Energy Landscapes and Non-Archimedean Pseudo- Differential Operators as Tools for Studying the Spreading of Infectious Diseases in a Situation of Extreme Social Isolation

Abstract

In this article, we introduce a new type of pseudo-differential equations naturally connected with non-archimedean pseudo-differential operators and whose symbols are new classes of negative definite functions in the p-adic context and in arbitrary dimension. These equations are proposed as a mathematical models to study the spreading of infectious diseases (say COVID-19) through a random walk on a complex energy landscape and taking into account social clusters in a situation of extreme social isolation.