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IAENG International Journal of Applied Mathematics

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The COVID-19 pandemic has affected many people throughout the world. The objective of this research project was to find numerical solutions through the Gaussian Quadrature Method for the Volterra Integral Equation Model. The non-homogenous Volterra Integral Equation of the second kind is used to capture a broader range of disease distributions. Volterra Integral equation models are used in the context of applied mathematics, public health, and evolutionary biology. The mathematical models of this integral equation gave valid convergence results for the COVID-19 data for 3 countries Italy, South Africa and Brazil. The modeling of these countries was done using the Volterra Integral Equation, using the Gaussian Quadrature nodes. Inspired by the COVID-19 pandemic, the IRCD model included the number of initially infected individuals, the rate of infection, contact rate, death rate, fraction of recovered individuals, and the mean time an individual remains infected. This research investigated the feasibility of obtaining accurate convergence results for two models of the Volterra Integral Equation for the geographic locations of Italy, South Africa and Brazil. The IRCD model accounted for the infected rate, number of recovered, contact rate, and the death rate. The first 365 days of the pandemic were analyzed for the IRCD model. The ISR model accounted for the number of initially infected individuals, susceptible individuals, removed individuals, number of contacts per person, the recovery rate, and the total population. The ISR model specifically looked at COVID-19 in Brazil and South Africa for the first 300 days of the pandemic. Both models are mathematically and epidemiologically well posed.