Modeling COVID-19 Pandemic by the \(\lambda\)ISR Volterra-Fredholm Integral Equation: A Case Study of South Africa
Journal of Advances in Mathematics and Computer Science · pp. 1–8 · Published 24 Feb 2023
10.9734/jamcs/2023/v38i41752Abstract
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].
References (6)
- 1 A global database of COVID-19 vaccinations [DOI]
- 2 Associations between blood type and COVID-19 infection, intubation, and death [DOI]
- 3 Association between ABO blood groups and COVID-19 infection, severity and demise: A systematic review and meta-analysis [DOI]
- 4 Some Powerful Techniques for Solving Nonlinear Volterra-Fredholm Integral Equations [DOI]
- 5 Journal of Applied Nonlinear Dynamics [DOI]
- 6 Generalized differential equation compartmental models of infectious disease transmission [DOI]
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