Age Dependent Epidemic Modeling of COVID-19 Outbreak in Kuwait, France, and Cameroon

Abstract

Revisiting the classical model by Ross and Kermack-McKendrick, the Susceptible−Infectious−Recovered (SIR) model used to formalize the COVID-19 epidemic, requires improvements which will be the subject of this article. The heterogeneity in the age of the populations concerned leads to considering models in age groups with specific susceptibilities, which makes the prediction problem more difficult. Basically, there are three age groups of interest which are, respectively, 0−19 years, 20−64 years, and >64 years, but in this article, we only consider two (20−64 years and >64 years) age groups because the group 0−19 years is widely seen as being less infected by the virus since this age group had a low infection rate throughout the pandemic era of this study, especially the countries under consideration. In this article, we proposed a new mathematical age-dependent (Susceptible−Infectious−Goneanewsusceptible−Recovered (SIGR)) model for the COVID-19 outbreak and performed some mathematical analyses by showing the positivity, boundedness, stability, existence, and uniqueness of the solution. We performed numerical simulations of the model with parameters from Kuwait, France, and Cameroon. We discuss the role of these different parameters used in the model; namely, vaccination on the epidemic dynamics. We open a new perspective of improving an age-dependent model and its application to observed data and parameters.

Keywords: COVID-19; SIR model; age-dependent modeling; demographic model; epidemic model.

Figure 1

Dependence of the case fatality rate (from cumulative deaths on the 20 May 2020) vs. median age of several countries in 2017 (from [1]). The area of a country circle is proportional to the number of cumulated deaths due to COVID-19 on the 20 May 2020, e.g., for the USA: 99,643 (in red).

Figure 2

Top left: COVID-19 percentage of death in France by age class [23]. Bottom left: Influence of age (curves with color coding) on COVID-19 hospitalizations in France in the extreme age classes [23]. Bottom right: age classes pyramid in 2020 in France (total population size: 65,273,512) [24].

Figure 3

Curves of COVID-19 weekly ICU admissions in Kuwait by age classes (two on the left and four on the right) and gender from 27 February 2020 to 9 March 2021.

Figure 4

Left: Distribution of cumulated confirmed cases of COVID-19 by age group and gender in Cameroon as of 23 June 2021 [25]. Right: Distribution of deaths due to COVID-19 infection by age group and gender in Cameroon as of 23 June 2021 (after [34]).

Figure 5

Age-dependent scheme for COVID-19 outbreak modeling.

Figure 6

Numerical simulation of the variables I₁ and I₂, R₁ and R₂, G₁ and G₂ for Kuwait.

Figure 7

Numerical simulation of the variables I₁ and I₂, R₁ and R₂, G₁ and G₂ for France.

Figure 8

Numerical simulation of the variables I₁ and I₂, R₁ and R₂, G₁, G₂ for Cameroon.

Figure 8

Numerical simulation of the variables I₁ and I₂, R₁ and R₂, G₁, G₂ for Cameroon.