Epidemiological dynamics in populations with demographic and spatial structure

The dynamics of infectious disease epidemics are driven by transmission, transmission depends on contact and contact patterns are determined by the relationships between individuals. The goal of this research is to explore the roles of some of these contact processes using mathematical models that account for spatial and demographic structures within the population. The results of this research will enhance our understanding of the spread of infectious diseases and may lead to improved surveillance or control strategies.
We will use a metapopulation framework to incorporate spatial structure into our models. The premise is to view the population as a collection of connected, but semi-autonomous, subpopulations. These subpopulations may correspond to regions of a city or country and be coupled via temporary (commuter) movement or permanent (migratory) movement. Typically, we are concerned with how the composition and coupling of these subpopulations impacts the persistence and spatial spread of the infectious disease.
We will use a household framework to incorporate demographic structure into our models. Here, the total population is viewed as small groups of cohabiting individuals. Stochastic effects are important when modelling the interactions between individuals within the household because we are considering small numbers of individuals who share frequent and lengthy contacts. The resultant contact chains are often modelled as Markov processes. Analysis focuses on how household composition and the coupling between households impacts the risk of an epidemic.
We aim to further develop the theory of epidemiological dynamics in metapopulation and household modelling frameworks. Our approach will combine mathematical analysis of simple models, computational analysis of more complex models, and empirically driven simulation using agent-based models. We anticipate that the simplest models will offer key insights, but will not capture some important aspects of the real world circumstance. More realistic models may become rather complex and we will need to develop numerically efficient methods for calculating essential metrics of epidemiological analysis such as reproduction numbers.
We have identified two initial projects. We expect that these will lead to an abundance of other research avenues. In project 1 we will develop a framework based on a metapopulation of households on a city scale. We will group households into spatially delimited subpopulations, and couple these subpopulations by the movement of people. We hypothesise that, in many cities, districts often have distinct demographic characteristics, including the household size distribution. We expect that these characteristics, together with the district size and pattern of mixing with other districts will impact the risk, persistence, and spatial spread of infectious diseases. Ulaanbaatar in Mongolia may be a good case study. We are in contact with possible collaborators from UNICEF and The National University of Mongolia.
In project 2 we will develop a model for vector-borne disease epidemiology based on the household framework. We anticipate that, in this framework, it will be important to consider the household composition in terms of the number of people and the number of mosquitoes living there. We hypothesise that transmission between households can occur through two routes: (1) An infectious person visits another household and is bitten by a susceptible mosquito who becomes infected, (2) a susceptible person visits another household and is bitten by an infectious mosquito. These routes will likely have different roles in the epidemiological dynamics. Dengue virus may be a good case study. The main mosquito that transmits dengue often remain within the same house throughout its life, and can be modelled as an inhabitant.