Quantitative Biology

2-colored best match graphs (2-BMGs) form a subclass of sink-free bi-transitive graphs that appears in phylogenetic combinatorics. There, 2-BMGs describe evolutionarily most closely related genes between a pair of species. They are explained by a unique least resolved tree (LRT). Introducing the concept of support vertices we derive an O(|V|+|E| log 2 |V|) -time algorithm to recognize 2-BMGs and to construct its LRT. The approach can be extended to also recognize binary-explainable 2-BMGs with the same complexity. An empirical comparison emphasizes the efficiency of the new algorithm.

Though pandemic preparedness has been a focus of public health planning for centuries, during which our understanding of infectious disease dynamics has grown, our methodologies for managing outbreaks have remained relatively unchanged. We propose leveraging this history to identify opportunities for actual progress. We contrast current plans with historical outbreak control measures and isolate how the complexities of a modern era yield additional challenges in how best to anticipate and mitigate outbreaks. We analyze a diversity of publicly available modern preparedness plans against the context of a historically-based fictional outbreak control strategy described in Defoe's A Journal of the Plague Year (published 1720). We identify themes in preparedness planning that remain unchanged from historical settings even though they continue to be actively evaluated in planning efforts. More importantly, we isolate critical modern challenges in preparedness planning that remain predominantly unsolved. These modern, unsolved issues offer best avenues for meaningful improvement. Shifting our planning efforts to focus on identified novel issues may greatly strengthen our local- to global- capacity to deal with infectious threats.

Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introduce a disease model with an underlying genotype network to account for two important mechanisms. One, the disease can mutate along network pathways as it spreads in a host population. Two, the genotype network allows us to define a genetic distance across strains and therefore to model the transcendence of immunity often observed in real world pathogens. We study the emergence of epidemics in this model, through its epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases, large scale fluctuations, sequential epidemic transitions, as well as localization around specific strains of the associated pathogen. More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the "one disease equals one pathogen" paradigm.

The generalized logistic equation is used to interpret the COVID-19 epidemic data in several countries: Austria, Switzerland, the Netherlands, Italy, Turkey and South Korea. The model coefficients are calculated: the growth rate and the expected number of infected people, as well as the exponent indexes in the generalized logistic equation. It is shown that the dependence of the number of the infected people on time is well described on average by the logistic curve (within the framework of a simple or generalized logistic equation) with a determination coefficient exceeding 0.8. At the same time, the dependence of the number of the infected people per day on time has a very uneven character and can be described very roughly by the logistic curve. To describe it, it is necessary to take into account the dependence of the model coefficients on time or on the total number of cases. Variations, for example, of the growth rate can reach 60%. The variability spectra of the coefficients have characteristic peaks at periods of several days, which corresponds to the observed serial intervals. The use of the stochastic logistic equation is proposed to estimate the number of probable peaks in the coronavirus incidence.

We demonstrate that a simple model based on reaction-diffusion-advection (RDA) equation forced by realistic surface velocities and nutrients is skilled in reproducing the distributions of the surface phytoplankton chlorophyll in the tropical Pacific. We use the low-complexity RDA model to investigate the scale-relationships in the impact of different drivers (turbulent diffusion, mean and eddy advection, primary productivity) on the phytoplankton chlorophyll concentrations. We find that in the 1/4° (~25km) model, advection has a substantial impact on the rate of primary productivity, whilst the turbulent diffusion term has a fairly negligible impact. Turbulent diffusion has an impact on the phytoplankton variability, with the impact being scale-propagated and amplified by the larger scale surface currents. We investigate the impact of a surface nutrient decline and some changes to mesoscale eddy kinetic energy (climate change projections) on the surface phytoplankton concentrations. The RDA model suggests that unless mesoscale eddies radically change, phytoplankton chlorophyll scales sub-linearly with the nutrients, and it is relatively stable with respect to the nutrient concentrations. Furthermore we explore how a white multiplicative Gaussian noise introduced into the RDA model on its resolution scale propagates across spatial scales through the non-linear model dynamics under different sets of phytoplankton drivers. The unifying message of this work is that the low complexity (e.g. RDA) models can be successfully used to realistically model some specific aspects of marine ecosystem dynamics and by using those models one can explore many questions that would be beyond computational affordability of the higher-complexity ecosystem models.

The effect of masking the general population on a COVID-19 epidemic is estimated by computer simulation using two separate state-of-the-art web-based softwares, one of them calibrated for the SARS-CoV-2 virus. The questions addressed are these: 1. Can mask use by the general population limit the spread of SARS-CoV-2 in a country? 2. What types of masks exist, and how elaborate must a mask be to be effective against COVID-19? 3. Does the mask have to be applied early in an epidemic? 4. A brief general discussion of masks and some possible future research questions regarding masks and SARS-CoV-2. Results are as follows: (1) The results indicate that any type of mask, even simple home-made ones, may be effective. Masks use seems to have an effect in lowering new patients even the protective effect of each mask (here dubbed "one-mask protection") is low. Strict adherence to mask use does not appear to be critical. However, increasing the one-mask protection to > 50% was found to be advantageous. Masks seemed able to reduce overflow of capacity, e.g. of intensive care. As the default parameters of the software included another intervention, it seems possible to combine mask and other interventions. (2) Masks do seem to reduce the number of new cases even if introduced at a late stage in an epidemic. However, early implementation helps reduce the cumulative and total number of cases. (3) The simulations suggest that it might be possible to eliminate a COVID-19 outbreak by widespread mask use during a limited period. The results from these simulations are encouraging, but do not necessarily represent the real-life situation, so it is suggested that clinical trials of masks are now carried out while continuously monitoring effects and side-effects.

During the COVID-19 pandemic, the scientific community developed predictive models to evaluate potential governmental interventions. However, the analysis of the effects these interventions had is less advanced. Here, we propose a data-driven framework to assess these effects retrospectively. We use a regularized regression to find a parsimonious model that fits the data with the least changes in the Rt parameter. Then, we postulate each jump in Rt as the effect of an intervention. Following the do-operator prescriptions, we simulate the counterfactual case by forcing Rt to stay at the pre-jump value. We then attribute a value to the intervention from the difference between true evolution and simulated counterfactual. We show that the recommendation to use facemasks for all activities would reduce the number of cases by 170000 (95% CI 160000 to 180000) in Connecticut, Massachusetts, and New York State. The framework presented here might be used in any case where cause and effects are sparse in time.

HIV-1 affects tens of millions of people worldwide. Current treatments often involve a cocktail of antiretroviral drugs, which are effective in reducing the virus and extending life spans. However, there is currently no FDA-approved HIV-1 transcription inhibitor. Furthermore, there have only been a few attempts to model the transcription process in HIV-1. In this work, we extend a novel three-state model of HIV-1 transcription introduced in DeMarino et al. (2020) that has been developed and validated against experimental data. After fitting this model to in vitro data, significant differences in the transcription process of HIV-1 in T-cells and macrophages have been observed. In particular, the activation of the HIV-1 promoter in T-cells appears to take place rapidly as the Tat protein approaches a critical threshold. In contrast, the same process occurs smoother in macrophages. In this work, we carry out systematic mathematical analyses of the model to complement experimental data fitting and sensitivity analysis performed earlier. We derive explicit solutions of the model to obtain exact transcription process decay rates for the original model and then study the effect of nonlinearity on the system behavior, including the existence and the local and global stability of the positive equilibrium. We were able to show the stability of the positive steady state in limiting cases, with the global stability in the general case remaining an open question. By modeling the effect of transcription-inhibiting drug therapy, we provide a nontrivial condition for it to be effective in reducing viral load. Moreover, our numerical simulations and analysis point out that the effect of the transcription-inhibitor can be enhanced by synchronizing with standard treatments, such as combination antiretroviral therapy, to allow the reduction of total dosages and toxicity.

An epidemiological compartmental model was used to simulate social distancing strategies to contain the COVID-19 pandemic and prevent a second wave in Sao Paulo, Brazil. Optimization using genetic algorithm was used to determine the optimal solutions. Our results suggest the best-case strategy for Sao Paulo is to maintain or increase the current magnitude of social distancing for at least 60 more days and increase the current levels of personal protection behaviors by a minimum of 10% (e.g., wearing facemasks, proper hand hygiene and avoid agglomeration). Followed by a long-term oscillatory level of social distancing with a stepping-down approach every 80 days over a period of two years with continued protective behavior.

The paper formulates and solves the problem of identification of unknown parameters of mathematical models of the spread of COVID-19 coronavirus infection, based on SEIR type models, based on additional information about the number of detected cases, mortality, self-isolation coefficient and tests performed for the Moscow city and the Novosibirsk Region from 03.23.2020. Within the framework of the models used, the population is divided into seven (SEIR-HCD) and five (SEIR-D) groups with similar characteristics with transition probabilities between groups depending on a specific region. Identifiability analysis of the SEIR-HCD mathematical model was carried out, which revealed the least sensitive unknown parameters to additional measurements. The tasks of refining the parameters are reduced to minimizing the corresponding target functionals, which were solved using stochastic methods (simulating annealing, differential evolution, genetic algorithm, etc.). For a different amount of tested data, a prognostic scenario for the development of the disease in the city of Moscow and the Novosibirsk region was developed, the peak is predicted the development of the epidemic in Moscow with an error of 2 days and 174 detected cases, and an analysis of the applicability of the developed models was carried out.