## Thesis Format

Integrated Article

# Study of Behaviour Change and Impact on Infectious Disease Dynamics by Mathematical Models

## Degree

Doctor of Philosophy

## Program

Applied Mathematics

Zou, Xingfu

## Abstract

This thesis uses mathematical models to study human behaviour changes' effects on infectious disease transmission dynamics. It centers on two main topics. The first concerns how behaviour response evolves during epidemics and the effects of adaptive precaution behaviour on epidemics. The second topic is how to build general framework models incorporating human behaviour response in epidemiological modelling.

In the first project, based on the fact that a fraction of the epidemiologically susceptible population is actually susceptible due to precautions, we present a novel perspective on understanding the infection force, incorporating human protection behaviours. This view explains many existing infection force functions and motivates new forms of infection force functions. We demonstrate an SIRS model with time delay, considering disease surveillance of both the current and the past. This delay model aims to answer a specific question: How do disease surveillance data assigned varying weights affect disease control measures? Is it related to how recent these data are? To do so, we study the local bifurcation caused by delay and the parameter reflecting the weight of past epidemics.

In the second project, motivated by the view of infection force in the first project, we propose a general framework model for the above-mentioned second topic. This framework is based on the Kermack-McKendrick model with infection age and can be reduced to various models by choosing particular kernels. We derive renewal equations for the incidence and the infection force, which are integral equations and focus on the processes. Besides generalizing the infection force function in the first project into renewal equations, another primary objective of this project is to explore how human behaviour changes affect the final epidemic size. We found that non-pharmaceutical precautions adoption can reduce the final epidemic size.

In the last project, we formulated a general framework with evolving precaution levels through some specific SIS type of disease models to the first concerned topic. These models attempt to answer the two questions: (1). How does the behaviour response impact the disease dynamics? (2). How does the response level evolve with the disease? In addition, we consider the time lag in behaviour response since it takes time for humans to process the epidemiological information and plan non-pharmaceutical precautions.

## Summary for Lay Audience

Human behaviour plays a key role in infectious disease transmission, especially for those infectious diseases that are transmitted through close person-to-person contact. Triggered by psychological factors (mainly perception of risk and infection fear), people spontaneously change their behaviour, like adopting various control interventions over time, to reduce their susceptibility in response to an epidemic threat. Roles of human behaviour in transmission motivate the necessity of including behaviour response in mathematical epidemiological models. This thesis mainly studies the interaction between human behaviour change as well as its determinants (psychological factors) and infectious disease transmission by mathematical epidemiological models.

Among epidemiology concepts, infection force relates to the probability of a susceptible getting infected and can describe the impact of individual behaviour. We start by revisiting the infection force from a new angle and justifying the notion of infection force from the viewpoint of susceptibility. After that, we study behaviour change from two sides in mathematical modelling: (1). the impacts of human behavioural response on epidemics; (2). the adaptive evolution of behavioural response levels with epidemic dynamics. In addition, we answer the main three questions by mathematical theoretical techniques: (1). Is it possible for an ”epidemic” to become ”endemic” when precautionary intervention is employed? What are the necessary conditions? (2). Which factors affect disease control measures if disease surveillance data of present and past time are weighted differently? How is it related to data recentness and weight? (3). Without demography, will some fraction of the population escape infection over whole epidemics if precautionary behaviour is involved? If so, how large is this fraction? How does behaviour response affect this fraction?

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