Quantitative Biology

The Susceptible-Infected-Recovered (SIR) epidemic model is extensively used for the study of the spread of infectious diseases. Even that the exact solution of the model can be obtained in an exact parametric form, in order to perform the comparison with the epidemiological data a simple but highly accurate representation of the time evolution of the SIR compartments would be very useful. In the present paper we obtain a series representation of the solution of the SIR model by using the Laplace-Adomian Decomposition Method to solve the basic evolution equation of the model. The solutions are expressed in the form of infinite series. The series representations of the time evolution of the SIR compartments are compared with the exact numerical solutions of the model. We find that there is a good agreement between the Laplace-Adomian semianalytical solutions containing only three terms, and the numerical results.

We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time and the individual's nourishment history. A food-limited environment induces intraspecific competition and henceforth the carrying capacity of the medium may be finite, often emulating the qualitative features of logistic growth. Inherently non-logistic behavior is also obtained by suitable change of the few parameters involved, composing a wide variety of dynamical features. Some analytical results are obtained. Beyond the rich phenomenology observed, we expect that possible modifications of our model may account for an even broader scope of collective population growth phenomena.

We propose a stochastic SIR model, specified as a system of stochastic differential equations, to analyse the data of the Italian COVID-19 epidemic, taking also into account the under-detection of infected and recovered individuals in the population. We find that a correct assessment of the amount of under-detection is important to obtain reliable estimates of the critical model parameters. Moreover, a single SIR model over the whole epidemic period is unable to correctly describe the behaviour of the pandemic. Then, the adaptation of the model in every time-interval between relevant government decrees that implement contagion mitigation measures, provides short-term predictions and a continuously updated assessment of the basic reproduction number.

To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the presence of quarantine areas, to capture the evolutionary dynamics of such diseases.

We developed a model and a software package for stochastic simulations of transmission of COVID-19 and other similar infectious diseases, that takes into account contact network structures and geographical distribution of population density, detailed up to a level of location of individuals. Our analysis framework includes a surrogate model optimization process for quick fitting of the model's parameters to the observed epidemic curves for cases, hospitalizations and deaths. This set of instruments (the model, the simulation code, and the optimizer) is a useful tool for policymakers and epidemic response teams who can use it to forecast epidemic development scenarios in local environments (on the scale from towns to large countries) and design optimal response strategies. The simulation code also includes a geospatial visualization subsystem, presenting detailed views of epidemic scenarios directly on population density maps. We used the developed framework to draw predictions for COVID-19 spreading in the canton of Geneva, Switzerland.

COVID-19 is a new pandemic disease that is affecting almost every country with a negative impact on social life and economic activities. The number of infected and deceased patients continues to increase globally. Mathematical models can help in developing better strategies to contain a pandemic. Considering multiple measures taken by African governments and challenging socio-economic factors, simple models cannot fit the data. We studied the dynamical evolution of COVID-19 in selected African countries. We derived a time-dependent reproduction number for each country studied to offer further insights into the spread of COVID-19 in Africa.

A number of models in mathematical epidemiology have been developed to account for control measures such as vaccination or quarantine. However, COVID-19 has brought unprecedented social distancing measures, with a challenge on how to include these in a manner that can explain the data but avoid overfitting in parameter inference. We here develop a simple time-dependent model, where social distancing effects are introduced analogous to coarse-grained models of gene expression control in systems biology. We apply our approach to understand drastic differences in COVID-19 infection and fatality counts, observed between Hubei (Wuhan) and other Mainland China provinces. We find that these unintuitive data may be explained through an interplay of differences in transmissibility, effective protection, and detection efficiencies between Hubei and other provinces. More generally, our results demonstrate that regional differences may drastically shape infection outbursts. The obtained results demonstrate the applicability of our developed method to extract key infection parameters directly from publically available data so that it can be globally applied to outbreaks of COVID-19 in a number of countries. Overall, we show that applications of uncommon strategies, such as methods and approaches from molecular systems biology research to mathematical epidemiology, may significantly advance our understanding of COVID-19 and other infectious diseases.

Motivated by the recent outbreak of coronavirus (COVID-19), we propose a stochastic model of epidemic temporal growth and mitigation based on a time-modulated Hawkes process. The model is sufficiently rich to incorporate specific characteristics of the novel coronavirus, to capture the impact of undetected, asymptomatic and super-diffusive individuals, and especially to take into account time-varying counter-measures and detection efforts. Yet, it is simple enough to allow scalable and efficient computation of the temporal evolution of the epidemic, and exploration of what-if scenarios. Compared to traditional compartmental models, our approach allows a more faithful description of virus specific features, such as distributions for the time spent in stages, which is crucial when the time-scale of control (e.g., mobility restrictions) is comparable to the lifetime of a single infection. We apply the model to the first and second wave of COVID-19 in Italy, shedding light into several effects related to mobility restrictions introduced by the government, and to the effectiveness of contact tracing and mass testing performed by the national health service.

A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of individuals which mate and produce offspring is controlled by a binomial distribution with size given by this number of individuals and probability of success depending on the density of preys per predator. The resulting model enables us to depict the typical cyclic behaviour of predator-prey systems under some mild assumptions on the shape of the function that characterises the probability of survival of the previous binomial distribution. We present some basic results about fixation and extinction of both species as well as conditions for the coexistence of both of them. We also analyse the suitability of the process to model real ecosystems comparing our model with a real dataset.

Currently, due to the COVID-19 pandemic the public life in most European countries stopped almost completely due to measures against the spread of the virus. Efforts to limit the number of new infections are threatened by the advent of new variants of the SARS-COV-2 virus, most prominent the B.1.1.7 strain with higher infectivity. In this article we consider a basic two-strain SIR model to explain the spread of those variants in Germany on small time scales. For a linearized version of the model we calculate relevant variables like the time of minimal infections or the dynamics of the share of variants analytically. These analytical approximations and numerical simulations are in a good agreement to data reported by the Robert Koch Institute (RKI) in Germany.