Junling Ma

Political instability often exhibits long-term oscillatory patterns, commonly referred to in Structural-Demographic Theory as secular cycles. Although existing computational approaches, such as the Multi-Path Forecasting framework, can reproduce historical instability trends through high-dimensional simulations, they often lack the analytical tractability needed to clarify the structural mechanisms underlying these oscillations. To address this limitation, we propose a reduced-dimensional continuous-time model consisting of three coupled ordinary differential equations that capture the nonlinear feedback among radicalization, collective violence, and accumulated structural pressure. Using a mean-field approximation for the population reservoir, we derive a minimal dynamical system that preserves the essential structure of the original framework. Stability analysis based on the Routh–Hurwitz criterion shows that equilibrium stability is governed by the rate of exogenous economic decline. We further establish the occurrence of a supercritical Hopf bifurcation, whereby sufficiently severe economic deterioration destabilizes the equilibrium and gives rise to a stable limit cycle representing persistent secular cycles of political violence. Numerical simulations support the analytical results and provide a rigorous mathematical foundation for the endogenous periodicity of social unrest.

The northward expansion of Lyme disease in North America poses a major public health concern, with migratory birds acting as key vectors of Borrelia burgdorferi. Focusing on the seasonal activity synchrony between larvae and nymphs of Ixodes scapularis, this study developed a multi-species patch-based mathematical model to investigate its effects on tick population dynamics, infection prevalence, and spatial spread. Simulation results show that moderate synchrony between larval and nymphal activity maximizes the proportion of infected nymphs, whereas complete asynchrony favors the maximization of tick population size. Activity synchrony also accelerates pathogen colonization in newly invaded regions. Sensitivity analysis confirms that activity synchrony is the most critical factor influencing local tick infection prevalence and population size. The findings of this study provide strong theoretical support for elucidating the transmission characteristics of Lyme disease and establishing regionally targeted precision prevention and control systems.

Accurate estimation of the initial growth rate of an epidemic is critical for assessing transmissibility and guiding early interventions. Standard regression-based methods, such as negative binomial regression, often rely on independence assumptions that may underestimate uncertainty. We propose a hidden Markov model (HMM) framework that explicitly accounts for the unobserved infectious population. Using data generated from a stochastic linear SEIR model, we compare the performance of different methods for estimating the exponential growth rate. Our results show that HMMs yield more robust and reliable estimates than negative binomial regression, with improved coverage probabilities of the 95 % credible intervals. In particular, modelling the infectious population with a negative binomial distribution (with a constant probability parameter) or a binomial distribution provides more accurate inference than the other methods considered. Moreover, this framework is extended beyond the exponential phase by combining it with a logistic model to account for the slowing down of the exponential growth due to the depleting of the susceptible population. We apply this extended method to data on the early stage of COVID-19 pandemic in Africa and Ontario, Canada to estimate the initial growth rate, and we demonstrate that the HMM-logistic framework improves stability and reliability of estimates.

Background: Highly pathogenic avian influenza (HPAI) viruses, particularly subtypes such as H5N1 and H7N9, have caused widespread outbreaks in wild birds, poultry, livestock and occasionally humans, raising concerns about cross-species transmission and pandemic potential. Effective control and surveillance strategies require a thorough understanding of HPAI transmission dynamics, which can be supported by mathematical modelling. Objective: This scoping review aimed to identify mechanistic models used to study HPAI transmission. Specifically, we sought to categorize model types, describe their application contexts (e.g., wild birds, poultry, livestock, and humans), and highlight modelling gaps relevant to understanding and mitigating the risks of HPAI spread. Methods: Following PRISMA guidelines and the PRISMA extension for scoping reviews (PRISMA-ScR), we conducted systematic searches of PubMed and Web of Science to identify peer-reviewed studies employing deterministic and stochastic models to analyze HPAI transmission. Eligible articles published between January 2023 and June 2025 were screened and grouped by model structure, host populations, transmission pathways, and modelling objectives. Results: After screening, 30 studies published after 2023 were included in this scoping review. Compartmental models were the most common (26 studies), with 16 deterministic and 10 stochastic approaches. These models were primarily used to describe transmission among wild birds, poultry, livestock, and humans and to evaluate interventions such as culling, vaccination, and movement restrictions. Agent-based models (2 studies) captured individual-level interactions and spatial heterogeneity, while network models (2 studies) represented contact structures and transmission pathways between farms or species. Conclusions: Currently, mechanistic modelling of HPAI is dominated by compartmental approaches, including both deterministic and stochastic formulations, whereas agent-based and network models remain relatively underused. Although most studies focus on transmission in wild birds and poultry, and in some cases spillover infections to humans, few explicitly examine infection dynamics in livestock or in transmission between livestock and humans, despite the importance of livestock (e.g., cattle) as potential intermediaries in human infection. Key gaps persist in the integration of empirical data, representation of multi-host interactions, and evaluation of realistic intervention strategies. Addressing these limitations is essential to improve predictive accuracy and to strengthen the role of modelling in informing HPAI surveillance and control.

The unmitigated spread of novel infectious pathogens, such as SARS-CoV-2, can result in significant disease burdens and widespread societal impacts. The magnitude, severity, and duration of these events are influenced by factors such as contact patterns and the application and effectiveness of public health control measures. Many non-pharmaceutical interventions (NPIs) were implemented to target these heterogeneous drivers and modifiers of wild-type SARS-CoV-2 transmission in Canada; however, determining and understanding their individual and joint effectiveness on different populations is challenging. In this retrospective study, we delineate the impacts of age-specific NPIs in three urban Canadian regions (Calgary, Greater Vancouver, and the Greater Toronto Area) prior to widespread vaccination availability (March 2020-February 2021) and identify relative age-specific NPI effectiveness on mitigating wild-type SARS-CoV-2 transmission. We developed an age-structured Susceptible-Exposed-Infectious-Recovered (SEIR) deterministic model and stratified our population into two age groups: children and youth (0-19 years) and adults (20+ years). The model incorporated contact mixing rates, wild-type SARS-CoV-2 age-specific susceptibility, and NPI strength. Detailed timelines for each region were compiled, capturing the time-dependent implementation of age-specific and population wide NPIs. Using maximum likelihood estimation, we determined regional baseline transmission probabilities in the absence of widespread NPIs, then estimated the subsequent time-dependent and age-specific NPI strength on transmission reduction. Finally, we considered counterfactual NPI scenarios and compared simulated regional age-specific epidemic trajectories with reported SARS-CoV-2 case data. The age-specific and sequential time-dependent NPI strength on wild-type SARS-CoV-2 transmission reduction was estimated for each region during March 2020-February 2021. We observed that adult-specific contacts play a large role in transmission, and moderately-strengthened adult-specific NPIs were more effective in reducing transmission across all regions compared to a drastic strengthening of NPIs in children and youth (i.e., closing schools). These results held when varying temporal applications of singular and joint counterfactual NPI scenarios; however, regional contexts and data uncertainties caused varied levels of effectiveness. By considering population heterogeneity, our retrospective study provides insight into age-specific NPI effectiveness on wild-type SARS-CoV-2 transmission. These findings and associated model can inform decision-making related to targeted NPI implementation and aid in resource planning and preparedness for future emerging disease outbreaks.

Contact tracing is an important public health measure to control disease transmission. However, it is difficult to assess contact tracing during the exponential stage of an epidemic with multiple control measures, because the exponential growth rate is influenced by all measures. We present new SEIR and SEAIR contact tracing models that track contacts in randomly mixed populations, and calibrate them to simulated epidemic curves to determine the data that allow us to assess the effect of contact tracing. We find that new-case counts, counts of cases identified by contact tracing (or voluntary tests), and counts of symptomatic onset are necessary to identify model parameters and evaluate the effect of contact tracing. We fit our contact tracing models to COVID-19 pandemic data in Ontario, Canada, during March 16–May 1, 2020. Our results show that approximately 29% of cases were identified via contact tracing of close contacts. Contact tracing moderately reduces the control reproduction number by about 25%, but significantly reduces the prevalence by more than half. Ignoring asymptomatic transmissions gives similar estimates for the effect of contact tracing, but significantly underestimates the prevalence.

We use mathematical modeling to study the proliferation dynamics of CD4+ T cells within an immune response. This proliferation is driven by the autocrine reaction of helper T cells and interleukin-2 (IL-2), and regulated by natural regulatory T cells (nTregs). Previous studies suggested that a fratricidal mechanism is necessary to eliminate helper T cells post-infection. Contrary to this, our mathematical analysis establishes that the depletion of these cells is due to two pivotal factors: the saturation in the proliferation rate of helper CD4+ T cells at high IL-2 concentrations, and the activation rate of nTregs outpacing their death rate. This yields an excitable process, such that the proliferation starts once the helper T cell population passes a threshold. Additionally, we find that when the proliferation of nTregs lags behind their mortality, induced regulatory T cells (iTregs) are crucial to curbing the proliferation of helper CD4+ T cells.

Even with daily case counts, the true scope of the COVID-19 pandemic in Canada is unknown due to undetected cases. We develop a novel multisite disease analytics model which estimates undetected cases using discrete-valued multivariate time series in the framework of Bayesian hidden Markov modelling techniques. We apply our multisite model to estimate the pandemic scope using publicly available disease count data including detected cases, recoveries among detected cases, and total deaths. These counts are used to estimate the case detection probability, the infection fatality rate through time, the probability of recovery, and several important population parameters including the rate of spread and importation of external cases. We estimate the total number of active COVID-19 cases per region of Canada for each reporting interval. We applied this multisite model Canada-wide to all provinces and territories, providing an estimate of the total COVID-19 burden for the 90 weeks from 23 April 2020 to 10 February 2022. We also applied this model to the five health authority regions of British Columbia, Canada, describing the pandemic in B.C. over the 31 weeks from 2 April 2020 to 30 October 2020.

Non-pharmaceutical interventions (NPIs) are effective in mitigating infections during the early stages of an infectious disease outbreak. However, these measures incur significant economic and livelihood costs. To address this, we developed an optimal control framework aimed at identifying strategies that minimize such costs while ensuring full control of a cross-regional outbreak of emerging infectious diseases. Our approach uses a spatial SEIR model with interventions for the epidemic process, and incorporates population flow in a gravity model dependent on gross domestic product (GDP) and geographical distance. We applied this framework to identify an optimal control strategy for the COVID-19 outbreak caused by the Delta variant in Xi’an City, Shaanxi, China, between December 2021 and January 2022. The model was parameterized by fitting it to daily case data from each district of Xi’an City. Our findings indicate that an increase in the basic reproduction number, the latent period or the infectious period leads to a prolonged outbreak and a larger final size. This indicates that diseases with greater transmissibility are more challenging and costly to control, and so it is important for governments to quickly identify cases and implement control strategies. Indeed, the optimal control strategy we identified suggests that more costly control measures should be implemented as soon as they are deemed necessary. Our results demonstrate that optimal control regimes exhibit spatial, economic, and population heterogeneity. More populated and economically developed regions require a robust regular surveillance mechanism to ensure timely detection and control of imported infections. Regions with higher GDP tend to experience larger-scale epidemics and, consequently, require higher control costs. Notably, our proposed optimal strategy significantly reduced costs compared to the actual expenditures for the Xi’an outbreak.

The adaptive immune system has two types of plasma cells (PC), long-lived plasma cells (LLPC) and short-lived plasma cells (SLPC), that differ in their lifespan. In this paper, we propose that LLPC is crucial to the clearance of viral particles in addition to reducing the viral basic reproduction number in secondary infections. We use a sequence of within-host mathematical models to show that, CD8 T cells, SLPC and memory B cells cannot achieve full viral clearance, and the viral load will reach a low positive equilibrium level because of a continuous replenishment of target cells. However, the presence of LLPC is crucial for viral clearance.