Author: Zhao, Shi
Title: Mathematical modelling of the spread of mosquito-borne diseases and childhood infections
Advisors: He, Daihai (AMA)
Yiu, Ka-fai Cedric (AMA)
Degree: M.Phil.
Year: 2018
Subject: Hong Kong Polytechnic University -- Dissertations
Emerging infectious diseases
Communicable diseases -- Mathematical models
Department: Department of Applied Mathematics
Pages: xxiv, 157 pages : color illustrations
Language: English
Abstract: Introduction Emerging infectious diseases (EIDs) in recent years have captured worldwide attention due to their potential for the rapid spread between countries and continents. In this thesis, we are going to explore the characteristics and try to explain the patterns of infectious diseases including Yellow Fever (YF) in Luanda, Angola 2015-16, Zika Virus Diseases (ZVD) in Northeastern (NE) Brazil 2015-16, Japanese Encephalitis (JE) in Hong Kong 2004-16 and Varicella (or chickenpox) in Shenzhen, China 2013-15, in order to further interpret the features and key factors of infectious diseases including potential impact factors (e.g., climatic factors, vector abundance, human behaviors and vaccination programs ... etc.). We also combined the game theoretical framework with an epidemic model (based on the compartmental SIR model) to study the decision-making process regarding to travelling during an outbreak, and to investigate the effects of travel strategies on local disease control. Data Collection Cases data were collected from various public domains: Center of Health Protection (CHP) of Hong Kong government, Yellow Fever situation reports of the World Health Organization (2016), Shenzhen Centers for Disease Control and Prevention (CDC) and Minister of Health of Brazil. Besides, regional climatic data were also collected for analysis. Methods On the basis of classical models in epidemiology, we constructed innovative compartmental models and agent-based models for specified infectious diseases and for particular research goals. For Yellow Fever (YF), a novel compartmental model was built up, which includes both host and vector populations and time-dependent vector abundance. In addition, we also considered the local vaccination campaign. For Zika Virus Diseases (ZVD), we also established compartmental model with hosts' and time-dependent vectors' populations, we model ZVD epidemics according to local GBS time series (in Northeastern Brazil, where ZVD hit hardest among the world from 2015-16) and we studied the relationship between the possible infectivity of asymptomatic infection and the final ZVD infection attack rate (IAR). For Japanese Encephalitis (JE), as the ratio of pig population and human JE cases was also explored in the same level, we build up an epidemiology model among local pig population and connect to human cases with a spill-over rate. In the model, we considered long-term mosquitoes, pigs and humans dynamic, we studied the "skip-and-resurge" of JE epidemics in Hong Kong and hypothesize that "new JEV strain invaded Hong Kong around 2011". For Varicella, an agent-based model is constructed to study the varicella infection among school children, and simulate the effects of different school-based vaccination programs. Last but not least, game theory is employed to model the individual decision-making process. A game theoretical framework is combined with an epidemic model to study the decision-making process regarding to travelling during an outbreak. The group optimal strategy that maximizes overall population utility is also computed.
Results For YF, the local vaccination campaign saved 5.1-fold more people from death (with 73 death reported originally), the possible human reaction to recent YF deaths (i.e., the death-driven transmissibility) is likely to explain the transmission pattern of the YF epidemic in Luanda, and we report very low YF IAR (0.09-0.15%) and high YF cases reporting ratio (71%). For ZVD, we found the exceeding local GBS time series can explain the first ZVD epidemics (the first wave) of NE Brazil in 2015-16 and the infectivity of asymptomatic infections are positively related to the ZVD IAR of 2015-16. For JE, the simple mathematical model can re-generate the long-term JE epidemics in Hong Kong, we report without vectors JEV cannot maintain among swine, the dramatical decrease of local living pigs was likely to be responsible for "skip" of JE from 2006-10, and we show high confidence in the hypothesis that "the resurge of JE since 2011 was likely due to new strain invaded Hong Kong". For varicella, our agent-based (or school-based) model fits the observed cases data well and introducing school-based vaccination program can effectively prevent large-scale varicella outbreaks (particularly during summer). At last, for the epidemiological travelling game, we find perfect agreement between individual and group optimal strategies for a range of epidemiologically and economically plausible values. However, in regions where disagreement occurs, the conflict between the individual optimum (corresponding to a "voluntary entrance" scheme) and the group optimum (a "restricted entrance" scheme) is often extreme. In this region, model outcomes are highly sensitive to small changes in the infection transmissibility and traveller costs/benefits. Conclusion Infectious disease is a great threat to human health all over the world, with the ability to spread among the population. Simple ODE equations and compartmental model plays an important role in studying the spreading pattern and transmission of infectious diseases. Our mathematical frameworks have significant theoretical value for exploring infectious diseases, improving our understanding of the dynamics and helping us to take appropriate strategies. Regarding to the travelling game theory framework, we conclude that a conflict between individually optimal and group optimal travel strategies during an outbreak may not occur under many scenarios, but in other cases, extreme conflicts could emerge suddenly even under slight changes in epidemiological or economic conditions.
Rights: All rights reserved
Access: open access

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