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Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders. (C) 2016 The Authors. Published by Elsevier B.V.

Thesis--Auburn University, 2008. / Abstract. Vita. Includes bibliographical references (p. 60-90).

The red squirrel (Sciurus vulgaris) is native to Eurasia, but in the UK its survival is being threatened by the non-native grey squirrel (Sciurus carolinensis). Since its introduction to the UK from the USA the grey squirrel has increased its range at the expense of the red squirrel. Although competition for resources clearly plays a role in this replacement, an infectious viral disease, caused by squirrelpox virus (SQPV) and hosted apparently asymptomatically by the grey squirrels, has now been recognised as a major contributing factor. Little is known about the pathogenesis of infection in grey squirrels in comparison to red squirrels, but understanding this is essential to determining how the virus spreads within and between the red and grey squirrels. The aims of this thesis were to investigate the course of SQPV infection in red and grey squirrels and possible routes of virus transmission. Specifically, for the first time, a novel Real Time PCR (qPCR) assay and immunohistochemistry were used to investigate the presence of SQPV in various tissues from naturally infected red squirrels and experimentally infected grey squirrels. In diseased red squirrels SQPV DNA was found in several tissues with the highest amounts being found in skin samples. This reflects the multiple lesions that were easily visible on the red squirrel carcasses. There was no indication of systemic disease although the viral DNA was detected, at lower levels, in other internal organs. Grey squirrels were experimentally infected with SQPV isolated from naturally-infected red squirrels with fatal clinical disease. In contrast to SQPV-infected red squirrels no clinical lesions, other than mild scab formation at the site of inoculation, were found in the grey squirrels post-infection. No gross pathological changes indicative of systemic infection were observed and these findings were reflected in the qPCR and histopathology results. Viral DNA was only detected by qPCR in samples from the site of inoculation (scarified skin) and at lower concentrations in other skin tissues such as digital and eyelid skin. In addition, histopathology and immunohistochemistry examination revealed evidence of infection characterized by ballooning degeneration of keratinocytes, and acanthosis and spongiosis of the epidermis. These skin lesions were self limiting and minor compared to the infected red squirrel skin samples. The molecular variation in the virus isolated over time from different parts of the UK was also investigated. Seven SQPV isolates (4 from Scotland and 3 from England) were tested and results indicated that there are no significant changes in the amino acid sequence of any of the three genes examined apart from one amino acid change (one base change) in one gene. All Scottish isolates examined showed this change in comparison to English isolates. The results in this thesis show that there is a mild pathology associated with SQPV infection in grey squirrels. Scabs form at the site of infection but are less proliferative than in infected red squirrels, though they may still serve to contaminate the environment with virus leading to further outbreaks of disease. In contrast it seems likely that the proliferative lesions suffered by red squirrels and the greater amounts of virus that this leads to are likely to be more significant to the epidemiology of disease in localised outbreaks.

Mathematical models have long been used to describe complex biological interactions with the aim of predicting mechanistic interactions hard to distinguish from data. This dissertation uses modeling, mathematical analyses, and data fitting techniques to provide hypotheses on the mechanisms of immune response formation and function. The immune system, comprised of the innate and adaptive immune responses, is responsible for protecting the body against invading pathogens, with disease or vaccine induced immune memory leading to fast responses to subsequent infections. While there is some agreement about the underlying mechanisms of adaptive immune memory, innate immune memory is poorly understood. Stimulation with lipopolysaccharide induces differential phenotypes in innate immune cells depending on the strength of the stimulus, such that a secondary lipopolysaccharide encounter of a constant dose results in either strong or weak inflammatory cytokine expression. We model the biochemical kinetics of three molecules involved in macrophages responses to lipopolysaccharide and find that once a macrophage is programed to show a weak inflammatory response this cannot be reverted. Contrarily, a secondary lipopolysaccharide stimulus of a very high dose or applied prior to waning of the effects of the primary stimulus can induce a phenotype switch in macrophages initially programed to show strong inflammatory responses. Some pathogens, such as the hepatitis B virus, have developed strategies that hinder an efficient innate immune response. Hepatitis B virus infection is a worldwide pandemic with approximately 257 million chronically infected people. One beneficial event in disease progression is the seroclearance of hepatitis B e antigen often in combination with hepatitis B antibody formation. We propose mathematical models of within-host interactions and use them to predict that hepatitis B e antibody formation causes hepatitis B e antigen seroclearance and the subsequent reactivation of cytotoxic T cell immune responses. We use the model to quantify the time between antibody formation and antigen clearance and the average monthly hepatocyte turnover during that time. We further expand the study of hepatitis B infection, by investigating the kinetics of the virus under an experimental drug administered during a clinical trial. Available drugs usually fail to induce hepatitis B s antigen clearance, defined as the functional cure point of chronic hepatitis B infections. Drug therapy clinical trials that combined RNA interference drug ARC-520 with entecavir have shown promising results in reducing hepatitis B s antigen titers. We develop pharmacokinetic-pharmacodynamic models describing the mechanistic interactions of the drugs, hepatitis B virus DNA, and virus proteins. We fit the model to clinical trial data and predict that ARC-520 alone is responsible for the reduction of hepatitis B s and e antigens, while entecavir is the driving force behind viral reduction. This work was supported by Simons Foundation, Grant No. 427115, and National Science Foundation, Grant No. 1813011. / Doctor of Philosophy / Mathematical models have long been used to describe complex biological interactions with the aim of predicting interactions that explain observed data and informing new experiments. This dissertation uses modeling, mathematical analyses, and data fitting techniques to provide hypotheses on the mechanisms of immune response formation and function. The immune system, comprised of the innate and adaptive immune responses, is responsible for protecting the body against invading pathogens, such as viruses, bacteria, or fungi. If an immune response to a secondary pathogen encounter differs from the response when the body first encounters the specific pathogen, this is called immune memory. The mechanisms underlying the memory of immune responses are well understood in the context of adaptive immune responses, but less so for innate immune responses. Stimulation with lipopolysaccharide, a cell wall component of many bacteria, programs innate immune cells, such as macrophages, to be in one of two states, called phenotypes, depending on the strength of the stimulus. Based on their phenotype the macrophages show either a weak or strong inflammatory response upon a secondary lipopolysaccharide encounter of a constant dose. We model the biochemical kinetics of three molecules involved in macrophages responses to lipopolysaccharide. We find that once a macrophage is programed to show a weak inflammatory response this cannot be reverted. Contrarily, a secondary lipopolysaccharide stimulus that is either of a very high dose or applied before the effects of the primary stimulus have waned, can induce a phenotype switch in macrophages initially programed to show strong inflammatory responses. Some pathogens, such as the hepatitis B virus, have developed strategies that hinder an efficient innate immune response. Hepatitis B virus infection is a worldwide pandemic with approximately 257 million chronically infected people. Hepatitis B e antigen is a protein that infected liver cells release into blood and that impairs adaptive immune responses. It is considered a beneficial event in disease progression, and called hepatitis B e antigen clearance, when hepatitis B e antigen becomes indetectable in a patient's blood. We propose mathematical models of interactions between liver cells, the virus, hepatitis B e antigens and hepatitis B e antibodies, which neutralize the antigens. We predict that antibody formation causes antigen clearance and a reactivation of immune responses. We furthermore use the model to quantify the time between antibody formation and antigen clearance and the average number of liver cells killed during that time. We further expand the study of hepatitis B infection, by investigating the kinetics of the virus under an experimental drug administered during a clinical trial. Available drugs rarely induce hepatitis B s antigen clearance, but clinical trials that combined a novel drug, called ARC-520, with the commonly used drug entecavir have shown promising results in reducing hepatitis B s antigen titers in the blood of infected patients. Following the clearance of hepatitis B s antigen, a protein that is released by infected cells and impairs adaptive immunity, the body usually has the capability to control the infection without medication. We develop mathematical models describing the interactions of the drugs, hepatitis B virus, and virus proteins. We fit the model to clinical trial data and predict that ARC-520 alone is responsible for the reduction of hepatitis B s and e antigens, while entecavir is the driving force behind viral reduction.