We developed a computational tool to assess the risks of novel coronavirus outbreaks outside of China. We estimate the dependence of the risk of a major outbreak in a country from imported cases on key parameters such as: (i) the evolution of the cumulative number of cases in mainland China outside the closed areas; (ii) the connectivity of the destination country with China, including baseline travel frequencies, the effect of travel restrictions, and the efficacy of entry screening at destination; and (iii) the efficacy of control measures in the destination country (expressed by the local reproduction number $R_{\mathrm{loc}}$ ). We found that in countries with low connectivity to China but with relatively high $R_{\mathrm{loc}}$ , the most beneficial control measure to reduce the risk of outbreaks is a further reduction in their importation number either by entry screening or travel restrictions. Countries with high connectivity but low $R_{\mathrm{loc}}$ benefit the most from policies that further reduce $R_{\mathrm{loc}}$ . Countries in the middle should consider a combination of such policies. Risk assessments were illustrated for selected groups of countries from America, Asia, and Europe. We investigated how their risks depend on those parameters, and how the risk is increasing in time as the number of cases in China is growing.

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, which shows excellent agreement with results based on stochastic simulations. Furthermore, we analytically compute a new ${\mathcal{R}}_0$-like threshold quantity and an analytical relation between this and the final epidemic size. Additionally, we show that the pairwise model and the analytic results can be generalized to an arbitrary distribution of the infectious times, using integro-differential equations, and this leads to a general expression for the final epidemic size. By showing the rigorous link between non-Markovian dynamics and pairwise delay differential equations, we provide the framework for a more systematic understanding of non-Markovian dynamics.

A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R0, which is a threshold quantity for the stability of equilibria, is calculated. If $R_0$ < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if $R_0$ > 1, then an endemic equilibrium appears which is locally asymptotically stable. Applying a perma- nence theorem for infinite dimensional systems, we obtain that the disease is always present when $R_0$ > 1.

The management of COVID-19 appears to be a long-term challenge, even in countries that have managed to suppress the epidemic after their initial outbreak. In this paper, we propose a model predictive approach for the constrained control of a nonlinear compartmental model that captures the key dynamical properties of COVID-19. The control design uses the discrete-time version of the epidemic model, and it is able to handle complex, possibly time-dependent constraints, logical relations between model variables and multiple predefined discrete levels of interventions. A state observer is also constructed for the computation of non-measured variables from the number of hospitalized patients. Five control scenarios with different cost functions and constraints are studied through numerical simulations, including an output feedback configuration with uncertain parameters. It is visible from the results that, depending on the cost function associated with different policy aims, the obtained controls correspond to mitigation and suppression strategies, and the constructed control inputs are similar to real-life government responses. The results also clearly show the key importance of early intervention, the continuous tracking of the susceptible population and that of future work in determining the true costs of restrictive control measures and their quantitative effects.

Clarithromycin is a macrolide antibiotic widely used for eradication ofHelicobacter pyloriinfection, and thus resistance to this antibiotic is a major cause of treatment failure. Here, we present the results of a retrospective observational study of clarithromycin resistance (Cla-res) in 4744H. pylori-infected patients from Central Hungary. We use immunohistochemistry and fluorescence in situ hybridization on fixed gastric tissue samples to determineH. pyloriinfection and to infer Cla-res status, respectively. We correlate this information with macrolide dispensing data for the same patients (available through a prescription database) and develop a mathematical model of the population dynamics of Cla-resH. pyloriinfections. Cla-res is found in 5.5% of macrolide-naive patients (primary Cla-res), with no significant sex difference. The model predicts that this primary Cla-res originates from transmission of resistant bacteria in 98.7% of cases, and derives from spontaneous mutations in the other 1.3%. We find an age-dependent preponderance of female patients among secondary (macrolide-exposed) clarithromycin-resistant infections, predominantly associated with prior use of macrolides for non-eradication purposes. Our results shed light into the sources of primary resistant cases, and indicate that the growth rate of Cla-res prevalence would likely decrease if macrolides were no longer used for purposes other thanH. pylorieradication.

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.