Un modèle épidémique dans un environnement qui oscille rapidement

On étudie un modèle épidémique non linéaire de type S-I-R dans l'approximation de champ moyen lorsque le taux de contact oscille rapidement de manière périodique. La taille finale de l'épidémie est proche de celle que l'on obtient en remplaçant le taux de contact par sa moyenne. Une approximation de la correction peut être calculée analytiquement lorsque la reproductivité de l'épidémie est proche de 1. La correction, qui peut être positive ou négative, est proportionnelle à la fois à la période des oscillations et à la fraction initiale de personnes infectées

Un modèle épidémique dans un environnement qui oscille rapidement

On étudie un modèle épidémique non linéaire de type S-I-R dans l'approximation de champ moyen lorsque le taux de contact oscille rapidement de manière périodique. La taille finale de l'épidémie est proche de celle que l'on obtient en remplaçant le taux de contact par sa moyenne. Une approximation de la correction peut être calculée analytiquement lorsque la reproductivité de l'épidémie est proche de 1. La correction, qui peut être positive ou négative, est proportionnelle à la fois à la période des oscillations et à la fraction initiale de personnes infectées

Viral Load Monitoring of Antiretroviral Therapy, cohort viral load and HIV transmission in Southern Africa: A Mathematical Modelling Analysis

In low-income settings, treatment failure is often identified using CD4 cell count monitoring. Consequently, patients remain on a failing regimen, resulting in a higher risk of transmission. We investigated the benefit of routine viral load monitoring for reducing HIV transmission

From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, $R_e$, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase $R_e$ and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of $R_e$ when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl

La sélection du taux de transmission des parasites par l'absence périodique de l'hôte

traduction en françaisTaduction française de l'aticle paru dans la revue Evolutionary Ecology (DOI 10.1007/s10682-010-9387-0 )In diesem Artikel wird die Auswirkung der periodischen Abwesenheit der Wirtspflanze auf die Entwicklung der Übertragungsraten von Pathogenen unter Verwendung von Maximierungstechniken von R0 untersucht. Die physiologische Folge einer erhöhten Übertragungsrate kann entweder eine erhöhte Virulenz sein (Kompromiss zwischen Übertragung und Virulenz) oder ein verringertes Überleben zwischen den Jahreszeiten (Kompromiss zwischen Übertragung und Überleben). Die Ergebnisse zeigen, dass der Typ des Kompromisses die Richtung der Auswahl bestimmt. Mit einem Kompromiss zwischen Übertragung und Virulenz wählen längere Abwesenheitszeiten vom Host die höheren Übertragungsraten aus. Mit einem Kompromiss zwischen Übertragung und Überleben zwischen den Jahreszeiten werden aber schwächere Übertragungsraten ausgewählt. Die Tatsache, dass für den Kompromiss zwischen Übertragung und Virulenz die beiden Kompromissparameter während der Anwesenheit der Wirtpflanze auftreten, während für den Kompromiss zwischen Übertragung und Überleben einer während der Anwesenheit der Wirtpflanze (Übertragung) und das andere (Überleben) während der Abwesenheit der Wirtpflanze ist die Hauptursache für diesen Unterschied in der Richtung der Selektion. Außerdem scheint die Abwesenheitszeit der Wirtpflanze der bestimmende Faktor für die Übertragungsrate des Erregers zu sein. Ein Vergleich von pflanzenpathologischen Systemen mit kontrastierenden biologischen Merkmalen zeigt, dass Pflanzenpathogene in der Luft bei längerer Abwesenheit vom Wirt anders reagieren als bodengetragene Pflanzenpathogene.Cet article explore l'effet de l'absence périodique de l'hôte sur l'évolution des taux de transmission des agents pathogènes en utilisant des techniques de maximisation de R0. La conséquence physiologique d'un taux de transmission accru peut être soit une virulence accrue (compromis entre transmission et virulence), soit une réduction de la survie entre les saisons (compromis entre transmission et survie). Les résultats révèlent que le type de compromis détermine la direction de la sélection, avec des périodes plus longues d'absence de l'hôte qui sélectionnent des taux de transmission plus élevés avec un compromis entre la transmission et la virulence, mais des taux de transmission plus faibles avec un compromis entre la transmission et la survie entre les saisons. Le fait que, pour le compromis entre transmission et virulence, les deux paramètres de compromis interviennent pendant la présence de l'hôte, alors que pour le compromis transmission-survie, l'un opère pendant la présence de l'hôte (transmission) et l'autre (survie) pendant la période d'absence de l'hôte, est la principale cause de cette différence dans le sens de la sélection. De plus, la période d'absence de l'hôte semble être le facteur déterminant du taux de transmission du pathogène. La comparaison de systèmes phytopathologiques qui présentent des caractéristiques biologiques contrastées suggère que les agents pathogènes des plantes présents dans l'air réagissent différemment à des périodes d'absence plus longues de l'hôte que les agents pathogènes des plantes transmis par le sol

A model of population dynamics of TB in a prison system and application to South Africa

BACKGROUND: Tuberculosis (TB) continues to spread in South African prisons in particular, as prisons are over-capacitated and have poor ventilation. The awaiting trial detainees are not screened on admission and are at high risk of getting infected with TB. RESULTS: We propose a compartmental model to describe the population dynamics of TB disease in prisons. Our model considers the inflow of susceptible, exposed and TB infectives into the prison population. Removal of individuals out of the prison population can be either by death or by being released from prison, as compared to a general population in which removal is only by death. We describe conditions, including non-inflow of infectives into the prison, which will ensure that TB can be eradicated from the prison population. The model is calibrated for the South African prison system, by using data in existing literature. The model can be used to make quantitative projections of TB prevalence and to measure the effect of interventions. Illustrative simulations in this regard are presented. The model can be used for other prison populations too, if data is available to calculate the model parameters. CONCLUSIONS: Various simulations generated with our model serve to illustrate how it can be utilized in making future projections of the levels of prevalence of TB, and to quantify the effect of interventions such as screening, treatment or reduction of transmission parameter values through improved living conditions for inmates. This makes it particularly useful as there are various targets set by the World Health Organization and by governments, for reduction of TB prevalence and ultimately its eradication. Towards eradication of TB from a prison system, the theorem on global stability of the disease-free state is a useful indicator

Periodic Host Absence Can Select for Higher or Lower Parasite Transmission Rates

This paper explores the effect of discontinuous periodic host absence on the evolution of pathogen transmission rates by using Ro maximisation techniques. The physiological consequence of an increased transmission rate can be either an increased virulence, i.e. there is a transmission-virulence trade-off or ii) a reduced between season survival, i.e. there is a transmission-survival trade-off. The results reveal that the type of trade-off determines the direction of selection, with relatively longer periods of host absence selecting for higher transmission rates in the presence of a trade-off between transmission and virulence but lower transmission rates in the presence of a trade-of between transmission and between season survival. The fact that for the transmission-virulence trade-off both trade-off parameters operate during host presence whereas for the transmission-survival trade-off one operates during host presence (transmission) and the other (survival) during the period of host absence is the main cause for this difference in selection direction. Moreover, the period of host absence seems to be the key determinant of the pathogens transmission rate. Comparing plant patho-systems with contrasting biological features suggests that airborne plant pathogen respond differently to longer periods of host absence than soil-borne plant pathogens

Treatment as prevention: preparing the way

Potent antiretroviral therapy (ART) reduces mortality and morbidity in people living with HIV by reducing viral load and allowing their immune systems to recover. The reduction in viral load soon after starting ART has led to the hypothesis that early and widespread ART could prevent onward transmission and therefore eliminate the HIV epidemic in the long term. While several authors have argued that it is feasible to use HIV treatment as prevention (TasP), provided treatment is started sufficiently early, others have reasonably drawn attention to the many operational difficulties that will need to be overcome if the strategy is to succeed in reducing HIV transmission. Furthermore, international public health policy must be based on more than theoretical studies, no matter how appealing. Community randomized controlled trials provide the gold standard for testing the extent to which early treatment reduces incidence, but much still needs to be understood and the immediate need is for operational studies to explore the practical feasibility of this approach. Here, we examine some of the issues to be addressed, the obstacles to be overcome, and strategies that may be necessary if TasP is to be effective. Studies of this kind will provide valuable information for the design of large-scale trials, as well as essential information that will be needed if early treatment is to be incorporated into public health policy

Expanding ART for Treatment and Prevention of HIV in South Africa: Estimated Cost and Cost-Effectiveness 2011-2050

Background: Antiretroviral Treatment (ART) significantly reduces HIV transmission. We conducted a cost-effectiveness analysis of the impact of expanded ART in South Africa. Methods: We model a best case scenario of 90% annual HIV testing coverage in adults 15-49 years old and four ART eligibility scenarios: CD4 count <200 cells/mm3(current practice), CD4 count <350, CD4 count <500, all CD4 levels. 2011-2050 outcomes include deaths, disability adjusted life years (DALYs), HIV infections, cost, and cost per DALY averted. Service and ART costs reflect South African data and international generic prices. ART reduces transmission by 92%. We conducted sensitivity analyses. Results: Expanding ART to CD4 count <350 cells/mm3prevents an estimated 265,000 (17%) and 1.3 million (15%) new HIV infections over 5 and 40 years, respectively. Cumulative deaths decline 15%, from 12.5 to 10.6 million; DALYs by 14% from 109 to 93 million over 40 years. Costs drop $504 million over 5 years and$3.9 billion over 40 years with breakeven by 2013. Compared with the current scenario, expanding to <500 prevents an additional 585,000 and 3 million new HIV infections over 5 and 40 years, respectively. Expanding to all CD4 levels decreases HIV infections by 3.3 million (45%) and costs by $10 billion over 40 years, with breakeven by 2023. By 2050, using higher ART and monitoring costs, all CD4 levels saves$0.6 billion versus current; other ART scenarios cost $9-194 per DALY averted. If ART reduces transmission by 99$17.5 billion. Sensitivity analyses suggest that poor retention and predominant acute phase transmission reduce DALYs averted by 26% and savings by 7%. Conclusion: Increasing the provision of ART to <350 cells/mm3 may significantly reduce costs while reducing the HIV burden. Feasibility including HIV testing and ART uptake, retention, and adherence should be evaluated