Infectious Disease Modelling

The Hajj is an annual pilgrimage made by millions of Muslims to Mecca in the Kingdom of Saudi Arabia (KSA). The large number of international attendees at the Hajj increases the risk of global infectious disease spread. However, we know very little about the benefits, costs, and cost-effectiveness of testing and quarantining strategies to contain epidemic spread during mass gathering events. In this work we developed a stochastic discrete-time compartmental metapopulation model to simulate international epidemics of infectious pathogens and their potential importation into KSA during the Hajj. We used the model and an epidemic simulation study to evaluate the impact and cost-effectiveness of three testing and quarantining strategies for arriving pilgrims: randomly testing 99% of pilgrims, 80% of pilgrims, or using a symptom-based screening strategy. The simulations lasted 100 days, covering the 30 days before the Hajj and 65 days after the Hajj. Under the conditions assumed in our simulation study, there was strong evidence that testing and quarantining strategies are cost-effective measures for controlling epidemic threats at the Hajj. The median net monetary benefits of intervention strategies ranged from Intl$-41.89M [95% quantile range Intl$-42.37M to Intl$3.18B] to Intl$12.68B [Intl$-8.70B to Intl$13.82B] across scenarios with different pathogen characteristics (based on the natural histories of SARS-CoV-2 and H1N1 Influenza) and epidemic seed locations. Our results were sensitive to the data sources that were used to estimate the number of pilgrims travelling to KSA by origin country, with flight passenger statistics providing biased estimates of pilgrim numbers. Our work provides an adaptable tool to inform infectious disease risk assessments and evaluate the cost-effectiveness of possible disease control measures for the Hajj, and could be extended to other mass gathering events.

Malaria transmission in Nigeria is highly seasonal and climate-sensitive, yet routine surveillance and meteorological datasets remain underutilized for predictive modelling at subnational levels. This study modelled seasonal malaria incidence trends in Nasarawa State, Nigeria using routine surveillance and climatic data. A retrospective ecological time-series study was conducted using monthly confirmed malaria incidence data from all 13 Local Government Areas of Nasarawa State between 2021 and 2025. Rainfall and temperature were examined as the climatic predictors. Seasonal decomposition and cross-correlation analyses were performed to identify the temporal patterns and lag structures. Seasonal Autoregressive Integrated Moving Average (SARIMA) and Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX) models were developed using the Box-Jenkins framework. Model performance was evaluated using the Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). Malaria incidence showed pronounced seasonal peaks, with the highest transmission occurring during the rainy season. Cross-correlation analysis identified rainfall at a one-month lag and contemporaneous temperature as significant predictors of malaria incidence. The SARIMAX model outperformed the univariate SARIMA model, achieving strong predictive accuracy (MAPE = 8.7%). Forecast projections indicate sustained transmission with a peak incidence expected between June and August 2026. Malaria transmission in Nasarawa follows a predictable seasonal pattern that is influenced by climatic variability. Incorporating rainfall and temperature into SARIMAX models improves the forecasting performance and provides evidence supporting climate-informed malaria surveillance and preparedness in endemic settings.

Canine rabies persists in NDjamena (Chad) despite vaccination campaigns exceeding 70% coverage, suggesting a role for dog mobility and spatial heterogeneity. We propose a metapopulation SEIR model incorporating distance-modulated dog movements and an explicit vaccinated class. Analysis of the isolated patch establishes global stability of the disease-free equilibrium via a Lyapunov function. For the metapopulation, a composite Lyapunov function shows that elimination is governed by a reproduction number [R]v. Calibrated with field data (2012-2022), simulations reveal that uniform vaccination of both patches reduces [R]v by 46% (from 2.84 to 1.52) but does not achieve elimination, while targeted strategies are less effective. These results demonstrate that exhaustive vaccination coverage across the entire urban network and increased vaccination intensity are necessary to eliminate canine rabies in NDjamena. Our model provides a quantitative framework for planning effective control strategies.

Malaria persists worldwide, exerting its greatest impact in sub-Saharan Africa. This study develops and uses a mathematical model to assess how sub-optimum versus optimum treatment of malaria drives asymptomatic infections, immunity build-up, and sustained transmission, providing insights for effective control. Fitted to case data from Kenya and Nigeria, the framework is used to quantify the burden of malaria and the additional cost associated with sub-optimum treatment. Global sensitivity analysis identifies mosquito demographic parameters, biting rates, and malaria treatment rate among major disease drivers under sub-optimum treatment, emphasizing the need for integrated strategies that improve access to optimum treatment and reduce mosquito-human contact. Model simulations show that sub-optimum treatment amplifies asymptomatic prevalence, sustaining/increasing malaria transmission and burden. Further simulations reveal that optimum treatment could avert more than one-third of infections and deaths, while asymptomatic infections contribute up to $96%$ ($75%$) of malaria-related Years Lived with Disability in Kenya (Nigeria). Cost analysis shows that optimum treatment lowers malaria burden significantly and can reduce annual total treatment costs by $\approx $12$ million, underscoring the substantial economic and public health gains of limiting sub-optimum care. This study demonstrates that effective and sustained malaria control requires strengthening adherence to treatment, minimizing sub-optimum treatment, reducing mosquito-human contact, and targeting asymptomatic carriers to curb hidden transmission and reduce long-term health and economic losses.

Artemisinin partial resistance has not yet been reported in southern Africa. Therefore, the magnitude of the spread of artemisinin partial resistance in this region is yet to be quantified. Using a two strain metapopulation modelling framework, we explored possible spread of artemisinin partial resistance in eight connected countries with high level of human movement. We explored three scenarios in which artemisinin partial resistance may first enter circulation: low malaria transmission level country; high malaria transmission level country and all countries and compared to an artemisinin partial resistance free scenario. Partial rank correlation coefficient sensitivity analysis was performed to identify key parameters that drive artemisinin partial resistance spread. Our model simulations show that high mobility between countries can increase the spread of mutations associated with delayed clearance. Suggesting that artemisinin partial resistance will be confirmed (>5% partial resistant cases) after 14 years of circulation if it is to appear in southern Africa. We confirm that human movement, both human-to-mosquito and mosquito-to-human probabilities of transmission, were significant and highly sensitive parameters in the spread of artemisinin partial resistance. Human mobility between countries can facilitate the spread of artemisinin partial resistance. More research is needed to identify strategies to preserve the efficacy of artemisinin-based combination therapies in the presence of partial artemisinin resistance, which may eventually lead to treatment failure and necessitate regimen replacement.

Coinfection of COVID-19 and malaria in endemic regions may generate complex epidemiological interactions that influence susceptibility patterns, disease burden, and outbreak risk. Although malaria-acquired immunity has been hypothesized to modulate host responses to other infections, its population-level implications for COVID-19 transmission under uncertainty remain insufficiently understood. In this study, we develop a deterministic-stochastic compartmental model for the coupled dynamics of COVID-19, malaria, and their co-infection. Malaria-acquired partial immunity is incorporated through a relative susceptibility parameter that reduces the risk of COVID-19 infection among malaria-recovered individuals. For the deterministic system, we establish positivity, boundedness, an invariant feasible region, and basic reproduction numbers for the COVID-19-only and malaria-only subsystems. We then use numerical simulations to examine how immunity-mediated reductions in susceptibility may influence COVID-19 incidence, peak burden, hospitalization, and cumulative mortality. To account for environmental and transmission variability, we extend the deterministic model to an Ito stochastic differential equation framework and use repeated realizations to characterize uncertainty in epidemic trajectories, peak distributions, and outbreak risk. In addition, global sensitivity analysis based on partial rank correlation coefficients (PRCCs) is performed to identify the parameters with the greatest influence on COVID-19 outcomes. Our results suggest that, under the assumed modeling framework, malaria-acquired partial immunity may reduce the peak infectious burden and cumulative mortality associated with COVID-19. The stochastic simulations further show substantial variability around deterministic trajectories and indicate a non-negligible probability of large outbreak events that are not fully captured by mean-field predictions alone. Overall, the proposed framework provides an uncertainty-aware, mechanistic basis for studying COVID-19-malaria co-dynamics and for assessing how interacting disease processes may shape epidemic outcomes in endemic settings.

Vaccine-acquired immunity plays an important role in controlling the spread of many infectious diseases; however, vaccine efficacy can diminish over time. This work uses a mathematical model to study the effects of waning vaccination-acquired immunity on infection incidence. With an SEIR-type compartmental model that considers both vaccinated and unvaccinated populations (and their mixing), we present mathematical conditions under which vaccinated individuals drive ongoing growth in infections, i.e., over half of the daily incidence arises from vaccinated individuals. Analysis of a mathematical model of COVID-19 spread in the state of Colorado suggests how and for what duration vaccinated individuals could have sustained such growth. Importantly, our model demonstrates that, despite potential for brief vaccinated-driven periods of growth in infections, which occur among unvaccinated-driven periods of growth in infections, increased vaccination coverage always reduces total cases and total hospitalizations. This work provides insight into how waning immunity in vaccinated populations can contribute to ongoing infection incidence and demonstrates the value of complementary interventions to prevent disease spread in vaccinated populations.

Temperate regions of the world, such as southern Australia, often experience increased health burden from respiratory pathogens during winter. The ability to forecast short-term trends in cases of these pathogens is of significant interest to public health. Across the 2024 southern hemisphere winter period, the Australia--Aotearoa Consortium for Epidemic Forecasting and Analytics (ACEFA) ran a pilot respiratory virus forecasting initiative in collaboration with the Victorian Department of Health. Each week from the 9th of May 2024 through to 12th September 2024, the consortium solicited 28-day forecasts of daily case incidence for influenza, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), and respiratory syncytial virus (RSV) from multiple research groups. Four component model forecasts were contributed by three different research groups, with a fourth group utilising the component forecasts to generate ensemble forecasts (making a total of six models, four component models and two ensembles). Here we statistically evaluated the performance of each forecast and a baseline model against the observed case data. The two ensemble models were found to be frequently the top performing models. All models performed worse than the baseline model around the epidemic peaks for each pathogen.

Tetanus is a severe disease of the nervous system, transmitted through bacteria in the environment. In the absence of medical attention, case fatality rates are extremely high. Despite progress towards maternal and neonatal tetanus elimination targets, tetanus remains a serious public health problem. Routine infant and maternal vaccination have contributed to considerable reduction in cases and deaths from tetanus globally. However, protective immunity wanes over time. To increase duration of protection, the World Health Organization recommends three diphtheria-tetanus-pertussis-containing vaccine booster doses be given in early childhood, childhood, and adolescence. Evidence to support country-level decision-making about the introduction of these booster doses is critical. We have developed a novel age-structured, deterministic compartmental model of tetanus transmission and vaccination. The model is driven by environmental transmission and incorporates interventions like hygiene and safe birth practices to reduce the magnitude of environmental transmission. It explicitly models vaccination, separating each dose of the primary series, booster doses, and maternal vaccination to capture dose-specific effectiveness and duration of protection. The model captures heterogeneous immunity profiles by dose and age, and the cumulative nature of vaccine-derived protection. The immune dynamics follow the patterns described in literature and can replicate seroprevalence studies, although the exact characterisation of immunity in the literature still has gaps. This model presents a substantial advancement on previously published models and is well positioned to inform tailored vaccination strategies to reduce neonatal and non-neonatal tetanus.

The emergence of a hantavirus variant aboard a commercial cruise ship presents a significant public health concern. This study develops a discrete-time stochastic Susceptible-Exposed-Infectious-Recovered-Dead model to estimate transmission dynamics, hidden exposed infections, and outbreak risk among passengers and crew. Epidemiological parameters and latent disease states were inferred using an Ensemble Adjustment Kalman Filter calibrated to reported case data from WHO and ECDC situation reports. The estimated basic reproduction number was 2.76, with a 95% confidence interval of 2.52-2.99, indicating substantial potential for sustained onboard transmission before strict quarantine measures. Simulations further suggest that several exposed individuals may remain unidentified during the early outbreak phase, creating a hidden reservoir that symptom-based surveillance alone may fail to detect. These findings highlight the importance of rapid surveillance, widespread testing, targeted quarantine, and active monitoring of exposed individuals in confined travel settings. The proposed modeling framework can support timely outbreak assessment and intervention planning for infectious-disease events in similarly dense and spatially constrained populations.

Infectious disease dynamics are strongly shaped by human mobility, social structure, and heterogeneous contact patterns, yet many epidemic models do not jointly capture these features. This study develops a spatial metapopulation epidemic model incorporating recurrent group-switch interactions to represent real-world transmission processes. Building on the Movement-Interaction-Return framework, the model integrates household structure, age-stratified contacts, and mobility between locations within a single SEIR framework. Using UK demographic, mobility, and social contact data, the model quantifies how within- and between-group interactions, mobility rates, and location connectivity influence epidemic spread. Both deterministic and stochastic simulations are implemented to analyse outbreak dynamics, variability, and fade-out probabilities for COVID-19-like and Ebola-like infections. Results shows that highly connected locations drive faster transmission, earlier epidemic peaks, and greater difficulty in containment, whereas larger but less connected locations tend to produce slower, more localised outbreaks despite their population size. Comparative analysis reveals that COVID-19-like infections spread rapidly and remain difficult to control even under interventions, while Ebola-like infections exhibit slower dynamics and are more effectively contained, particularly under targeted measures. Non-pharmaceutical interventions, particularly widespread closures, substantially reduce infections, hospitalisations, and deaths, although effectiveness depends on timing and pathogen characteristics. These findings highlight the importance of integrating mobility, clustering, and demographic heterogeneity to inform targeted and effective epidemic control strategies.

Malaria remains a major public health challenge in sub-Saharan Africa, with pronounced spatial and temporal variation in transmission intensity that complicates effective control strategies. Accurate classification of transmission states is essential for guiding targeted interventions and strengthening early warning systems. This study develops a machine learning framework for the classification of malaria transmission states in Kenya using monthly panel data from 47 counties spanning the period 2015 to 2025. Transmission was categorised into four operationally relevant states based on incidence thresholds. Four supervised learning models, namely multinomial logistic regression, random forest, extreme gradient boosting, and support vector machine, were trained using temporally lagged features and evaluated under a forward chaining validation scheme to preserve temporal structure. Model performance was assessed using accuracy, macro averaged F1 score, Matthews correlation coefficient, and Brier score, complemented by calibration analysis. Extreme gradient boosting achieved the best overall performance, with accuracy of 0.9918, macro averaged F1 score of 0.9647, and Matthews correlation coefficient of 0.9831, alongside the lowest Brier score of 0.0031, indicating highly reliable probability estimates. Feature importance analysis revealed that lagged incidence, vegetation index, precipitation, and insecticide treated net coverage were the most influential predictors. Partial dependence analysis demonstrated nonlinear relationships and clear seasonal patterns in transmission dynamics. The findings show that machine learning approaches can accurately classify malaria transmission states while providing interpretable and well calibrated outputs for decision making. This framework offers a practical tool for supporting malaria surveillance and resource allocation. Further validation in different epidemiological settings is recommended to assess generalisability.

BackgroundDengue remains a major public health challenge in Thailand despite decades of vector control implementation. While mathematical models have explored dengue transmission dynamics, systematic evaluation of current control strategies under realistic operational conditions remains limited. MethodsWe developed a temperature-dependent, multi-serotype dengue transmission model that explicitly incorporates three primary vector control strategies: reduction in mosquito biting rates through personal protection measures, further reduction in mosquito birth rates beyond current larval control efforts, and further increase in adult mosquito mortality beyond current adulticide application levels. Using Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC), we fitted the model to dengue hemorrhagic fever (DHF) surveillance data from nine province-year combinations representing high (Rayong), moderate (Ratchaburi), and low (Phrae) transmission settings across three years (2006, 2015, and 2017). The model accounts for four dengue serotypes, temperature-dependent mosquito dynamics, and temporary cross-protective immunity between serotypes. ResultsThe model closely reproduced observed monthly DHF case counts across all nine province-year combinations. Estimated reporting proportions ranged from 1.4% to 16.7%, with the highest values occurring in high-transmission provinces during the 2015 outbreak year. When each strategy was independently intensified by 50% relative to fitted baseline levels, reducing mosquito biting rates and increasing adult mosquito mortality consistently produced greater reductions in transmission than reducing mosquito birth rates. In the highest-transmission scenario (Rayong, 2015), a 50% reduction in biting rate from the baseline level yielded a 96.4% reduction in cumulative infections (95% CrI: 95.4-97.3%), compared with 94.3% (95% CrI: 91.8-95.6%) for a 50% increase in adult mosquito mortality and 77.0% (95% CrI: 58.6-84.6%) for a 50% reduction in mosquito birth rate. Analysis of the time-varying reproduction number (Rt) confirmed that interventions targeting adult mosquito-human contact achieved the greatest sustained epidemic suppression, although the relative ranking between bite prevention and adulticide application varied by epidemiological setting. ConclusionsUnder the uniform 50% intensification scenario tested, interventions that directly disrupt adult mosquito-human contact, whether through personal protection or adulticide application, substantially outperformed larval control in reducing dengue transmission across diverse Thai settings. These findings support prioritizing personal protection and adulticide application, while the generalizability of this ranking to other intensification levels and settings warrants further investigation.

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.

Background: Accurate estimation of respiratory syncytial virus (RSV) disease burden is challenged by the imperfect testing performance that varies by clinical specimens, diagnostic tests, and timing of specimen collection. Although the use of multiple testing approaches (such as testing multiple clinical specimens or additional diagnostic tests) could increase the RSV detection, there is absence of a modelling framework to fully incorporate the complexity of heterogeneous diagnostic data. In this study, we proposed a novel Bayesian latent class model that accounted for heterogeneous data on the number of RSV tests and variable specimen collection time among individual patients, imperfect testing sensitivity and specificity of different combinations of clinical specimen and diagnostic test (i.e., testing approaches), and RSV seasonality. Methods: Using simulated datasets consisting of four different testing approaches that mimic real-world RSV epidemiologic characteristics in the UK under different sample size and testing practice scenarios, we assessed the model performance in estimating RSV disease burden as the annual RSV positive proportion in lower respiratory tract infection (LRTI) cases across three respiratory seasons (August 2021 to July 2024) in four adult age groups: 18 to 49 years, 50 to 64 years, 65 to 74 years and over 75 years. Results: We demonstrated that model performance increased substantially with increased sample size, achieving over 80% in accuracy at a sample size of 30,000 tests and 95% in accuracy at a sample size of 60,000 tests; by contrast, smaller sample size could lead to severe over-estimation of the RSV disease burden. In comparison with the existing approaches, both the naive model and the multiplier model systematically under-estimated the RSV disease burden regardless of sample size. The Bayesian model yielded more accurate estimates when the sample size reached 30,000 tests or more; its advantage over the other two models was even more pronounced if the number of testing approaches reduced to 3. Conclusion: The findings above suggest that the proposed Bayesian model provides a robust framework for estimating RSV burden by integrating complex, individual-level testing data when fitting with sufficient input data, offering a critical tool for generating more accurate RSV disease burden estimates to inform national immunisation policies.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity. Author SummaryAlthough the mechanisms driving seasonality of respiratory disease dynamics have been well-studied in temperate regions, they are unknown in the tropics. In this study, we used a 10-year influenza-like-illness (ILI) daily-reporting data set collected from outpatient clinics in Ho Chi Minh City (HCMC) in Vietnam to investigate the mechanisms associated with annual and nonannual ([~]215 days) periodic patterns in the data. By comparing seven mechanistic models against the data, we showed that the mechanism that best explains respiratory disease dynamics in HCMC is a stochastic susceptible-infected-recovered-susceptible (SIRS) model weakly driven by external drivers including specific humidity, temperature, and school term. The nonannual cycles duration is consistent with the inferred duration of immunity of the model. By showing the nonannual cycle as strong as in the data is only observed in stochastic model, we showed that the observed respiratory disease dynamics in HCMC is under the influence of stochasticity when external drivers are weak.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has continuously evolved since its emergence in the human population in 2019. As of 1st August 2025, more than 1,700 Omicron subvariants have been designated by the Pango nomenclature system. The Pango nomenclature system designates a new lineage based on genetic and epidemiological information of SARS-CoV-2 strains. However, there is a possibility that strains that have similar genetic backgrounds and the same phenotype are given different Pango lineage names. In this paper, we propose a new algorithm, called FindPart-w, which can identify groups of viral lineages that share the same relative effective reproduction numbers. We introduced a new lineage replacement model, called the constrained RelRe model, which constrains groups of lineages to have the same relative effective reproduction numbers. The FindPart-w algorithm searches the equality constraints that minimise the Akaike Information Criterion of constrained RelRe models. Using hypothetical observation count data created by simulation, we found that the FindPart-w algorithm can identify groups of lineages having the same relative effective reproduction number in a practical computational time. Applying FindPart-w to actual real-world data of time-stamped lineage counts from the United States, we found that the Pango lineage nomenclature system may have given different lineage names to SARS-CoV-2 strains even if they have the same relative effective reproduction number and similar genetic backgrounds. In conclusion, this study showed that viruses that had the same relative effective reproduction number were identifiable from temporal count data of viral sequences. These findings will contribute to the future development of lineage designation systems that consider both genetic backgrounds and transmissibilities of lineages.

Abstract Background Malaria remains a major public health challenge in Ghana, despite recent reductions in cases due to various interventions. The endemicity of the disease varies across regions, influenced by diverse seasonal and temporal factors that support mosquito proliferation and malaria cases. This study used a Generalised Additive Models to explore the impact of weather conditions on malaria cases in Ghana. Methods Generalised Additive Models were used to examine the nonlinear effects of weather conditions on malaria cases. Monthly aggregated malaria cases from the District Health Information Management System II and average monthly rainfall and temperature data from the Ghana Meteorological Agency were analysed, covering 2012 to 2023. Regional Generalised Additive Models incorporating weather variables were developed, fitted, and validated against observed data using model diagnostics to identify the most suitable model for each region. Results The analysis revealed complex temporal patterns in malaria cases across Ghana, influenced by seasonal and long-term trends. Regions constituting the Coastal and Transitional Forest zones exhibited bimodal peak malaria seasons, while the Guinea Savannah showed a unimodal peak. Significant interactions between rainfall and temperature were identified, particularly in the Eastern region, where higher rainfall combined with temperatures around 27-28 {degrees}C were associated with higher malaria cases, reflecting the complex and region-specific nature of meteorological influences. Conclusions The findings point to the dynamic and heterogeneous nature of malaria caseloads in Ghana, emphasising the need for region-specific control strategies tailored to local climatic conditions. A key recommendation is the systematic integration of meteorological data into the National Malaria Data Repository to enable continuous monitoring of climatic influences and support timely, evidence-based intervention decisions. Future research should incorporate socio-economic factors, intervention coverage data, vector surveillance, and demographic characteristics into mathematical modelling frameworks for a more comprehensive understanding of malaria cases in Ghana.

Infectious disease time series often show signs of epidemic transitions, such as the peaks and troughs of the time series. In these time series, key system parameters can lead to catastrophic changes in the dynamical system behaviour (often called critical transitions). Modellers have increasingly shown that early warning signals can anticipate these transitions, both critical and non-critical, in infectious disease time series. Existing methods, however, generally focus on univariate time series data, or ignore spatiotemporal patterns that may be present as a disease spreads through a population. Recent ecological literature developments expand existing temporal and spatial methods to consider the covariance matrix of multiple, related time series. However, many of these proposed signals still make an assumption of stationary time series/system equilibrium. Whilst often true in ecological modelling, disease systems are seldom at equilibrium. In this paper, we propose the usage of the eigendecomposition of the non-stationary covariance matrix as a more suitable early warning signal for epidemiological data. We first analyse the expected trends in the eigenvalues and eigenbasis of the covariance matrix on approach to a transition. Next we apply these methods to a spatially-structured susceptible-infectious-recovered model to explore how the eigenbasis may provide extra information to modellers. Finally, we test these methods on SARS-CoV-2 case data during the 2020-2021 pandemic period in England.

Scrub typhus remains a persistent public health concern with strong spatial and temporal variability. This study analyses the spatio-temporal distribution, clustering patterns, and forecasting of scrub typhus across five districts, Chittoor, Ranipet, Tirupattur, Vellore, and Tiruvannamalai, using long-term surveillance data from May 2005 to May 2024. We applied spatio-temporal exploratory analysis to identify trends, seasonal behaviour, and inter-district heterogeneity in disease incidence. Hotspot analysis was conducted using the Getis-Ord Gi* statistics to detect statistically significant hotspots and coldspot clusters and examine their evolution over time. To support decision-making, we developed statistical, machine learning (ML), and deep learning (DL) based forecasting models using monthly scrub typhus and climatic features. Root mean square error (RMSE), and R-square error (R2) evaluation metrics are used to compare the performance of the prediction model. Scrub typhus shows clear and recurring seasonal peaks across all five districts, and incidence increases are associated with precipitation, dew point, relative humidity, and vegetation cover. Temperature shows a strong negative correlation, while relative humidity and normalized difference vegetation index (NDVI) show strong positive correlations in all districts. Hotspot analysis identifies Vellore and Chittoor as persistent core transmission zones, with weaker clustering in surrounding districts. Forecasting results indicate that model performance varies by location. The results reveal persistent hotspots, clear seasonal signals, and short-term forecasts across districts. This integrated spatiotemporal and forecasting framework provides actionable insights for targeted surveillance and timely intervention strategies to control scrub typhus.