Modeling COVID-19 Pandemic by the \(\lambda\)ISR Volterra-Fredholm Integral Equation: A Case Study of South Africa

Abstract

Inspired by the COVID-19 pandemic, this paper investigates the feasibility of obtaining good convergence results for a nonhomogeneous Volterra-Fredholm integral equation model of the second kind. Volterra-Fredholm integral equations are often used to model infection and recovery of diseases in a population and can be used to model a pandemic or an endemic. This model uses a Volterra-Fredholm integral equation of the second kind to predict the number of individuals recovered from the COVID-19 pandemic in South Africa. The integral model was approximated by using the Gaussian Quadrature Method. The \(\lambda\)ISR model accounts for many variables of the pandemic including the number of initially infected individuals I0, susceptible individuals S0, and removed individuals R0. It also accounts for the initial recovery rate \(\gamma\), the infectivity of the virus \(\beta\) , removal rate \(\mu\) , and the total population of South Africa N. In addition to these, we also considered blood type S (x), and the rh factor \(\lambda\)(x) .
 The model was constructed in “person-days,” which is the combined variable of time (t, days) and the number of individuals (x). Specific blood types and presence of the rh factor have been shown to have varying susceptibility to infection and severity of infection (requiring intubation), therefore this was an important parameter for this model [1,2].

An integral equation approach for long COVID-19

“…Each of these variables was included in a multiple regression analysis to verify each variable's significance and the significant variables were added to the Volterra-Fredholm Integral LC Model. The LC (Long COVID) model was modified from the COVID-19 models previously built by one of the authors [2,3] . The model also includes the infection rate 𝛾.…”