Julien Arino

Spread of a Novel Influenza A (H1N1) Virus via Global Airline Transportation

International air travelers departing from Mexico in March and April 2009 were unknowingly transporting a novel influenza A (H1N1) virus around the world. The purpose of this analysis was to show h...

GLOBAL RESULTS FOR AN EPIDEMIC MODEL WITH VACCINATION THAT EXHIBITS BACKWARD BIFURCATION

Vaccination of both newborns and susceptibles is included in a transmission model for a disease that confers immunity. The interplay of the vaccination strategy together with the vaccine efficacy and waning is studied. In particular, it is shown that a backward bifurcation leading to bistability can occur. Under mild parameter constraints, compound matrices are used to show that each orbit limits to an equilibrium. In the case of bistability, this global result requires a novel approach since there is no compact absorbing set.

A multi-city epidemic model

Some analytical results are given for a model that describes the propagation of a disease in a population of individuals who travel between n cities. The model is formulated as a system of 2n 2 ordinary differential equations, with terms accounting for disease transmission, recovery, birth, death, and travel between cities. The mobility component is represented as a directed graph with cities as vertices and arcs determined by outgoing (or return) travel. An explicit formula that can be used to compute the basic reproduction number, {\cal R}_0 , is obtained, and explicit bounds on {\cal R}_0 are determined in the case of homogeneous contacts between individuals within each city. Numerical simulations indicate that {\cal R}_0 is a sharp threshold, with the disease dying out if {\cal R}_0 1 .

Simple models for containment of a pandemic

Stochastic simulations of network models have become the standard approach to studying epidemics. We show that many of the predictions of these models can also be obtained from simple classical deterministic compartmental models. We suggest that simple models may be a better way to plan for a threatening pandemic with location and parameters as yet unknown, reserving more detailed network models for disease outbreaks already underway in localities where the social networks are well identified. We formulate compartmental models to describe outbreaks of influenza and attempt to manage a disease outbreak by vaccination or antiviral treatment. The models give an important prediction that may not have been noticed in other models, namely that the number of doses of antiviral treatment required is extremely sensitive to the number of initial infectives. This suggests that the actual number of doses needed cannot be estimated with any degree of reliability. The model is applicable to pre-epidemic vaccination, such as annual vaccination programs in anticipation of an ‘ordinary’ influenza outbreak with limited drift, and as a combination of treatment both before and during an epidemic.

A model for influenza with vaccination and antiviral treatment

Compartmental models for influenza that include control by vaccination and antiviral treatment are formulated. Analytic expressions for the basic reproduction number, control reproduction number and the final size of the epidemic are derived for this general class of disease transmission models. Sensitivity and uncertainty analyses of the dependence of the control reproduction number on the parameters of the model give a comparison of the various intervention strategies. Numerical computations of the deterministic models are compared with those of recent stochastic simulation influenza models. Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models.

Effect of media-induced social distancing on disease transmission in a two patch setting.

Abstract We formulate an SIS epidemic model on two patches. In each patch, media coverage about the cases present in the local population leads individuals to limit the number of contacts they have with others, inducing a reduction in the rate of transmission of the infection. A global qualitative analysis is carried out, showing that the typical threshold behavior holds, with solutions either tending to an equilibrium without disease, or the system being persistent and solutions converging to an endemic equilibrium. Numerical analysis is employed to gain insight in both the analytically tractable and intractable cases; these simulations indicate that media coverage can reduce the burden of the epidemic and shorten the duration of the disease outbreak.

The Basic Reproduction Number in a Multi-city Compartmental Epidemic Model

A directed graph with cities as vertices and arcs determined by outgoing (or return) travel represents the mobility component in a population of individuals who travel between n cities. A model with 4 epidemiological compartments in each city that describes the propagation of a disease in this population is formulated as a system of 4n 2 ordinary dieren tial equations. Terms in the system account for disease transmission, latency, recovery, temporary immunity, birth, death, and travel between cities. The basic reproduction number R0 is determined as the spectral radius of a nonnegative matrix product, and easily computable bounds on R0 are obtained.

Global Public Health Implications of a Mass Gathering in Mecca, Saudi Arabia During the Midst of an Influenza Pandemic

BACKGROUND Every year millions of pilgrims from around the world gather under extremely crowded conditions in Mecca, Saudi Arabia to perform the Hajj. In 2009, the Hajj coincided with influenza season during the midst of an influenza A (H1N1) pandemic. After the Hajj, resource-limited countries with large numbers of traveling pilgrims could be vulnerable, given their limited ability to purchase H1N1 vaccine and capacity to respond to a possible wave of H1N1 introduced via returning pilgrims. METHODS We studied the worldwide migration of pilgrims traveling to Mecca to perform the Hajj in 2008 using data from the Saudi Ministry of Health and international air traffic departing Saudi Arabia after the 2008 Hajj using worldwide airline ticket sales data. We used gross national income (GNI) per capita as a surrogate marker of a countrys ability to mobilize an effective response to H1N1. RESULTS In 2008, 2.5 million pilgrims from 140 countries performed the Hajj. Pilgrims (1.7 million) were of international (non-Saudi) origin, of which 91.0% traveled to Saudi Arabia via commercial flights. International pilgrims (11.3%) originated from low-income countries, with the greatest numbers traveling from Bangladesh (50,419), Afghanistan (32,621), and Yemen (28,018). CONCLUSIONS Nearly 200,000 pilgrims that performed the Hajj in 2008 originated from the worlds most resource-limited countries, where access to H1N1 vaccine and capacity to detect and respond to H1N1 in returning pilgrims are extremely limited. International efforts may be needed to assist resource-limited countries that are vulnerable to the impact of H1N1 during the 2009 to 2010 influenza season.

Infectious disease surveillance and modelling across geographic frontiers and scientific specialties.

Infectious disease surveillance for mass gatherings (MGs) can be directed locally and globally; however, epidemic intelligence from these two levels is not well integrated. Modelling activities related to MGs have historically focused on crowd behaviours around MG focal points and their relation to the safety of attendees. The integration of developments in internet-based global infectious disease surveillance, transportation modelling of populations travelling to and from MGs, mobile phone technology for surveillance during MGs, metapopulation epidemic modelling, and crowd behaviour modelling is important for progress in MG health. Integration of surveillance across geographic frontiers and modelling across scientific specialties could produce the first real-time risk monitoring and assessment platform that could strengthen awareness of global infectious disease threats before, during, and immediately after MGs. An integrated platform of this kind could help identify infectious disease threats of international concern at the earliest stages possible; provide insights into which diseases are most likely to spread into the MG; help with anticipatory surveillance at the MG; enable mathematical modelling to predict the spread of infectious diseases to and from MGs; simulate the effect of public health interventions aimed at different local and global levels; serve as a foundation for scientific research and innovation in MG health; and strengthen engagement between the scientific community and stakeholders at local, national, and global levels.

A metapopulation model for malaria with transmission-blocking partial immunity in hosts

A metapopulation malaria model is proposed using SI and SIRS models for the vectors and hosts, respectively. Recovered hosts are partially immune to the disease and while they cannot directly become infectious again, they can still transmit the parasite to vectors. The basic reproduction number