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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. [ABSTRACT FROM AUTHOR]

In this paper we propose a three-dimensional numerical study of the coastal currents produced by the wave motion in the area opposite the Cetraro harbour (Italy), during the most significant wave event for the coastal sediment transport. The aim of the present study is the characterization of the current patterns responsible for the siltation that affects the harbour entrance area and the assessment of a project solution designed to limit this phenomenon. The numerical simulations are carried out by a three-dimensional non-hydrostatic model that is based on the Navier–Stokes equations expressed in integral and contravariant form on a time-dependent curvilinear coordinate system, in which the vertical coordinate moves in order to follow the free surface variations. The numerical simulations are carried out in two different geometric configurations: a present configuration, that reproduces the geometry of the coastal defence structures currently present in the harbour area and a project configuration, which reproduces the presence of a breakwater designed to modify the coastal currents in the area opposite the harbour entrance. [ABSTRACT FROM AUTHOR]

The article provides information on the proceedings of the symposium on the numerical treatment of ordinary differential equations, integral and integro-differential equations, convened by the Provisional International Computation Centre, in Rome, Italy from September 20 to 24, 1960.