arXiv subjects

Abid Ali Lashari

Publications and source records attributed to Abid Ali Lashari.

3 recordsLinked to original sources

arXiv2024

Modelling the spread of two successive SIR epidemics on a configuration model network

We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one. The first epidemic is analysed through a bond percolation model, while the second epidemic is approximated by a three-type branching process in which the types of individuals depend on their position in the percolation clusters used for the first epidemic. This branching process approximation enables us to calculate, in the large population limit and conditional upon a large outbreak in the first epidemic, a threshold parameter and the probability of a large outbreak for the second epidemic. A second branching process approximation enables us to calculate the fraction of the population that are infected by such a second large outbreak. We illustrate our results through some specific cases which have appeared previously in the literature and show that our asymptotic results give good approximations for finite populations.

q-bio.PE↗

arXiv2020

The duration of an $SIR$ epidemic on a configuration model

We consider the spread of a supercritical stochastic SIR (Susceptible, Infectious, Recovered) epidemic on a configuration model random graph. We mainly focus on the final stages of a large outbreak and provide limit results for the duration of the entire epidemic, while we allow for non-exponential distributions of the infectious period and for both finite and infinite variance of the asymptotic degree distribution in the graph. Our analysis relies on the analysis of some subcritical continuous time branching processes and on ideas from first-passage percolation. As an application we investigate the effect of vaccination with an all-or-nothing vaccine on the duration of the epidemic. We show that if vaccination fails to prevent the epidemic, it often -- but not always -- increases the duration of the epidemic.

math.PR↗

arXiv2017

Analysis of a model for hepatitis C virus transmission that includes the effects of vaccination with waning immunity

This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments for individuals who are under treatment and those who have had vaccination against HCV infection. It is assumed that the immunity provided by the vaccine fades with time. The basic reproduction number, $R_0$, and the equilibrium solutions of the model are determined. The model exhibits the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever $R_0$ is less than unity. It is shown that the use of only a perfect vaccine can eliminate backward bifurcation completely. Furthermore, a unique endemic equilibrium of the model is proved to be globally asymptotically stable under certain restrictions on the parameter values. Numerical simulation results are given to support the theoretical predictions. [epidemiological model; equilibrium solutions; backward bifurcation; global asymptotic stability; Lyapunov function.]

q-bio.PE↗