Gergely Röst

Emergence of drug resistance: implications for antiviral control of pandemic influenza.

Given the danger of an unprecedented spread of the highly pathogenic avian influenza strain H5N1 in humans, and great challenges to the development of an effective influenza vaccine, antiviral drugs will probably play a pivotal role in combating a novel pandemic strain. A critical limitation to the use of these drugs is the evolution of highly transmissible drug-resistant viral mutants. Here, we develop a mathematical model to evaluate the potential impact of an antiviral treatment strategy on the emergence of drug resistance and containment of a pandemic. The results show that elimination of the wild-type strain depends crucially on both the early onset of treatment in indexed cases and population-level treatment. Given the probable delay of 0.5–1 day in seeking healthcare and therefore initiating therapy, the findings indicate that a single strategy of antiviral treatment will be unsuccessful at controlling the spread of disease if the reproduction number of the wild-type strain exceeds 1.4. We demonstrate the possible occurrence of a self-sustaining epidemic of resistant strain, in terms of its transmission fitness relative to the wild-type, and the reproduction number . Considering reproduction numbers estimated for the past three pandemics, the findings suggest that an uncontrollable pandemic is likely to occur if resistant viruses with relative transmission fitness above 0.4 emerge. While an antiviral strategy is crucial for containing a pandemic, its effectiveness depends critically on timely and strategic use of drugs.

Domain-decomposition method for the global dynamics of delay differential equations with unimodal feedback

The dynamics generated by the delay differential equation with unimodal feedback is studied. The existence of the global attractor is shown and bounds of the attractor are given. We find attractive invariant intervals and give sufficient conditions that guarantee that all solutions enter the domain where f′ is negative with respect to a positive equilibrium, so the results for delayed monotone feedback can be applied to describe the asymptotic behaviour of solutions. In particular, the existence of heteroclinic orbits from the trivial equilibrium to a periodic orbit oscillating around the positive equilibrium is established. Numerical examples using Nicholsons blowflies equation and the Mackey–Glass equation are provided to illustrate the main results.

Post-exposure prophylaxis during pandemic outbreaks

BackgroundWith the rise of the second pandemic wave of the novel influenza A (H1N1) virus in the current season in the Northern Hemisphere, pandemic plans are being carefully re-evaluated, particularly for the strategic use of antiviral drugs. The recent emergence of oseltamivir-resistant in treated H1N1 patients has raised concerns about the prudent use of neuraminidase inhibitors for both treatment of ill individuals and post-exposure prophylaxis of close contacts.MethodsWe extended an established population dynamical model of pandemic influenza with treatment to include post-exposure prophylaxis of close contacts. Using parameter estimates published in the literature, we simulated the model to evaluate the combined effect of treatment and prophylaxis in minimizing morbidity and mortality of pandemic infections in the context of transmissible drug resistance.ResultsWe demonstrated that, when transmissible resistant strains are present, post-exposure prophylaxis can promote the spread of resistance, especially when combined with aggressive treatment. For a given treatment level, there is an optimal coverage of prophylaxis that minimizes the total number of infections (final size) and this coverage decreases as a higher proportion of infected individuals are treated. We found that, when treatment is maintained at intermediate levels, limited post-exposure prophylaxis provides an optimal strategy for reducing the final size of the pandemic while minimizing the total number of deaths. We tested our results by performing a sensitivity analysis over a range of key model parameters and observed that the incidence of infection depends strongly on the transmission fitness of resistant strains.ConclusionOur findings suggest that, in the presence of transmissible drug resistance, strategies that prioritize the treatment of only ill individuals, rather than the prophylaxis of those suspected of being exposed, are most effective in reducing the morbidity and mortality of the pandemic. The impact of post-exposure prophylaxis depends critically on the treatment level and the transmissibility of resistant strains and, therefore, enhanced surveillance and clinical monitoring for resistant mutants constitutes a key component of any comprehensive plan for antiviral drug use during an influenza pandemic.

Generalization of Pairwise Models to non-Markovian Epidemics on Networks.

In this letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations (DDE), which shows excellent agreement with results based on explicit stochastic simulations of non-Markovian epidemics on networks. Furthermore, we analytically compute a new R0-like threshold quantity and an implicit analytical relation between this and the final epidemic size. In addition we show that the pairwise model and the analytic calculations can be generalized in terms of integro-differential equations to any distribution of the infectious period, and we illustrate this by presenting a closed form expression for the final epidemic size. By showing the rigorous mathematical link between non-Markovian network epidemics and pairwise DDEs, we provide the framework for a deeper and more rigorous understanding of the impact of non-Markovian dynamics with explicit results for final epidemic size and threshold quantities.

Dichotomy results for delay differential equations with negative Schwarzian derivative

Abstract We gain further insight into the use of the Schwarzian derivative to obtain new results for a family of functional differential equations including the famous Wright’s equation and the Mackey-Glass type delay differential equations. We present some dichotomy results, which allow us to get easily computable bounds of the global attractor. We also discuss related conjectures, and formulate new open problems.

Transmission Dynamics and Final Epidemic Size of Ebola Virus Disease Outbreaks with Varying Interventions

The 2014 Ebola Virus Disease (EVD) outbreak in West Africa was the largest and longest ever reported since the first identification of this disease. We propose a compartmental model for EVD dynamics, including virus transmission in the community, at hospitals, and at funerals. Using time-dependent parameters, we incorporate the increasing intensity of intervention efforts. Fitting the system to the early phase of the 2014 West Africa Ebola outbreak, we estimate the basic reproduction number as 1.44. We derive a final size relation which allows us to forecast the total number of cases during the outbreak when effective interventions are in place. Our model predictions show that, as long as cases are reported in any country, intervention strategies cannot be dismissed. Since the main driver in the current slowdown of the epidemic is not the depletion of susceptibles, future waves of infection might be possible, if control measures or population behavior are relaxed.

Global analysis for spread of infectious diseases via transportation networks

We formulate an epidemic model for the spread of an infectious disease along with population dispersal over an arbitrary number of distinct regions. Structuring the population by the time elapsed since the start of travel, we describe the infectious disease dynamics during transportation as well as in the regions. As a result, we obtain a system of delay differential equations. We define the basic reproduction number

Persistence, Permanence and Global Stability for an n -Dimensional Nicholson System

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