Modelling and data analysis of the transmission of Avian Influenza, Ebola Virus Disease and Middle East Respiratory Syndrome Coronavirus

Abstract

Emerging infectious diseases (EIDs) in recent years have captured worldwide attention due to their potential for rapid spread between countries and continents. In this thesis, we explored the characteristics and explained the patterns of infectious diseases including Avian Influenza A(H7N9), Ebola Virus Disease (EVD) and Middle East Respiratory Syndrome Coronavirus (MERS-CoV) and human influenza A(H1N1). For Avian Influenza A(H7N9),a Susceptible-Exposed-Infectious-Recovered-Virus-Susceptible (SEIRVS) model was developed, which included a special "V" compartment representing the H7N9 viruses in the environment. In addition, periodic transmission and non-periodic transmission were also considered. For Ebola Virus Disease, spatio-temporal analysis was conducted by calculating correlation between average epidemic week and longitude, latitude and along seashore, and we developed a Susceptible-Exposed-Infectious-Recovered-Death (SEIRD) model. In the SEIRD model, the compartment "D" represented the unprocessed dead human bodies which were reported to still spread Ebola viruses to susceptible individuals. For MERS-CoV, the potential correlation between MERS-CoV and influenza was explored by graphical comparison of the reported cases of both influenza and MERS-CoV in the Middle East. In addition, we studied the time-line of MERS-CoV cases, segregating the time period by Ramadan and Hajj. The ratio of camel cases and human cases was also studied by a Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS) model with non-periodic transmission rate. For human influenza A(H1N1) pandemic in 1918, the corresponding influence of human behavior on reported mortality was investigated, by adding new compartment "P" for human behavioral reactions and comparing different forms of reaction terms. Finally, simulation on all 334 districts was conducted. SEIRVS model with non-periodic transmission for H7N9 cases provided the best model fit, which confirmed the influence of environmental transmission. Mean lifetime of 2.5 year for chickens were used, and virus importing rate of 1.8 per year, persistence duration of 115.85 days was estimated by the model. For EVD, we identified significantly positive correlation between average epidemic week and longitude, latitude and along seashore, indicating the transmission pattern was from southeast to northwest along the seashore. Non-periodic transmission under-performed compared to the seasonally period transmission, which referred to the dominant roles of control measures in West Africa countries. For MERS-CoV, the epidemic waves were very closely followed the Influenza waves in the Middle East. Besides, the number of MERS-CoV cases remained low consistently during Ramadan and had sharp increases displayed consistently after Hajj. For A(H1H1) human influenza in 1918, our model that used a modified-Hill function as reaction term provided a substantially good simulation for 334 administrative districts in the United Kingdom, with a median Pearson correlation coefficient of 0.6362. Infectious disease is a great threat to human health all over the world, with the ability to spread among populations. Using simple Ordinary Differential Equations (ODE) and compartmental modelling techniques, as well as spatial analysis played an important role in studying the spreading pattern and transmission of infectious diseases. Our mathematical frameworks have significant theoretical value for exploring infectious diseases, which improved our understanding of the transmission dynamics and helped us to take appropriate intervention strategies.