Epidemiological Modeling on Networks

Abdoulaye Ali Ibrahima; Nakolemda Roger; Aboussaghid Alkabouss Sakha

Abdoulaye Ali Ibrahima Department of Exact Sciences, Faculty of Science and Technology, André Salifou University, Zinder, Niger
Nakolemda Roger Norbert ZONGO Univerty, Energy Research and Spase Meteorology Laboratory, Koudougou, Burkina Faso
Aboussaghid Alkabouss Sakha Department of Exact Sciences, Faculty of Science and Technology, André Salifou University, Zinder, Niger

Keywords: Epidemic, SIR, a compartmentalized model, heterogeneity, Networks

Abstract

The world is facing health crises which have caused a lot of material and human damage. Modeling epidemics allows us to have control over the evolution and spread of the disease as well as its mode of operation. The susceptible-infected-recovered (SIR) mass action model is the basic model in mathematical epidemiology but it does not take into account heterogeneity of contacts.. However, the rate of contact between people is heterogeneous; it depends from one person to another. In this study we will introduce a compartmentalized model based on the edges and which takes into account the heterogeneity of the contacts. However, we will end up with a differential equation whose resolution of the system allows us to see the equilibrium points and the stability of the disease. We also introduce numerical simulations on different types of graphs to see the spread of the disease on the way in which contact rates are distributed.