Quantitative Biology

treePL uses a penalised likelihood approach to produce a dated phylogeny in a maximum likelihood framework. Since its publication in 2012, few resources have been developed to explain how to use it properly. In this guide, I provide a step-by-step protocol for producing a dated phylogeny using treePL, based on my experience building a large dated phylogeny with it and conducting additional tests on a smaller phylogeny. I also provide the necessary data to reproduce one of the example phylogenies presented. I compare these treePL phylogenies to BEAST2-built counterparts. Even though I cannot explain precisely how treePL works, the evidence discussed in this guide suggest that the empirical protocol presented is reliable.

We propose a mathematical model to analyze the time evolution of the total number of infected population with Covid-19 disease at a region in the ongoing pandemic. Using the available data of Covid-19 infected population on various countries we formulate a model which can successfully track the time evolution from early days to the saturation period in a given wave of this infectious disease. It involves a set of effective parameters which can be extracted from the available data. Using those parameters the future trajectories of the disease spread can also be projected. A set of differential equations is also proposed whose solutions are these time evolution trajectories. Using such a formalism we project the future time evolution trajectories of infection spread for a number of countries where the Covid-19 infection is still rapidly rising.

Between pandemics, the influenza virus exhibits periods of incremental evolution via a process known as antigenic drift. This process gives rise to a sequence of strains of the pathogen that are continuously replaced by newer strains, preventing a build up of immunity in the host population. In this paper, a parsimonious epidemic model is defined that attempts to capture the dynamics of evolving strains within a host population. The `evolving strains' epidemic model has many properties that lie in-between the Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models, due to the fact that individuals can only be infected by each strain once, but remain susceptible to reinfection by newly emerged strains. Coupling results are used to identify key properties, such as the time to extinction. A range of reproduction numbers are explored to characterize the model, including a novel quasi-stationary reproduction number that can be used to describe the re-emergence of the pathogen into a population with `average' levels of strain immunity, analogous to the beginning of the winter peak in influenza. Finally the quasi-stationary distribution of the evolving strains model is explored via simulation.

An epidemiological model is developed for the spread of COVID-19 in South Africa. A variant of the classical compartmental SEIR model, called the SEIQRDP model, is used. As South Africa is still in the early phases of the global COVID-19 pandemic with the confirmed infectious cases not having peaked, the SEIQRDP model is first parameterized on data for Germany, Italy, and South Korea - countries for which the number of infectious cases are well past their peaks. Good fits are achieved with reasonable predictions of where the number of COVID-19 confirmed cases, deaths, and recovered cases will end up and by when. South African data for the period from 23 March to 8 May 2020 is then used to obtain SEIQRDP model parameters. It is found that the model fits the initial disease progression well, but that the long-term predictive capability of the model is rather poor. The South African SEIQRDP model is subsequently recalculated with the basic reproduction number constrained to reported values. The resulting model fits the data well, and long-term predictions appear to be reasonable. The South African SEIQRDP model predicts that the peak in the number of confirmed infectious individuals will occur at the end of October 2020, and that the total number of deaths will range from about 10,000 to 90,000, with a nominal value of about 22,000. All of these predictions are heavily dependent on the disease control measures in place, and the adherence to these measures. These predictions are further shown to be particularly sensitive to parameters used to determine the basic reproduction number. The future aim is to use a feedback control approach together with the South African SEIQRDP model to determine the epidemiological impact of varying lockdown levels proposed by the South African Government.

We investigate how the initial number of infected individuals affects the behavior of the critical susceptible-infected-recovered process. We analyze the outbreak size distribution, duration of the outbreaks, and the role of fluctuations.

There is a near consensus view that SARS-CoV-2 has a natural zoonotic origin; however, several characteristics of SARS-CoV-2 taken together are not easily explained by a natural zoonotic origin hypothesis. These include: a low rate of evolution in the early phase of transmission; the lack of evidence of recombination events; a high pre-existing binding to human ACE2; a novel furin cleavage site insert; a flat glycan binding domain of the spike protein which conflicts with host evasion survival patterns exhibited by other coronaviruses, and high human and mouse peptide mimicry. Initial assumptions against a laboratory origin, by contrast, have remained unsubstantiated. Furthermore, over a year after the initial outbreak in Wuhan, there is still no clear evidence of zoonotic transfer from a bat or intermediate species. Given the immense social and economic impact of this pandemic, identifying the true origin of SARS-CoV-2 is fundamental to preventing future outbreaks. The search for SARS-CoV-2's origin should include an open and unbiased inquiry into a possible laboratory origin.

The current outbreak is known as Coronavirus Disease or COVID-19 caused by the virus SAR-COV-2 which continues to wreak havoc across the globe. The World Health Organization (WHO) has declared the outbreak a Public Health Emergency of International Concern. In Pakistan, the spread of the virus is on the rise with the number of infected people and causalities rapidly increasing. In the absence of proper vaccination and treatment, to reduce the number of infections and casualties, the only option so far is to educate people regarding preventive measures and to enforce countrywide lock-down. Any strategy about the preventive measures needs to be based upon detailed analysis of the COVID-19 outbreak and accurate scientific predictions. In this paper, we conduct mathematical and numerical analysis to come up with reliable and accurate predictions of the outbreak in Pakistan. The time-dependent Susceptible-Infected-Recovered (SIR) model is used to fit the data and provide future predictions. The turning point of the peak of the pandemic is defined as the day when the transmission rate becomes less than the recovering rate. We have predicted that the outbreak will reach its maximum peak occurring from late May to 9 June with unrecovered number of Infectives in the range 20000-47000 and the cumulative number of infected cases in the range of 57500-153100. The number of Infectives will remain at the lower end in the lock-down scenario but can rapidly double or triple if the spread of the epidemic is not curtailed and localized. The uncertainty on single day projection in our analysis after April 15 is found to be within 5\%.

The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common representation of the SIR-type stochastic epidemiological models. This representation is a discrete time transition model, which allows us to classify the epidemiological models with respect to the number of states (compartments) and their interpretation. Additionally, the transition model eliminates several limitations of the deterministic continuous time epidemiological models which are pointed out in the paper. We also show that all SIR-type models have a nonlinear (pseudo) state space representation and are easily estimable from an extended Kalman filter.

This article contains a series of analyses done for the SARS-CoV-2 outbreak in Rio Grande do Sul (RS) in the south of Brazil. These analyses are focused on the high-incidence cities such as the state capital Porto Alegre and at the state level. We provide methodological details and estimates for the effective reproduction number R t , a joint analysis of the mobility data together with the estimated R t as well as ICU simulations and ICU LoS (length of stay) estimation for hospitalizations in Porto Alegre/RS.

An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in lnS and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model. This is achieved through an asymptotic approximant (Barlow et. al, 2017, Q. Jl Mech. Appl. Math, 70 (1), 21-48) in the form of a modified symmetric Padé approximant that incorporates this damping. The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic.