arXiv subjects

Dongni Zhang

Publications and source records attributed to Dongni Zhang.

6 recordsLinked to original sources

arXiv2026

Constructing Contact and Connectivity Matrices for Infectious Disease Modelling

Contact (or mixing, or more generally connectivity) matrices are a fundamental component of modelling and inference for infectious disease epidemiology. Their structure and parametrisation directly accounts for the frequency of interactions between different subpopulations of individuals, as well as having the potential to encode dynamic heterogeneity in these interactions across demographic axes, space and time. Considerable research has been devoted to the structure and estimation of (components of) these matrices to help inform outbreak control and forecast disease spread. In this paper, we review the existing literature on the data types used to construct contact matrices and the methods for incorporating uncertainties and heterogeneities into them. We also highlight remaining challenges and future directions in the use of these contact matrices for epidemiological research.

stat.AP↗

arXiv2025

A Behaviour and Disease Model of Testing and Isolation

There has been interest in the interactions between infectious disease dynamics and behaviour for most of the history of mathematical epidemiology. This has included consideration of which mathematical models best capture each phenomenon, as well as their interaction, but typically in a manner that is agnostic to the exact behaviour in question. Here, we investigate interacting behaviour and disease dynamics specifically related to decisions around testing and isolation. To carry out our investigation we extend an existing "behaviour and disease" (BaD) model by incorporating the dynamics of symptomatic testing and isolation, including the influence of positive tests on perception of infection risk. We provide a dynamical systems analysis of the ordinary differential equations that define this model, providing theoretical results on its behaviour early in a new outbreak (particularly its basic reproduction number) and endemicity of the system (its steady states and associated stability criteria). We then supplement these findings with a numerical analysis to inform how temporal and cumulative outbreak metrics depend on the model parameter values for epidemic and endemic regimes. We observe novel model outputs such as epidemics that have more observed cases detected through increased testing, but are less objectively severe in terms of total number of infections.

q-bio.PE↗

arXiv2025

Epidemic models with digital and manual contact tracing

We analyze a Markovian SIR epidemic model where individuals either recover naturally or are diagnosed, leading to isolation and potential contact tracing. Our focus is on digital contact tracing via a tracing app, considering both its standalone use and combination with manual tracing. We prove that as the population size $n$ grows large, the epidemic process converges to a limiting process, which, unlike typical epidemic models, is not a branching process due to dependencies created by contact tracing. However, by grouping to-be-traced individuals into macro-individuals, we derive a multi-type branching process interpretation, allowing computation of the reproduction number $R$. This is then converted to an individual reproduction number $R^{(ind)}$, which, contrary to $R$, decays monotonically with the fraction of app-users while both share the same threshold at 1. Finally, we compare digital (only) contact tracing and manual (only) contact tracing, proving that the critical fraction app-users $π_c$ required for $R=1$ is higher than the critical fraction manually contact traced $p_c$ for manual tracing.

math.PR↗

arXiv2025

Sideward contact tracing in an epidemic model with mixing groups

We consider a stochastic epidemic model with sideward contact tracing. We assume that infection is driven by interactions within mixing events (gatherings of two or more individuals). Once an infective is diagnosed, each individual who was infected at the same event as the diagnosed individual is contact traced with some given probability. Assuming few initial infectives in a large population, the early phase of the epidemic is approximated by a branching process with sibling dependencies. To address the challenges given by the dependencies, we consider sibling groups (individuals who become infected at the same event) as macro-individuals and define a macro-branching process. This allows us to derive an expression for the effective macro-reproduction number which corresponds to the effective individual reproduction number and represents a threshold for the behaviour of the epidemic. Through numerical examples, we show how the reproduction number varies with the distribution of the mixing event size, the mean size, the rate of diagnosis and the tracing probability.

q-bio.PE↗

arXiv2024

An SEIR network epidemic model with manual and digital contact tracing allowing delays

We consider an SEIR epidemic model on a network also allowing random contacts, where recovered individuals could either recover naturally or be diagnosed. Upon diagnosis, manual contact tracing is triggered such that each infected network contact is reported, tested and isolated with some probability and after a random delay. Additionally, digital tracing (based on a tracing app) is triggered if the diagnosed individual is an app-user, and then all of its app-using infectees are immediately notified and isolated. The early phase of the epidemic with manual and/or digital tracing is approximated by different multi-type branching processes, and three respective reproduction numbers are derived. The effectiveness of both contact tracing mechanisms is numerically quantified through the reduction of the reproduction number. This shows that app-using fraction plays an essential role in the overall effectiveness of contact tracing. The relative effectiveness of manual tracing compared to digital tracing increases if: more of the transmission occurs on the network, when the tracing delay is shortened, and when the network degree distribution is heavy-tailed. For realistic values, the combined tracing case can reduce $R_0$ by $20-30\%$, so other preventive measures are needed to reduce the reproduction number down to $1.2-1.4$ for contact tracing to make it successful in avoiding big outbreaks.

physics.soc-ph↗

arXiv2022

Analysing the Effect of Test-and-Trace Strategy in an SIR Epidemic Model

Consider a Markovian SIR epidemic model in a homogeneous community. To this model we add a rate at which individuals are tested, and once an infectious individual tests positive it is isolated and each of their contacts are traced and tested independently with some fixed probability. If such a traced individual tests positive it is isolated, and the contact tracing is iterated. This model is analysed using large population approximations, both for the early stage of the epidemic when the "to-be-traced components" of the epidemic behaves like a branching process, and for the main stage of the epidemic where the process of to-be-traced components converges to a deterministic process defined by a system of differential equations. These approximations are used to quantify the effect of testing and of contact tracing on the effective reproduction numbers (for the components as well as for the individuals), the probability of a major outbreak, and the final fraction getting infected. Using numerical illustrations when rates of infection and natural recovery are fixed, it is shown that Test-and-Trace strategy is effective in reducing the reproduction number. Surprisingly, the reproduction number for the branching process of components is not monotonically decreasing in the tracing probability, but the individual reproduction number is conjectured to be monotonic as expected. Further, in the situation where individuals also self-report for testing, the tracing probability is more influential than the screening rate (measured by the fraction infected being screened).

q-bio.PE↗