Frontiers in Physics

This study presents a theoretical and mathematical framework for understanding the dynamical behavior of infectious disease spread using a compartmental modeling approach. The proposed model incorporates memory effects to capture temporal dependencies that are not adequately represented by classical formulations. Qualitative analysis is employed to investigate the stability properties of the system and the role of key mechanisms in shaping long term dynamics. Publicly available surveillance information is used only to illustrate the consistency of the model behavior with observed trends. The results highlight the value of memory based modeling structures for describing complex biological processes and provide a general mathematical perspective for studying epidemic dynamics.

In this research, we create a new fractional-order SEIHRD framework to examine how the Nipah virus moves from one species to another (zoonotic spillover) and how it later spreads throughout a community (via contact with one another) or in a hospital or isolation situation (via entering into a hospital or being placed under quarantine). We used the fractional-derivative formulation of the SEIHRD model to demonstrate memory-based effects related to the progression of an infection and also reflect time-distributed effects associated with surveillance and control measures placed on an infected patient. We first demonstrated that the basic epidemiologic properties of the model were consistent by showing that the solutions of the SEIHRD differential equations will always yield positive and bounded solutions within biologically relevant parameter ranges. We then established the well-posedness of this model by transforming the SEIHRD differential equations into an equivalent integral operator and applying various fixed-point arguments to demonstrate that there will always be unique solution(s) to the SEIHRD differential equations. To evaluate the threshold parameter for the transmission of Nipah virus within a given population we calculated the threshold level through the next generation method to determine the expected number of secondary infections from a new or chronically infected host. One of the main contributions of this work is to include an analysis of the robustness of a given solution to all potential perturbations (i.e., Ulam-Hyers and generalized Ulam-Hyers stability). In addition, we provide analytic results guaranteeing that small perturbations due to approximate modeling, numerical approximation (discretization), or the lack of data fidelity will produce controlled deviations in the solutions. To finish this project, we perform a global sensitivity analysis on uncertain coefficients to evaluate their contribution to the uncertainty of each coefficient and to find out the coefficients that most strongly influence major outcome metrics. This will allow us to develop a priority order for prioritizing spillover control (reduction of human contact and/or isolation), contact reduction, and expenditure of resources towards isolation-related interventions. The resulting framework converts fractional epidemic modeling from a descriptive simulation to a replicable method with robustly defined behavior and equal response prediction.

This paper looked at the exploration of Lassa fever transmission dynamics through stochastic models which yielded valuable insights into the interplay of factors influencing the probability of extinction and persistence of the virus within a population. By embracing the inherent randomness and variability in the system, the model provided a more realistic representation of the complex ecological and epidemiological dynamics of Lassa fever. We developed the deterministic model using a system of ordinary differential equations and the stochastic model using the Continuous Time Markov Chain. The probability of extinction and persistence underscored the need for a proactive and flexible approach to public health management. Our study revealed that introducing Lassa virus at the onset of an epidemic through various routes affects the likelihood of pathogen extinction. The presence of multiple infection routes increased the probability of pathogen persistence, highlighting complex transmission dynamics. Variations in contact rates, particularly between susceptible rodents and the environment community pathogen load, play a crucial role in influencing pathogen dynamics. This interconnected nature of transmission pathways underscores the factors governing Lassa virus persistence or extinction in a population, providing valuable insights for targeted management and control strategies for Lassa fever.

With significant population fractions in many societies who refuse vaccines, it is important to reconsider how vaccination is incorporated into compartmental epidemiology models. It is still most common to apply the vaccination rate to the entire class of susceptibles, rather than to use the more realistic assumption that the vaccination rate function should depend only on the population of susceptibles who are willing and able to receive a vaccination. This study uses a simple generic disease model to address two questions: (1) How much error is introduced in key model outcomes by neglecting vaccine unwillingness?, and (2) Can the error be reduced by incorporating vaccine unwillingness into the vaccination rate constant rather than the rate diagram? The answers depend greatly on the time scale of interest. For the endemic time scale, where longterm behavior is studied with equilibrium point analysis, the error in neglecting unwillingess is large and cannot be improved upon by decreasing the vaccination rate constant. For the epidemic time scale, where the first big epidemic wave is studied with numerical simulations, the error can still be significant, particularly for diseases that are relatively less infectious and vaccination programs that are relatively slow.

Using the example of an unknown emerging disease with simple SIR (susceptible-infectious-recovered) dynamics, we show that an efficacy randomized clinical trial (RCT) for a vaccine can be misleading when it comes to the cost-effectiveness of that vaccine. An RCT is more likely to demonstrate efficacy with a high confidence level if it is carried out during the peak of the outbreak. However, in this scenario, the vaccine also has a higher chance of being approved too late to be cost-effective. A vaccine is more likely to be cost-effective if vaccination is implemented in the early stages of an epidemic, but an RCT is more likely to fail to demonstrate efficacy if it is implemented too early, that is when disease transmission is too low.

BackgroundThe COVID-19 pandemic was strongly shaped by the interaction between population behaviour and transmission dynamics. Standard mathematical models do not account for this interaction, however. Objectivewe tested whether adding a mechanistic representation of population behavioural dynamics improves the ability of a mathematical model to explain and predict COVID-19 pandemic waves. MethodsWe compared a standard Susceptible-Infected-Recovered (SIR) model to a variant (SIRx) with a mechanistic representation of behavioural processes, including two-way coupling between behaviour and transmission dynamics. We used approximate Bayesian computation to parameterise the models with SARS-CoV-2 case incidence and the Oxford stringency index from 13 European countries. Models were fitted to the Spring 2020 wave, and their out-of-sample prediction for the Summer/Fall 2020 wave was tested. Outcome measures included the Akaike Information Criterion (AICc), the area between empirical and model epidemic curves, and predicted timing/magnitude of the second wave. ResultsThe average AICc for the SIRx model across all 13 countries was lower (-2638{+/-}345 versus - 2295{+/-}212 for SIR), meaning that the SIRx model explains the data more parsimoniously. The average area-between-curves was also lower (0.072{+/-}0.071 versus 0.16{+/-}0.11). The predicted peak magnitude for the SIRx model (0.0015{+/-}0.0014) was closer to the data (0.0006{+/-}0.0005) than the SIR prediction (0.0083{+/-}0.0090). The average day-of-peak for the SIRx model (283{+/-}19 days from first data point) was also closer to the data (278{+/-}25), than the SIR prediction (253{+/-}31), although the 95% credible intervals for individual countries were very large. ConclusionCoupling behavioural and disease dynamics improves the ability of mathematical models to explain and predict crucial features of pandemic waves. Research in contextO_ST_ABSEvidence before this studyC_ST_ABSMost mathematical models of infectious disease transmission do not explicitly account for behaviour, but the COVID-19 pandemic clarified the role of behavioural processes in determining the trajectory of infectious diseases in populations. On the other hand, many theoretical models of coupled behaviour-disease processes exist, although relatively few attempt to validate these models against data. We searched Google Scholar using the terms COVID-19 model, and behavio*-disease or behavio* epidem* from March 1, 2020 to October 8, 2025. We did not find any papers that compared retrospective out-of-sample model predictions of COVID-19 pandemic waves of a non-behavioural transmission model to the predictions of a coupled behaviour-disease model, in multiple populations. Added value of this studyWe carried out such a comparison for 13 European countries, by fitting models to the first COVID-19 wave in Spring 2020 and testing how well they would have predicted the second wave. We found that the coupled behaviour-disease model predicted the second wave better than the non-behavioural model, and was also more parsimonious, despite having more parameters. This study shows that feedback between disease dynamics and behavioural dynamics is a significant factor for determining the timing and magnitude of pandemic waves caused by an acute respiratory infection. It also shows that integrating population behaviour dynamics into transmission models is feasible, and can better explain observed temporal patterns in case incidence. Implications of all the available evidenceMathematical models that endogenously include the feedback between infectious disease dynamics and behavioural dynamics can add a unique and complementary tool to the public health modelling toolbox during a pandemic. Such models could help design public health interventions by improving our ability to anticipate population responses to both the interventions themselves, and a rapidly evolving epidemiological landscape.

Cervical cancer remains a significant cause of mortality and economic burden, particularly in developing countries with low rates of human papillomavirus (HPV) vaccination and screening. To address this, we present a mathematical model for controlling cervical cancer by integrating strategic HPV vaccination, screening and treatment. The population is divided into seven compartment: susceptible, vaccinated, infected with HPV, screened, cervical cancer, under treatment, and recovered. The models well-posedness is first established by proving the boundedness and non-negativity of solutions, ensuring biological relevance. The basic reproduction number R0 is computed using the next-generation matrix. The local and global stability of the disease-free equilibrium is analysed using the Jacobian matrix and Lyapunov function respectively. Furthermore, bifurcation analysis is performed using the Castillo-Chavez and Song theorem and sensitivity analysis is conducted on key parameters to identify their influence on disease dynamics. Numerical simulations of the model supports the analytical results. The findings of the study indicate that if the reproduction number is less than one, the solution converges to the disease-free state, signifying the asymptotic stability of the HPV-Cervical cancer free steady state. Crucially, the model demonstrates that increasing vaccination, screening and treatment rates significantly reduces HPV and cervical cancer incidence. This study underscores the value of mathematical modeling in informing the public health policy and provides a framework for optimizing control measures against HPV and Cervical cancer.

Collective interaction of individuals in various settings is crucial for exposure to infections, encompassing complex viral interplay and amplifying infectious risk through phenomena such as social reinforcement, clustering and superspreading events, during the COVID-19 pandemic. However, standard epidemic models often inadequately capture such heterogeneity, overlooking the higher-order social structural. Spatiotemporal variation in transmission, an essential feature of the pandemic, remains poorly quantified at various scales, particularly in integrating high-resolution data streams and complex network approaches. We introduced a higher-order simplicial model that unifies human mobility data, genetic diversity and antigenic drift to systematically investigate the role of social reinforcement, spatiotemporal variation and genetic mutations in SARS-CoV-2 transmission. We found a median of 5.3% to 14.4% of infections across provinces were attributed to social reinforcement, while cluster heterogeneity contributed to a median of 17%-71% increase in susceptibility. Multiple viral interactions elevated transmissibility by 68%-70% across the periods of dominant variants. The reconstructed transmission networks underscored distinct spatiotemporal variation, with dynamic critical locations, varying mobility patterns, and evolving geographic cluster structures, by assessing complex networks. The influence of human mobility was found to be positive on transmission, effective distance was negatively associated with infection risks, while greater genetic diversity and antigenic drift were linked to higher susceptibility and transmissibility. Our proposed data-driven higher-order framework could help us to understand epidemics better by accounting the role of collective interactions, population mobility, and genetic mutation in transmission, which could inform the targeted interventions to mitigate SARS-CoV-2 and other respiratory pathogens.

To characterize tuberculosis transmission and assess the impact of important interventions, a data-driven SEITR TB model is created. The potential for disease persistence has been calculated using the basic reproduction number. To determine the factors most significantly affecting the spread of tuberculosis, stability and sensitivity analyses are conducted. Strengthened treatment measures and optimized distancing significantly lower infection levels, according to numerical simulations. The Least Squares Fitting technique is used to validate real epidemiological data with a model solution. And the results emphasize that the best combinations of social distancing and treatment not only reduce the number of infections but also provide a cost-effective strategy for public health planning. Additionally, two numerical techniques, namely Pearson correlation and Partial Rank Correlation Coefficients (PRCC), are utilized to assess the sensitivity of model parameters. It is noted that the outcomes of these two methods are in agreeable comparison with one another regarding sensitivity analysis.

The COVID-19 pandemic has presented severe challenges in understanding and predicting the spread of infectious diseases, necessitating innovative approaches beyond traditional epidemiological models. This study introduces an advanced method for automated model discovery using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, leveraging a dataset from the COVID-19 outbreak in Thuringia, Germany, encompassing over 400,000 patient records and vaccination data. By analysing this dataset, we develop a flexible, data-driven model that captures many aspects of the complex dynamics of the pandemics spread. Our approach incorporates external factors and interventions into the mathematical framework, leading to more accurate modelling of the pandemics behaviour. The fixed coefficient values of the differential equation as globally determined by the SINDy were not found to be accurate for locally modelling the measured data. We therefore refined our technique based on the differential equations as found by SINDy, by investigating three modifications that account for recent local data. In a first approach, we re-optimized the coefficient values using seven days of past data, without changing the globally determined differential equation. In a second approach, we allowed a temporal dependence of the coefficient values fitted using all previous data in combination with regularization. As a last method, we kept the coefficients fixed to the original values but augmented the differential equation with a small neural network, locally optimized to the data of the past week. Our findings reveal the critical role of vaccination and public health measures in the pandemics trajectory. The proposed model offers a robust tool for policymakers and health professionals to mitigate future outbreaks, providing insights into the efficacy of intervention strategies and vaccination campaigns. This study advances the understanding of COVID-19 dynamics and lays the groundwork for future research in epidemic modelling, emphasising the importance of adaptive, data-informed approaches in public health planning.

We describe a fast, noninvasive, low-cost survey method designed to understand the mode of transmission of an emerging pathogen. It is inspired from the standard household prevalence survey consisting in sampling households and counting the total number of people infected in each household, but refines it with the aim of improving diagnosis and estimating more parameters of the model of intra-household transmission. The survey was carried out in May-June 2020, during part of the first national French lockdown and received responses from more than 6,000 households involving a total of 20,000 people. We explain how we conceived the questionnaire, how we disseminated it, to the public through an open website hosted by CNRS, marketed through media and social media, and to a socially representative panel hosted by two survey institutes (BVA, Bilendi). We used the data obtained from the representative panel to correct for sampling biases in the CNRS survey using a classical raking procedure. Our results indicate that raking correctly canceled statistical biases between the two populations. We obtain the empirical distribution in households of the number and nature of symptoms. The main factors affecting the presence of symptoms are age, gender, body mass index (BMI), household size, but not necessarily in the expected direction. Our study shows that combining self-reporting and representative surveys allows investigators to obtain information on prevalence and household transmission mechanisms on emerging diseases at low cost.

The COVID-19 pandemic exposed major vulnerabilities of hospital capacity and management worldwide, particularly in intensive care units (ICUs) and emergency rooms (ER), imposing prompt adaptation and resource reallocation. Although SARS-CoV-2 is no longer endangering healthcare systems, winter seasons continue to bring recurrent overload of critical care services, primarily due to respiratory infections. In France e.g., this pattern led to the reactivation of the national emergency response plan during the 2024-2025 seasonal influenza peak, highlighting the continuous need for improved predictive tools. However, forecasting hospitalization surges at a local scale remains a methodological challenge because the (very) low incidence numbers are subject to strong stochasticity and therefore require additional input of information and dedicated approaches. This study investigates the potential for early forecasting of respiratory infection peaks by analyzing ER visit trends. By clustering all-cause ER visits during the 2023-2025 winter seasons from the Nimes University Hospital (France), we identified a strong temporal correlation between early pediatric hospitalizations ([≤]5 years old) and the following weeks adult hospitalization incidence for respiratory infections. The results suggest that tracking hospital admissions of pediatric ER visits, even without hospital care needs, can serve as a valuable early warning signal for upcoming peaks in respiratory-related hospitalizations. This predictive approach could improve hospital preparedness and resource management during seasonal influenza outbreaks. Author summaryThe epidemics of respiratory viruses present a significant challenge to hospitals in the temperate zone on an annual basis. Frequently, the hospital overload is mitigated by the late reactive allocation of human and material resources that are, hence, suboptimal. This study proposes a statistical framework to assist hospitals in anticipating bed requirements during seasonal influenza waves, despite high noise at the local level, by enhancing hospitalization forecasting with emergency room (ER) visit data. The prediction of the adult epidemic peak is possible through the analysis of the respiratory pediatric ER visits, which facilitates hospital management.

Influenza forecasting in (sub-)tropical regions remains understudied due to year-round, irregular transmission patterns. Further, the variation in seasonality and transmission characteristic of influenza in post-COVID-19 pandemic could be attributed to various drivers to quantify for better understanding. To address this issue, this study introduced an ensemble forecasting approach that incorporates varied dataset lengths to forecast influenza activity in Hong Kong, integrating multi-stream surveillance data, including absolute humidity, temperature, ozone, and school closures/holidays. We applied temporal cross-validation to evaluate forecasting performance for short- and long term separately across different training-sets and model variants, ultimately constructing ensemble forecasts weighted by individual model performance. The optimal ensemble model could forecast the 2019/20 winter influenza season onwards and evaluate the impact of COVID-19 public health and social measures (PHSMs). We further extended the framework to forecast influenza in post-pandemic period since March 2023, accounting for the impact of cessation of PHSMs and COVID-19-induced cross-protection/competition in population susceptibility. Forecasts showed two peaks in 2019/20 season, which could account for 95.2% (95% prediction interval (PI): 89.1%, 98.3%) reduction in attack rate for COVID-19 PHSMs. The post-pandemic forecasts indicated changes in influenza transmission dynamics and seasonality, highlighting the need to consider factors such as population immunity and co-circulation with COVID-19 in future influenza forecasts. This study emphasizes the importance of incorporating diverse factors for better influenza forecasts in (sub-)tropical regions. The proposed framework offers a scalable tool for forecasting other respiratory virus transmissions, supporting healthcare agencies in managing future infection burdens and enhancing preparedness. Author summaryReliable and proactive forecasts of influenza activity and timing of epidemic outcomes enable public health officials to plan targeted responses. However, unlike temperate locations, the irregular seasonality of influenza in tropical/subtropical locations leads to highly variable forecasting patterns when models use varying lengths of historical data, reducing the robustness of forecasts. By leveraging multi-stream surveillance data in Hong Kong, we developed a mechanistic model-based ensemble forecasting framework that integrate potential combinations of data and models for short-, medium-, and long-term forecasts of influenza outcomes. Beyond methodological advancement, this framework has broader implications in assessing the impact of COVID-19-related interventions on influenza dynamics during pandemic and evaluating potential co-circulation risk of respiratory viruses including influenza and COVID-19 in post-pandemic era.

Polygenic risk scores (PRSs) quantify an individuals genetic susceptibility to complex traits and diseases. Conventional PRSs, which are based on linear models, perform poorly for phenotypes with skewed distributions or with genetic effects that vary across the distribution. We propose a quantile regression-based PRS (QPRS) that can capture quantile-specific genetic effects. While existing PRSs provide only a single score, QPRS models genetic influences at multiple quantiles of the phenotype, thereby enhancing predictive performance by utilizing these multiple scores as covariates. We evaluate the performance of our method through both simulations and a real-data application. In simulations, QPRS significantly reduces the mean squared error (MSE) compared to the conventional PRS, both in the presence of variance quantitative trait loci and outliers. For real data analysis, we use data from Korea Genome and Epidemiology Study (KoGES) to evaluate predictive performance. We consider two prediction tasks: a continuous outcome (glucose level) and a binary outcome (diabetes status, derived from glucose level). For glucose-level prediction, the model incorporating QPRS achieves a R2 value 4.69 times higher than the model using conventional PRSs. For predicting diabetes status, the model with QPRS produces an area under the curve 1.06 times higher than the model with conventional PRSs.

Mathematical models of infectious disease dynamics are routinely fitted to surveillance data to estimate epidemiological parameters and inform public health decisions. Such data are typically discrete and noisy, but before attempting estimation, it is essential to ask whether the model structure itself permits unique parameter identification at least under perfect (continuous, noise-free) observations. This mathematical property of a model with respect to observation(s), known as structural identifiability, serves as a necessary precondition for reliable inference, since a model that fails this test cannot yield unique parameter estimates even from perfect data. In this study, we systematically investigate structural identifiability in various classes of compartmental epidemic models and establish two main findings. First, we present and deploy a methodology for assessing structural identifiability of epidemiological quantities of interest and demonstrate that the basic reproduction number exhibits identifiability across diverse model structures--including models with multiple transmission pathways and host-vector dynamics--even when individual parameters are not uniquely identifiable. These findings challenge the assumption that complete model identifiability is necessary for reliable epidemiological inference and suggest reformulating the central question from "is the model identifiable?" to "are the quantities that matter for the decision-making identifiable?" Second, we prove that incorporating minimal complementary data, as little as a single time-point measurement from an additional state variable, can make otherwise nonidentifiable models globally identifiable. This result has direct implications for surveillance design: rather than putting limited resources into frequent monitoring of multiple data streams or relying on external parameter estimates that may be uncertain or context-dependent, public health systems can strategically prioritize collecting high-quality complementary measurements.

Infectious diseases and chronic diseases are two major fields in epidemiology that have traditionally been studied separately because of their distinct etiologies and modeling methods. Infectious disease data are typically collected at an aggregated level and analyzed using compartmental models, most commonly the susceptible (S), infectious (I), and recovered (R) (SIR) model, whereas chronic disease data are usually collected at the individual level and analyzed using multi-state survival models. Previous studies have pointed out the link between compartmental models and survival analysis by reconstructing the aggregated infection disease data into individual-level data. However, these studies have largely focused on the two-state transition from S to I state, and few studies have simultaneously modeled the three-state process, S, I, and R. In this paper, we propose to use a discrete-time multi-state framework to model the three-state progression of infectious disease. We first introduce and compare the underlying methodological foundations for modeling infectious disease and chronic disease dynamics, then show the link between compartment models and multi-state models, and finally present how infectious disease can be modeled using the multi-state framework under the two scenarios: 1) all S, I, and R states are observed, and 2) only the I state is observed, with the R state treated as latent. In the application, we applied the multi-state approach to estimate the dynamics of influenza using the data in a British boarding school in 1978, where only the infected cases were observed over time. The estimated recovery rate was 0.42 and the corresponding contact rate was0.91 (95% CI: 0.84, 0.98). The basic reproductive number was 2.17 (95% CI: 2.00, 2.33), which declined to approximately 1 by day 6, and continued to decrease thereafter. Overall, we propose a unified multi-state approach for modeling infectious and chronic disease progression, which may provide evidence to inform timely and effective infectious disease prevention.

Visceral leishmaniasis (VL) is considerably more severe among individuals infected with human immunodeficiency virus (HIV), leading to higher parasite loads, frequent relapse, and increased mortality. To examine the epidemiological interaction between the two diseases, we develop a comprehensive VL-HIV co-infection model that incorporates transmission pathways, treatment effects, and relapse dynamics. The model is parameterized using real-time data from Bihar, India, including monthly VL-only and VL-HIV co-infected cases and annual HIV prevalence data. Our analysis shows that HIV infection drives the resurgence and persistence of VL even in settings where VL alone would not sustain transmission, underscoring the amplifying effect of HIV-induced immunosuppression on VL dynamics. We further demonstrate that increasing HIV treatment coverage substantially reduces co-infection prevalence and lowers VL relapse rates. Numerical simulations and optimal control analysis highlight the effectiveness of integrated intervention strategies that combine awareness, treatment enhancement, and vector control. Overall, this study emphasizes the need for coordinated VL and HIV control programs and provides data-driven guidance for designing sustainable intervention strategies in endemic regions.

The recent SARS-CoV-2 pandemic has highlighted the growing importance of infectious disease analysis. An accurate and robust model can empower public health leaders to make timely decisions on social distancing and vaccination policies, thereby reducing the number of cases, hospitalizations and deaths. However, the emergence of new variants and subvariants can significantly alter the transmissibility, immune escape capacity and virulence of the pathogen in a short time, making the number of cases, hospitalizations and deaths difficult to predict. To enhance the timeliness and accuracy of forecasting, SARS-CoV-2 sequencing data can be utilized. These data constitute a vast and continuously growing resource, with millions of sequences collected and reported over the past few years. By incorporating the evolution of SARS-CoV-2 virus into classic transmission models, we conclude that genomic data is crucial for capturing trends in epidemiological data when new variants and subvariants emerge, leading to the development of a more reliable model and enhancing our knowledge of transmission dynamics and control.

In 1798, Jenners smallpox vaccine made it possible to prevent the deadliest of childhood diseases. In Denmark the vaccine was used from 1801, and by 1810 a mandatory 1-dose childhood vaccination program was instituted, free of charge. As proof of vaccination (or natural immunity) was required for church confirmation around age 13, about 90 % of children were vaccinated and smallpox disappeared from Copenhagen after 1808. After a 16-year "honeymoon period", it returned in 1824 with a new face: a milder disease in mostly young adults (1, 2). Here we investigate the effects of smallpox vaccination on the epidemic patterns through the post-honeymoon era (1824-1875). We accessed data from the hospital "Sokvaesthuset" where all smallpox cases, mild and severe, were hospitalized during 1824-1835 in order to contain the outbreak. We identified [~]3000 smallpox cases and four separate epidemics occurring during this period (1-3). We used a mechanistic model (SEIR) to assess factors playing a role in explaining the return of smallpox, and the changing age distribution. These factors included vaccination coverage, duration of immunity from vaccination and from natural infections, and the fate of the "lost generation" of persons born around 1800, too early to get vaccinated and too late to have been infected with smallpox. Our model tracks well the disappearance and return of smallpox in 1824, the interval between epidemic peaks, and the aging pattern. We propose vaccine waning after [~]20 years as the primary reason explaining the return of smallpox and the epidemic pattern. SignificanceSmallpox has played a major role in shaping modern medicine. Recently, it has received renewed attention due to fears of bioterrorism and the emergence of the closely related mpox. In this article, we use data from the carefully recorded smallpox outbreaks in Copenhagen in the 1800s to study its dynamics following vaccine rollout. We show that the vaccine likely induced a long-lived but finite immunity and that the "lost generation" who were neither vaccinated nor had contracted smallpox in childhood continued to be plagued by the disease in the following decades. The study is relevant for understanding how smallpox was eradicated and the role of vaccination in dealing with present epidemic threats.

Schistosomiasis is a neglected parasitic disease caused by various trematode species of the genus Schistosoma for which 251 million people needed treatment in 2021. Many mathematical models of Schistosoma mansoni transmission incorporate the effect of chemoprophylaxis on parasite burden within the human host. While praziquantel is the most commonly implemented pharmaceutical used to control schistosomiasis, due to its applicability over several species and its negligible side effects, it is not very effective against juvenile schistosomes in humans. This limited efficacy on the juvenile life-stage of the parasite may be an important factor in the persistence of the disease. The demographic consequences of praziquantel use on schistosome population age and sex composition within the human host may obfuscate the effectiveness of these chemoprophylactic control strategies. Furthermore, the effectiveness of this treatment is heavily dependent on the force of infection to humans and the frequency at which these pharmaceuticals are administered. Using a stochastic mechanistic model, we investigated the effects of inconsistent drug efficacy among parasite life stages, varying parasite population structure within the human host, and alternative treatment regimes to the prevailing once-yearly strategy. This allowed us to identify the reduction in infection prevalence under differing infection risk scenarios, parasite population structures at the time of treatment, and treatment schedules. Our results indicate that if elimination is the goal, then widespread (>75% of the population) treatment should be the target and that more frequent treatment schedules are useful up to several treatments a year.