Epidemic in a structured host population : dynamic hydra effect

The aim of this project is to investigate the hydra effect occurring in a population infected by a disease. First, I will explain what exactly the hydra effect is. Intuitively, higher mortality rate applied to a population will decrease the size of that population, but this is not always the case. Under some circumstances the population size might increase with higher mortality, causing the phenomenon called by Abrams and Matsuda (2005) the 'hydra effect', after the mythological beast, who grew two heads in place of one removed. Abrams (2009) lists in a few mechanisms underlying the hydra effect from which the one I will focus onis a temporal separation of mortality and density dependence. Most work on the hydra effect involved explicit increase of a death rate, for example by harvesting. The idea of this thesis is to investigate the existence of the hydra effect due to mortality increased not explicitly, but through a lethal disease. Such an approach has not been shown in any published work so far. Instead of harvesting, we will have a virulence, the disease-induced mortality. In this project, I fi rst briefly explain some theory underlying my model. In chapter 2 I look at disease-free population and bifurcation analysis when varying the birth rate. In chapter 3 I propose the model and continue with population dynamics analysis. I look at bifurcations of equilibria when varying birth rate, virulence and transmission rate. Then in section 3.4 I investigate whether it is possible to observe the hydra effect if there exists a trade-off between virulence and transmission rate, and derive a condition for transcritical and fold bifurcation to occur. In chapter 4 I focus on evolution of traits. First I study evolution of the pathogen, assuming the same trade-off as earlier. Finally I look at evolution of host's traits, immunity and birth rate, using Adaptive Dynamics framework (Geritz et al. 1998). I compare two possible trade-off functions and show that with a concave trade-off, the host will evolve to getting rid of the disease despite increasing its immunity

Inference of COVID-19 epidemiological distributions from Brazilian hospital data

Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalised with COVID-19 using a large dataset ($N=21{,}000-157{,}000$) from the Brazilian Sistema de Informa\c{c}\~ao de Vigil\^ancia Epidemiol\'ogica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2-17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalised log-normal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity

Genomics and epidemiology of the P.1 SARS-CoV-2 lineage in Manaus, Brazil

Cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in Manaus, Brazil, resurged in late 2020 despite previously high levels of infection. Genome sequencing of viruses sampled in Manaus between November 2020 and January 2021 revealed the emergence and circulation of a novel SARS-CoV-2 variant of concern. Lineage P.1 acquired 17 mutations, including a trio in the spike protein (K417T, E484K, and N501Y) associated with increased binding to the human ACE2 (angiotensin-converting enzyme 2) receptor. Molecular clock analysis shows that P.1 emergence occurred around mid-November 2020 and was preceded by a period of faster molecular evolution. Using a two-category dynamical model that integrates genomic and mortality data, we estimate that P.1 may be 1.7- to 2.4-fold more transmissible and that previous (non-P.1) infection provides 54 to 79% of the protection against infection with P.1 that it provides against non-P.1 lineages. Enhanced global genomic surveillance of variants of concern, which may exhibit increased transmissibility and/or immune evasion, is critical to accelerate pandemic responsiveness

Time-dependent reproduction number.

Time-dependent reproduction number generated by models with the highest evidence calculated using the Laplace approximation (orange lines) and referenced TI (blue lines). Note, the fitting data in this example contains superspreading events (which leads to very high values of Rt on certain days) so is not representative of SARS-CoV-2 transmission generally.</p

Bias and variance.

Evaluating normalising constants is important across a range of topics in statistical learning, notably Bayesian model selection. However, in many realistic problems this involves the integration of analytically intractable, high-dimensional distributions, and therefore requires the use of stochastic methods such as thermodynamic integration (TI). In this paper we apply a simple but under-appreciated variation of the TI method, here referred to as referenced TI, which computes a single model’s normalising constant in an efficient way by using a judiciously chosen reference density. The advantages of the approach and theoretical considerations are set out, along with pedagogical 1 and 2D examples. The approach is shown to be useful in practice when applied to a real problem —to perform model selection for a semi-mechanistic hierarchical Bayesian model of COVID-19 transmission in South Korea involving the integration of a 200D density.</div

Log-evidence estimated by Laplace and referenced TI approximations.

In each section, model with the highest log-evidence estimated by Laplace or referenced TI method is indicated in bold. The credible intervals for log-evidence comes from calculating the quantiles of the integral from Eq 2, where the integral values were obtained from the spline interpolated using running means of the expecations per λ over all iterations.</p

Spatial and temporal fluctuations in COVID-19 fatality rates in Brazilian hospitals

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Gamma variant of concern has spread rapidly across Brazil since late 2020, causing substantial infection and death waves. Here we used individual-level patient records after hospitalization with suspected or confirmed coronavirus disease 2019 (COVID-19) between 20 January 2020 and 26 July 2021 to document temporary, sweeping shocks in hospital fatality rates that followed the spread of Gamma across 14 state capitals, during which typically more than half of hospitalized patients aged 70 years and older died. We show that such extensive shocks in COVID-19 in-hospital fatality rates also existed before the detection of Gamma. Using a Bayesian fatality rate model, we found that the geographic and temporal fluctuations in Brazil’s COVID-19 in-hospital fatality rates were primarily associated with geographic inequities and shortages in healthcare capacity. We estimate that approximately half of the COVID-19 deaths in hospitals in the 14 cities could have been avoided without pre-pandemic geographic inequities and without pandemic healthcare pressure. Our results suggest that investments in healthcare resources, healthcare optimization and pandemic preparedness are critical to minimize population-wide mortality and morbidity caused by highly transmissible and deadly pathogens such as SARS-CoV-2, especially in low- and middle-income countries

The Thanzi La Onse Model

Our fundamental aim is to develop the use of epidemiological and economic science to effect a step-change in the way that health priorities are addressed through policy interventions in low-income countries. We are doing this by developing a model that represents explicitly the generation of health gains in a population, which can be used to examine the effect of resource allocation, management and clinical practice, in order to contribute to informing decision-making.If you use this software, please cite it using the metadata from this file