Modelling vector-borne diseases: epidemic and inter-epidemic activities with application to Rift Valley fever

A Thesis submitted to the Faculty of Science in ful lment of the requirements for the degree of Doctor of Philosophy, School of Computer Science and Applied Mathematics. Johannesburg, 2016.In this thesis in order to study the complex dynamics of Rift Valley fever (RVF) we combine two modelling approaches: equation-based and simulation-based modelling. In the first approach we first formulate a deterministic model that includes two vector populations, Aedes and Culex mosquitoes with one host population (livestock), while considering both horizontal and vertical transmissions. An easy applicable expression of the basic reproduction number, R0 is derived for both periodic and non-periodic environment. Both time invariant and time varying uncertainty and sensitivity analysis of the model is carried out for quantifying the attribution of model output variations to input parameters over time and novel relationships between R0 and vertical transmission are determined providing important information useful for improving disease management. Then, we analytically derive conditions for stability of both disease-free and endemic equilibria. Using techniques of numerical simulations we perform bifurcation and chaos analysis of the model under periodic environment for evaluating the effects of climatic conditions on the characteristic pattern of disease outbreaks. Moreover, extending this model including vectors other than mosquitoes (such as ticks) we evaluate the possible role of ticks in the spread and persistence of the disease pointing out relevant model parameters that require further attention from experimental ecologists to further determine the actual role of ticks and other biting insects on the dynamics of RVF. Additionally, a novel host-vector stochastic model with vertical transmission is used to analytically determine the dominant period of disease outbreaks with respect to vertical transmission efficiency. Then, novel relationships among vertical transmission, invasion and extinction probabilities and R0 are determined. In the second approach a novel individual-based model (IBM) of complete mosquito life cycle built under daily temperature and rainfall data sets is designed and simulated. The model is applied for determining correlation between abundance of mosquito populations and rainfall regimes and is then used for studying disease inter-epidemic activities. We find that indeed rainfall is responsible for creating intra- and inter-annual variations observed in the abundance of adult mosquitoes and the length of gonotrophic cycle, number of eggs laid per blood meal, adults age-dependent survival and fight behaviour are among the most important features of the mosquito life cycle with great epidemiological impacts in the dynamics of RVF transmission. These indicators could be of great epidemiological significance by allowing disease control program managers to focus their e orts on specific features of vector life cycle including vertical transmission ability and diapause. We argue that our IBM model is an ideal extendible framework useful for further investigations of other relevant host-vector ecological and epidemiological questions for providing additional knowledge important for improving the length and quality of life of humans and domestic animals.LG201

MATHEMATICAL MODELING OF CORONA VIRUS IN THE UNITED ARAB EMIRATES

The Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is a viral in-fectious disease that can be transmitted to humans through interaction with infected ani-mals or humans. The Middle East respiratory syndrome (MERS) is still one of the main public health concerns in the Gulf region including United Arab Emirates. The fact that diseases have been imported into other parts of the world show the possibility of has a MERS pandemic. In this work, we are aiming to study a mathematical model of the MERS transmission among the UAE population and camels. The goal is to determine what are the paths of communication and find out the best way to control the disease spread. We will calculate the basic reproduction number ℛ0 of the MERS model in the UAE, and we will compute disease-endemic equilibrium points. The sensitivity analysis of the basic reproduction number ℛ0 will be performed. Also, we will perform computer simulations to investigate the MERS model

The mathematical modelling of the Ross River Virus transmission

Ross River virus is one of the most severe communicable diseases in Australia. During the 1995/96 outbreak of Ross River virus in south-western Australia, over 1 ,300 human cases were reported. Since the symptoms of the disease are sometimes too weak to be diagnosed, it is important to determine the number of humans who actually contracted the virus during outbreaks. To do this, several mathematical models with different hypotheses are constructed and analysed mathematically. The threshold mathematical conditions of these models suggest that as well as the size of the vector mosquito population, the population size and length of viraemia periods; of host populations and the infection rates between the hosts and vectors play the main roles in the transmission. Several parameters in the transmission are currently unknown, so only simple models of RRV transmission are computer-simulated. Some of the unknown parameters are extrapolated from published studies of other arboviruses. The sensitivities of the models to some of the unknown parameters are also examined. Simulation results indicate the sero-conversion rates and ratios of clinical to subclinical human infections during the outbreaks which occurred in the Peel and Leschenault districts in Southwestern Australia

Mathematical Modeling Of Viral Zoonoses In Wildlife

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/89481/1/j.1939-7445.2011.00104.x.pd

Environmental risk factors in infectious diseases: studies in waterborne disease outbreaks, Ebola, and Lyme disease

Thesis (Ph.D.)--Boston UniversityThe resurgence of infectious diseases and global climate change's potential impact on them has refocused public health's attention on the environment's role in infectious disease. The studies in this dissertation utilize the increased availability of satellite image-derived data sets with fine temporal and geographic granularity and the expansion of epidemiologic methods to explore the relationship between the environment and infectious disease in three settings. The first study employed a novel study design and analytic methods to investigate the hypothesis that heavy rainfall is an independent risk factor for waterborne disease outbreaks (WBDOs). We found that a location experiencing a heavy rainfall event had about half the odds of a WBDO two or four weeks later than did a location without a heavy rainfall event. The location-based case-crossover study design utilized in this study may help to expand the research methods available to epidemiologists working in this developing field. The second study employed a location-based case-crossover study design to evaluate standardized differences from historic average of weekly rainfall in locations with a recorded introduction of Ebola into a human. For each 1.0 unit z-score decrease in total rainfall, the odds of an Ebola introduction three weeks later increased by 75%. Given the severity of Ebola outbreaks and the dearth of knowledge about indicators of increased risk, this finding is an important step in advancing our understanding of Ebola ecology. The third study used GIS methods on remote sensing data to estimate the association between peridomestic forest/non-forest interface within 100, 150, 250 meters and Lyme-associated peripheral facial palsy (LAPFP) among pediatric facial palsy patients. After adjustment for sex, age, and socio-economic status, children with the highest level of forest edge in the three radii of analysis had 2.74 (95% CI 1.15, 6.53), 4.58 (1.84, 11.41), and 5.88 (2.11, 16.4) times the odds of LAPFP compared to children with zero forest edge in those radii. This study is the first to examine environmental risk factors for LAPFP. Each of these studies advances the techniques used to investigate environmental risk factors for infectious disease through study design, case definition, data used, or exposure definitions

Mathematical Modelling of Spread of Vector Borne Disease In Germany

Ziel dieser Doktorarbeit ist ein mathematisches Modell zu entwickeln, um eine mögliche Ausbreitung des West-Nil-Virus (WNV) in Deutschland zu simulieren und zu bewerten. Das entwickelte Werkzeug soll auch auf eine weitere, durch Zecken übertragene Krankheit, dem Krim-Kongo-Hämorrhagischen Fieber (CCHFV) angewendet werden. Die durch den Klimawandel verursachte globalen Erwärmung unterstützt auch die Verbreitung und Entwicklung verschiedener Vektorpopulationen. Dabei hat eine Temperaturerhöhung einen positiven Einfluss auf den Lebenszyklus des Vektors und die Zunahme der Vektoraktivität. In dieser Arbeit haben wir ein Differentialgleichungsmodell (ODE) entwickelt, um den Einfluss eines regelmäßigen Eintrags von Infektionserregern auf die empfängliche Population unter Berücksichtigung des Temperatureinflusses zu verstehen. Als Ergebnis haben wir einen analytischen Ausdruck der Basisreproduktionszahl und deren Wechselwirkung mit der Temperatur gefunden. Eine Sensitivitätsanalyse zeigt, wie wichtig das Verhältnis der anfälligen Mücken zur lokalen Wirtspopulation ist. Als ein zentrales Ergebnis haben wir den zukünftigen Temperaturverlauf auf Basis der Modellergebnisse des IPCC in unser Modell integriert und Bedingungen gefunden, unter denen es zu einer dauerhaften Etablierung des West-Nil-Virus in Deutschland kommt. Darüber hinaus haben wir die entwickelten mathematischen Modelle verwendet, um verschiedene Szenarien zu untersuchen, unter denen sich CCHFV möglicherweise in einer naiven Population etablieren kann, und wir haben verschiedene Kontrollszenarien mathematisch abgeleitet, um die Belastung von einer Infektion durch Zecken zu bewältigen.The objective of this thesis is to develop the necessary mathematical model to assess the potential spread of West Nile Virus (WNV) in Germany and employ the developed tool to analyse another tick-borne disease Crimean- Congo Hemorrhagic Fever (CCHFV). Given the backdrop of global warming and the climate change, increasing temperature has benefitted the vector population. The increase in the temperature has a positive influence in the life cycle of the vector and the increase in its activities. In this thesis, we have developed an Ordinary Differential Equation (ODE) model system to understand the influence of the periodic introduction of infectious agents into the local susceptible population while taking account of influence of temperature. As results, we have found an analytic expression of the basic reproduction number and its interplay with the temperature. The sensitivity analysis shows us the importance of the ratio between the susceptible mosquitoes to the local host population. As a central result we have extrapolated the temperature trend under different IPCC conditions and found the condition under which the circulation of West Nile Virus will be permanent in Germany. Furthermore, we have utilised the developed mathematical models to examine different scenarios under which CCHFV can potentially establish in a naive population along with we mathematically derived different control scenarios to manage the burden of tick infection

The Rift Valley Fever Virus Replicative Cycle.

The Rift Valley fever virus (RVFV) is responsible for numerous, explosive epizootics throughout Africa and the Arabian Peninsula. The virus causes disease predominantly in humans and livestock, with sheep and cattle being particularly susceptible. In humans, the disease generally manifests as a flu-like illness; however, in a small percentage of cases, severe symptoms develop, such as encephalitis and hemorrhagic fever disease. In these severe cases, mortality rates are high. Livestock often succumb to the viral infection, and case-fatality rates are particularly high among young animals. Outbreaks are devastating to the public health and regional economies, and the development of antiviral therapies is difficult due to the limited understanding of the RVFV replicative cycle. We have developed a system for the generation of Rift Valley fever virus-like particles (RVF-VLPs). The RVF-VLPs are antigenically and morphologically indistinguishable from virulent RVFV virus, but can only perform a single round of infection. Using the virus-like particle system for RVFV, in combination with biochemical and crystallization techniques, we have elucidated the roles of the viral proteins in multiple steps of the viral replicative cycle. Specifically, we describe crucial interactions necessary for replication and transcription, elucidate the structure of the nucleocapsid protein, identify the envelope glycoprotein, Gn, as necessary and sufficient for the recruitment and packaging of the RdRp and encapsidated genome into virus particles, determine that the encapsidated genome triggers the efficient release of virus, and ascertain the limitations governing RVFV reassortment with other phleboviruses. Based on our results, we suggest targets for the development of therapeutics directed against RVFV and other phleboviruses.Ph.D.Cellular & Molecular BiologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/77935/1/mapipe_1.pd