outcome and findings of this study may be essential for policymakers and public health officials in making informed decisions and formulating effective strategies to govern and mitigate the spread of COVID-19. The understanding gained from this research may guide targeted strategies, promote efficient resource allocation, and contribute to the continuing efforts to mitigate and control the COVID-19 pandemic in Pakistan. Future research may focus on extending the proposed SVEIR model by incorporating additional factors, such as the efficacy of various vaccination techniques, the effects of non-pharmaceutical therapies, demographic characteristics, economic determinants, and seasonal variations in environmental and weather conditions weather.