Analysis of a Co-Epidemic Model

Abstract

Solutions to systems of differential equations which model disease transmission are of particular use and importance to epidemiologists who wish to study effective means to slow and prevent the spread of disease. In this paper, we examine a system that models two related diseases within a population, which is of particular importance to those studying co-infection and partial cross-immunity phenomena. Criteria for stability of equilibria are improved upon from previous research by Long, Vaidya, and Brandeau (2008).

Studies on the basic reproduction number in stochastic epidemic models with random perturbations

“…In the deterministic epidemic models, the disease-free equilibrium points are locally asymptotically stable if the reproduction number is less than unity. In contrast, the endemic equilibrium point is locally asymptotically stable if the reproduction number exceeds unity (see [ 23 ]). For the SEIR model, assume and for any t , and for the models SIS and SIR, .…”

Limits of Compartmental Models and New Opportunities for Machine Learning: A Case Study to Forecast the Second Wave of COVID-19 Hospitalizations in Lombardy, Italy

“…q)S(I + θ A) 0 0 βc(t)qS(I + θ A) + (δ I (t)+ I + γ I + α)I σ(ρ − 1)E + γ A A δ q + q E q − q E q − I I + (δ L + γ L + α)L −δ I (t)I − δ q E q − δ L L + (γ H + α)HConsidering the following hypothesis regarding the Disease-Free Equilibrium (DFE), which is defined as the point at which no disease is present in the population,[47]:DFE = (s * , 0, • • • , 0) it follows that S = dS dt = −(βc(t) + c(t)q(1 − β))S(I + θ A) + λS q |DFE = 0 ⇒ −(βc(t) + c(t)q(1 − β))s * (0) + λ0 = 0…”