First Principles Modeling of Nonlinear Incidence Rates in Seasonal Epidemics

In this paper we used a general stochastic processes framework to derive from first principles the incidence rate function that characterizes epidemic models. We investigate a particular case, the Liu-Hethcote-van den Driessche's (LHD) incidence rate function, which results from modeling the number of successful transmission encounters as a pure birth process. This derivation also takes into account heterogeneity in the population with regard to the per individual transmission probability. We adjusted a deterministic SIRS model with both the classical and the LHD incidence rate functions to time series of the number of children infected with syncytial respiratory virus in Banjul, Gambia and Turku, Finland. We also adjusted a deterministic SEIR model with both incidence rate functions to the famous measles data sets from the UK cities of London and Birmingham. Two lines of evidence supported our conclusion that the model with the LHD incidence rate may very well be a better description of the seasonal epidemic processes studied here. First, our model was repeatedly selected as best according to two different information criteria and two different likelihood formulations. The second line of evidence is qualitative in nature: contrary to what the SIRS model with classical incidence rate predicts, the solution of the deterministic SIRS model with LHD incidence rate will reach either the disease free equilibrium or the endemic equilibrium depending on the initial conditions. These findings along with computer intensive simulations of the models' Poincaré map with environmental stochasticity contributed to attain a clear separation of the roles of the environmental forcing and the mechanics of the disease transmission in shaping seasonal epidemics dynamics

Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem

The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts

Sub-Epidemic Generalized Logistic-Growth Model Performance for Influenza Season in the United States, October 2015–April 2019

INTRODUCTION: The public health response to an emerging infectious disease epidemic is based on risk assessments that predict the severity of the health threat. Although infectious disease surveillance data is often limited in scope, mathematical models can provide meaningful information about epidemic growth dynamics to inform development of public health interventions. AIM: This investigation aims to validate application of a sub-epidemic version of the generalized logistic-growth model (GLM) to a delineated period of epidemic growth representing the influenza season, using national surveillance data for incidence of influenza-like illness (ILI) in the United States. METHODS: Surveillance data for ILI case counts were obtained from the Centers for Disease Control and Prevention (CDC) website, FluView. GLM models with one, two, and three sub-epidemics were fit to four epidemic growth periods across four years, each containing 30 weekly ILI incidence counts. Parameter estimates were obtained through nonlinear least squares curve-fitting and sub-epidemic curves were aggregated into the best fit model. Model performance was evaluated using calculation of performance metrics, bootstrapping, and visual analysis. RESULTS: Model performance consistently improved across all four seasons as the number of sub-epidemics incorporated into the GLM increased (n=1 to n=3). The parameter and sub-epidemic estimates provided information about the growth dynamics of the epidemic period, identifying trends specific to each season. DISCUSSION: The sub-epidemic GLM provides useful results about epidemic dynamics using national case count data. In addition, while logistic growth models are often applied to discrete outbreaks, the results of this investigation support application of the model to periods of epidemic growth within seasonal trends as well. The findings support the continued use of this model for academic and other public health application

Dengue outbreaks pattern in southern Guatemala

This study analyses time series of dengue occurrence in the southern region of Guatemala. Temporal patterns of epidemic outbreaks in the department of Escuintla were investigated using the official reports from 2001 to 2013. In order to identify underlying associations with climate behavior, the epidemiological data were compared with historical reports available for temperature, rainfall and humidity. Preliminary results reveal that waves of dengue outbreaks exhibit a periodic pattern modulated by climatic conditions. A hierarchical cluster analysis allowed to indirectly estimate the degree of association of each climatic variable with dengue occurrences, showing the dominance of rainfall in dengue outbreaks patterns in three different localities. A further prospective analysis was performed to check whether epidemic trends driven by rainfall are hold in the subsequent years. Results presented here give support to predictive models for dengue incidence driven by climate

Stochastic analysis of a deterministic and seasonally forced SEI model for improved disease spread simulation

The geographic distribution of different viruses has developed widely, giving rise to an escalating number of cases during the past two decades. The deterministic Susceptible, Exposed, Infectious (SEI) models can demonstrate the spatio-temporal dynamics of the diseases and have been used extensively in modern mathematical and mechano-biological simulations. This article presents a functional technique to model the stochastic effects and seasonal forcing in a reliable manner by satisfying the Lipschitz criteria. We have emphasized that the graphical portrayal can prove to be a powerful tool to demonstrate the stability analysis of the deterministic as well as the stochastic modeling. Emphasis is made on the dynamical effects of the force of infection. Such analysis based on the parametric sweep can prove to be helpful in predicting the disease spread in urban as well as rural areas and should be of interest to mathematical biosciences researchers

Modelling the Epidemiological Dynamics of Seasonal Influenza Viruses at Local Scales

Seasonal influenza viruses are a substantial source of disease burden globally, causing epidemics across all climatic regions. Through error-prone RNA replication, influenza viruses can escape pre-existing humoral immunity and reinfect humans, resulting in recurrent epidemics within populations. From year to year, individual epidemics differ substantially in timing, duration and size. Despite intensive study, characterising the spatiotemporal patterns of virus circulation and identifying the underlying sources of this variability at global, regional and local scales remain as ongoing challenges. There is a need to reconcile environmental, virological and host drivers of virus epidemiological dynamics across diverse contexts. Such insights can only be generated through a holistic approach that integrates observational, ecological, experimental and modelling studies: this would enable more accurate and timely epidemiological forecasts and more efficient allocation of public health resources. In this thesis, I investigate the phylodynamical interactions between the seasonal influenza virus, environment and human host population, integrating analyses from observational study and theoretical modelling approaches. The current knowledge gap on the drivers of local city-level epidemics is identified in Chapter 2 and subsequently addressed over 4 research chapters. In Chapter 3, I review existing epidemic detection algorithms and present a novel statistical model that I developed for use with noisy disease surveillance data and is optimised for the context of seasonal influenza. In Chapter 4, I apply this novel algorithm and analyse a 15-year dataset of 18,250 typed, subtyped, and antigenically characterised seasonal influenza viruses from the five most populous cities in Australia. With the necessary geographical and virus resolution, I quantify the effects of previously hypothesised environmental and virological factors. Most surprisingly, despite an apparent lack of marked change in virus antigenicity, individual antigenic variants are capable of reinvading the same population over consecutive seasons, which runs contrary to predictions made by existing mathematical models. In Chapters 5 and 6, I investigate how antigenic variants are capable of causing recurrent epidemics at local scales by building upon previous theoretical modelling studies and developing a modelling framework to investigate the interactions between and joint effects exerted by the topology of cross-immunity and host contact structure within a population. In Chapter 5, I investigate the effects of correlations between network structure and individual susceptibility. In Chapter 6, I examine the population-level significance of age-specific changes to an individual's immune response. In Chapter 7, I review my findings and discuss how these new insights into virus ecology can open new avenues for better influenza control and future research