Quantitative Biology

Non-pharmaceutical interventions have been critical in the fight against the COVID-19 pandemic. However, these sanitary measures have been partially lifted due to socioeconomic factors causing a worrisome rebound of the epidemic in several countries. In this work, we assess the effectiveness of the mitigation implemented to constrain the spread of SARS-CoV-2 in the Mexican territory during 2020. We also investigate to what extent the initial deployment of the vaccine will help to mitigate the pandemic and reduce the need for social distancing and other mobility restrictions. Our modeling approach is based on a simple mechanistic Kermack-McKendrick-type model. To quantify the effect of NPIs, we perform a monthly Bayesian inference using officially published data. The results suggest that in the absence of the sanitary measures, the cumulative number of infections, hospitalizations, and deaths would have been at least twice the official number. Moreover, for low vaccine coverage levels, relaxing NPIs may dramatically increase the disease burden; therefore, safety measures are of critical importance at the early stages of vaccination. The simulations also suggest that it may be more desirable to employ a vaccine with low efficacy but reach a high coverage than a vaccine with high effectiveness but low coverage levels. This supports the hypothesis that single doses to more individuals will be more effective than two doses for every person.

We adapt the hybrid mechanistic-statistical approach of Ref. [1] to estimate the total number of undocumented Covid-19 infections in Cuba. This scheme is based on the maximum likelihood estimation of a SIR-like model parameters for the infected population, assuming that the detection process matches a Bernoulli trial. Our estimations show that (a) 60% of the infections were undocumented, (b) the real epidemics behind the data peaked ten days before the reports suggested, and (c) the reproduction number swiftly vanishes after 80 epidemic days.

Since the beginning of March 2020, the cumulative numbers of cases of infection with the novel coronavirus SARS-CoV-2 in Germany have been reported on a daily basis. The reports originate from national laws, according to which positive test findings must be submitted to the Federal Health Authorities, the Robert Koch Institute, via the local health authorities. Since an enormous number of unreported cases can be expected, the question of how widespread the disease has been in the population cannot be answered based on these administrative reports. Using mathematical modeling, however, estimates can be made. These estimates indicate that the small numbers of diagnostic tests carried out at the beginning of the outbreak overlooked considerable parts of the infection. In order to cover the initial phase of future waves of the disease, wide-spread and comprehensive tests are recommended.

Background: Wuhan, China was the epicenter of COVID-19 pandemic. The goal of current study is to understand the infection transmission dynamics before intervention measures were taken. Methods: Data and key events were searched through pubmed and internet. Epidemiological data were calculated using data extracted from a variety of data sources. Results: We established a timeline showing by January 1, 2020, Chinese authorities had been presented convincing evidence of human-to-human transmission; however, it was not until January 20, 2020 that this information was shared with the public. Our study estimated that there would have been 10989 total infected cases if interventions were taken on January 2, 2020, versus 239875 cases when lockdown was put in place on January 23, 2020. Conclusions: China's withholding of key information about the 2020 COVID-19 outbreak and its delayed response ultimately led to the largest public health crisis of this century and could have been avoided with earlier countermeasures.

The special epistemic characteristics of the COVID-19, such as the long incubation period and the infection through asymptomatic cases, put severe challenge to the containment of its outbreak. By the end of March 2020, China has successfully controlled the within-spreading of COVID-19 at a high cost of locking down most of its major cities, including the epicenter, Wuhan. Since the low accuracy of outbreak data before the mid of Feb. 2020 forms a major technical concern on those studies based on statistic inference from the early outbreak. We apply the supervised learning techniques to identify and train NP-Net-SIR model which turns out robust under poor data quality condition. By the trained model parameters, we analyze the connection between population flow and the cross-regional infection connection strength, based on which a set of counterfactual analysis is carried out to study the necessity of lock-down and substitutability between lock-down and the other containment measures. Our findings support the existence of non-lock-down-typed measures that can reach the same containment consequence as the lock-down, and provide useful guideline for the design of a more flexible containment strategy.

In times of outbreaks, an essential requirement for better monitoring is the evaluation of the number of undiagnosed infected individuals. An accurate estimate of this fraction is crucial for the assessment of the situation and the establishment of protective measures. In most current studies using epidemics models, the total number of infected is either approximated by the number of diagnosed individuals or is dependent on the model parameters and assumptions, which are often debated. We here study the relationship between the fraction of diagnosed infected out of all infected, and the fraction of infected with known contaminator out of all diagnosed infected. We show that those two are approximately the same in exponential models and across most models currently used in the study of epidemics, independently of the model parameters. As an application, we compute an estimate of the effective number of infected by the SARS-CoV-2 virus in various countries.

Bacteria typically reside in heterogeneous environments with various chemogradients where motile cells can gain an advantage over non-motile cells. Since motility is energetically costly, cells must optimize their swimming speed and behavior to maximize their fitness. Here we investigate how cheating strategies might evolve where slow or non-motile microbes exploit faster ones by sticking together and hitching a ride. Starting with physical and biological first-principles we computationally study the effects of sticking on the evolution of motility in a controlled chemostat environment. We find stickiness allows slow cheaters to dominate when nutrients are dispersed at intermediate distances. Here, slow microbes exploit faster ones until they consume the population, leading to a tragedy of commons. For long races, slow microbes do gain an initial advantage from sticking, but eventually fall behind. Here, fast microbes are more likely to stick to other fast microbes, and cooperate to increase their own population. We therefore find the nature of the hitchhiking interaction, parasitic or mutualistic, depends on the nutrient distribution.

We study effects of strategy-dependent time delays on equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we report a novel behavior. We show that microscopic models of evolutionary games with strategy-dependent time delays lead to a new type of replicator dynamics. It describes the time evolution of fractions of the population playing given strategies and the size of the population. Unlike in all previous models, stationary states of such dynamics depend continuously on time delays. We show that in games with an interior stationary state (a globally asymptotically stable equilibrium in the standard replicator dynamics), at certain time delays, it may disappear or there may appear another interior stationary state. In the Prisoner's Dilemma game, for time delays of cooperation smaller than time delays of defection, there appears an ustable interior equilibrium and therefore for some initial conditions, the population converges to the homogeneous state with just cooperators.

The dynamics of molecular collisions in a macroscopic body are encoded by the parameter Thermodynamic entropy - a statistical measure of the number of molecular configurations that correspond to a given macrostate. Directionality in the flow of energy in macroscopic bodies is described by the Second Law of Thermodynamics: In isolated systems, that is systems closed to the input of energy and matter, thermodynamic entropy increases. The dynamics of the lower level interactions in populations of replicating organisms is encoded by the parameter Evolutionary entropy, a statistical measure which describes the number and diversity of metabolic cycles in a population of replicating organisms. Directionality in the transformation of energy in populations of organisms is described by the Fundamental Theorem of Evolution: In systems open to the input of energy and matter, Evolutionary entropy increases, when the energy source is scarce and diverse, and decreases when the energy source is abundant and singular. This article shows that when rho to 0, and N to infinity, where rho is the production rate of the external energy source, and N denote the number of replicating units, evolutionary entropy, an organized state of energy; and thermodynamic entropy, a randomized state of energy, coincide. Accordingly, the Fundamental Theorem of Evolution, is a generalization of the Second Law of Thermodynamics.

In this work, some new exact and approximate analytical solutions are obtained for the SIR epidemic model, which is formulated in terms of dimensionless variables and parameters. The susceptibles population (S) is in this way explicitly related to the infectives population (I) using the Lambert W function (both the principal and the secondary branches). A simple and accurate relation for the fraction of the population that does not catch the disease is also obtained. The explicit time dependences of the susceptibles, infectives and removed populations, as well as that of the epidemic curve are also modelled with good accuracy for any value of R0 (basic multiplication number) using simple functions that are modified solutions of the R0 -> infinity limiting case (logistic curve). It is also shown that for I0 << S0 the effect of a change in the ratio I0/S0 on the population evolution curves amounts to a time shift, their shape and relative position being unaffected.