Sensitivity Analysis of COVID-19 Transmission Dynamics in Pakistan Using Mathematical Modelling

COVID-19 has profoundly impacted all countries' lives, social habits, and economies, resulting in a swift health system breakdown. This immense effect has caused worldwide research to assess its impact on various healthcare, socio-economic and demographic factors. This paper focuses on evaluating the impact of COVID-19 in Pakistan by adopting a mathematical model consisting of five population compartments: Susceptible (S), Vaccinated (V), Exposed (E), Infected (I), and Recovered (R) b y utilising COVID-19 data specific to Pakistan. The primary objective is to analyse the influence of various parameters within the model. Numerical simulations were obtained using the higher-order Runge-Kutta method for dependent variables and the basic reproduction number by varying the parameters. The sensitivity analysis was then performed to assess the effect of the parameters. From the analysis, it is revealed the key parameters, including death rate, vaccination rate, and vaccine wane rate are more sensitive to the proposed SVEIR model. The simulation of basic reproduction was also carried out by observing the simultaneous effect of the five parameters, which includes the probability of susceptibility to becoming infectious per contact, isolated infectious cases, infectious period, the average number of contacts per day per case and death rate. The simulations show that the death rate produces more variations in almost all classes of the population. Vaccination rate reveals a higher number of recovered populations and reduced infected populations, and vaccine wane rate is suitable for intermediate values of the selected interval. The basic reproduction number also remains significant for the combination of probability of susceptibility to becoming infectious per contact and death rate. These insights contribute to the understanding of the sensitivity of disease dynamics under the influence of various interaction parameters