Pub Date : 2025-12-03DOI: 10.1016/j.idm.2025.11.008
Anli Yao , Fengying Wei , Jianfeng Xie
Syphilis is a blood-borne disease with multiple hidden-transmission stages caused by Treponema pallidum, and most infected individuals are asymptomatic as reported by the World Health Organization. This study establishes a Susceptible-Exposed-Infected-Latent-Recovered-Susceptible syphilis model with the nonlinear incidence and early latent stage incorporating the psychological effect. Firstly, the basic reproduction number of the SEILRS syphilis model is derived using the next generation matrix method. Then, the local asymptotic stability of the syphilis-free equilibrium point is proved. The global asymptotic stabilities of the syphilis-free equilibrium point and an endemic equilibrium point are shown by LaSalle's invariance principle. Further, the key parameters of the SEILRS syphilis model are estimated by the least squares method against the surveillance data of Fujian Province, China. The numerical simulation demonstrates that the changes of transmission rate in the early latent stage, treatment rate in the secondary stage and psychological effect in the early latent stage present the significant influences on the infection scale of syphilis. The 2023–2030 tendency predictions of the infection scale with scenarios indicate that the transmission rates are most critical for the prevalence of syphilis. As a consequence, to more effectively reduce the transmission rates of syphilis, it is recommended to enhance testing and screening for high-risk groups, to ensure the effective and complete treatment for infected individuals in the secondary stage, and to vigorously publicize the asymptomatic but infectious characteristics of infected individuals in the early latent stage.
{"title":"Dynamic analysis of syphilis model with the saturated incidence and early latent stage","authors":"Anli Yao , Fengying Wei , Jianfeng Xie","doi":"10.1016/j.idm.2025.11.008","DOIUrl":"10.1016/j.idm.2025.11.008","url":null,"abstract":"<div><div>Syphilis is a blood-borne disease with multiple hidden-transmission stages caused by <em>Treponema pallidum</em>, and most infected individuals are asymptomatic as reported by the World Health Organization. This study establishes a Susceptible-Exposed-Infected-Latent-Recovered-Susceptible syphilis model with the nonlinear incidence and early latent stage incorporating the psychological effect. Firstly, the basic reproduction number of the SEILRS syphilis model is derived using the next generation matrix method. Then, the local asymptotic stability of the syphilis-free equilibrium point is proved. The global asymptotic stabilities of the syphilis-free equilibrium point and an endemic equilibrium point are shown by LaSalle's invariance principle. Further, the key parameters of the SEILRS syphilis model are estimated by the least squares method against the surveillance data of Fujian Province, China. The numerical simulation demonstrates that the changes of transmission rate in the early latent stage, treatment rate in the secondary stage and psychological effect in the early latent stage present the significant influences on the infection scale of syphilis. The 2023–2030 tendency predictions of the infection scale with scenarios indicate that the transmission rates are most critical for the prevalence of syphilis. As a consequence, to more effectively reduce the transmission rates of syphilis, it is recommended to enhance testing and screening for high-risk groups, to ensure the effective and complete treatment for infected individuals in the secondary stage, and to vigorously publicize the asymptomatic but infectious characteristics of infected individuals in the early latent stage.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":"11 2","pages":"Pages 527-548"},"PeriodicalIF":2.5,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-27DOI: 10.1016/j.idm.2025.11.006
Harikripal , S. Pascal Zabre , Ina Danquah , Samit Bhattacharyya
Malaria transmission in Sub-Saharan Africa is strongly influenced by seasonal climatic variations and human mobility, particularly occupation-driven rural-to-urban migration. These dynamics contribute to persistent endemicity and periodic outbreaks, especially during the monsoon season. To capture the interplay between age-specific migration and malaria transmission, a generalized compartmental model is formulated that incorporates both human and vector populations, with age-specific demographic and epidemiological characteristics. The model includes three distinct age groups to reflect heterogeneity in susceptibility, exposure, and mobility patterns. The basic reproduction number R0 is derived using the next-generation matrix approach to characterize disease invasion thresholds. Local and global stability of the equilibria are analyzed via Lyapunov methods, with application of a graph-theoretic approach. The model was validated using multiyear malaria reported case data from Ouagadougou, combined with annual migration records from Kossi province, Burkina Faso. The incidence pattern in different age-cohorts was nicely explained by the model with age-specific migration. Qualitative analysis and long-term simulation dynamics indicate the emergence of nonlinear amplification and synchrony in infection prevalence is partially driven by migration in different age-cohorts. This analysis, integrating empirical data provide robust insights for understanding malaria dynamics in the context of behavioural and demographic mobility, and supports the design of targeted intervention strategies in regions with pronounced seasonal migration.
{"title":"Impact of age-structured migration on malaria burden: A modelling-empirical analysis in sub-Saharan Africa","authors":"Harikripal , S. Pascal Zabre , Ina Danquah , Samit Bhattacharyya","doi":"10.1016/j.idm.2025.11.006","DOIUrl":"10.1016/j.idm.2025.11.006","url":null,"abstract":"<div><div>Malaria transmission in Sub-Saharan Africa is strongly influenced by seasonal climatic variations and human mobility, particularly occupation-driven rural-to-urban migration. These dynamics contribute to persistent endemicity and periodic outbreaks, especially during the monsoon season. To capture the interplay between age-specific migration and malaria transmission, a generalized compartmental model is formulated that incorporates both human and vector populations, with age-specific demographic and epidemiological characteristics. The model includes three distinct age groups to reflect heterogeneity in susceptibility, exposure, and mobility patterns. The basic reproduction number <em>R</em><sub>0</sub> is derived using the next-generation matrix approach to characterize disease invasion thresholds. Local and global stability of the equilibria are analyzed via Lyapunov methods, with application of a graph-theoretic approach. The model was validated using multiyear malaria reported case data from Ouagadougou, combined with annual migration records from Kossi province, Burkina Faso. The incidence pattern in different age-cohorts was nicely explained by the model with age-specific migration. Qualitative analysis and long-term simulation dynamics indicate the emergence of nonlinear amplification and synchrony in infection prevalence is partially driven by migration in different age-cohorts. This analysis, integrating empirical data provide robust insights for understanding malaria dynamics in the context of behavioural and demographic mobility, and supports the design of targeted intervention strategies in regions with pronounced seasonal migration.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":"11 2","pages":"Pages 499-526"},"PeriodicalIF":2.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-25DOI: 10.1016/j.idm.2025.11.009
Quinn H. Adams , Davidson H. Hamer , Lucy R. Hutyra , Gregory A. Wellenius , Kayoko Shioda
Background
Visceral leishmaniasis (VL) is a parasitic, zoonotic neglected tropical disease that remains a persistent public health challenge in endemic regions of Brazil, including the state of Maranhão. Transmission dynamics are complex, involving interactions between Lutzomyia longipalpis sandflies, canine reservoirs, and human hosts, and are influenced by environmental and climatic variability. Mathematical models are critical tools for understanding these dynamics and identifying opportunities to effectively disrupt transmission.
Methods
Our objective was to develop and calibrate a climate-informed mechanistic model of VL transmission in Maranhão, Brazil, and to evaluate the potential impacts of vector, environmental, and reservoir-targeted interventions. The model incorporates seasonally varying sandfly biting rates and vector recruitment and explicitly accounts for climate variability through the El Niño-Southern Oscillation (ENSO). Transmission rates between populations (human, canine reservoir, and sandfly vector) were calibrated using monthly reported human VL cases from 2007 to 2019 in Maranhão. We simulated the impact of four potential interventions on VL incidence: increased vector mortality, environmental sanitation (reducing vector maturation), expanded canine treatment, and increased canine culling.
Results
The model accurately reproduced the observed temporal trends in monthly human VL cases in Maranhão and quantified the nonlinear effects of potential interventions. Vector control was the most effective standalone strategy, with a 10 % increase in sandfly mortality reducing human cases by 43 %, and a 90 % increase leading to a 96 % decline. Environmental sanitation was similarly impactful, with a 50 % reduction in sandfly maturation lowering cases by 72 %, and a 90 % reduction leading to a 97 % decline. Canine-focused strategies were less effective: expanded canine treatment reduced human cases only up to 69 %, while increased euthanasia had only modest effects. A combined intervention strategy was more effective than any individual measure, reducing cases by 61 % at just a 10 % increase in coverage and achieving substantially greater declines at higher levels.
Conclusions
Climate variability and seasonal dynamics were key drivers of VL transmission in this setting. Our findings highlight the importance of integrating vector control and environmental management as core components of VL mitigation strategies. While canine-focused interventions may contribute incremental benefits, they are less effective than other interventions and are insufficient when implemented in isolation.
{"title":"Modeling the seasonal and climate-dependent dynamics of visceral leishmaniasis in Brazil: Implications for transmission and Control","authors":"Quinn H. Adams , Davidson H. Hamer , Lucy R. Hutyra , Gregory A. Wellenius , Kayoko Shioda","doi":"10.1016/j.idm.2025.11.009","DOIUrl":"10.1016/j.idm.2025.11.009","url":null,"abstract":"<div><h3>Background</h3><div>Visceral leishmaniasis (VL) is a parasitic, zoonotic neglected tropical disease that remains a persistent public health challenge in endemic regions of Brazil, including the state of Maranhão. Transmission dynamics are complex, involving interactions between <em>Lutzomyia longipalpis</em> sandflies, canine reservoirs, and human hosts, and are influenced by environmental and climatic variability. Mathematical models are critical tools for understanding these dynamics and identifying opportunities to effectively disrupt transmission.</div></div><div><h3>Methods</h3><div>Our objective was to develop and calibrate a climate-informed mechanistic model of VL transmission in Maranhão, Brazil, and to evaluate the potential impacts of vector, environmental, and reservoir-targeted interventions. The model incorporates seasonally varying sandfly biting rates and vector recruitment and explicitly accounts for climate variability through the El Niño-Southern Oscillation (ENSO). Transmission rates between populations (human, canine reservoir, and sandfly vector) were calibrated using monthly reported human VL cases from 2007 to 2019 in Maranhão. We simulated the impact of four potential interventions on VL incidence: increased vector mortality, environmental sanitation (reducing vector maturation), expanded canine treatment, and increased canine culling.</div></div><div><h3>Results</h3><div>The model accurately reproduced the observed temporal trends in monthly human VL cases in Maranhão and quantified the nonlinear effects of potential interventions. Vector control was the most effective standalone strategy, with a 10 % increase in sandfly mortality reducing human cases by 43 %, and a 90 % increase leading to a 96 % decline. Environmental sanitation was similarly impactful, with a 50 % reduction in sandfly maturation lowering cases by 72 %, and a 90 % reduction leading to a 97 % decline. Canine-focused strategies were less effective: expanded canine treatment reduced human cases only up to 69 %, while increased euthanasia had only modest effects. A combined intervention strategy was more effective than any individual measure, reducing cases by 61 % at just a 10 % increase in coverage and achieving substantially greater declines at higher levels.</div></div><div><h3>Conclusions</h3><div>Climate variability and seasonal dynamics were key drivers of VL transmission in this setting. Our findings highlight the importance of integrating vector control and environmental management as core components of VL mitigation strategies. While canine-focused interventions may contribute incremental benefits, they are less effective than other interventions and are insufficient when implemented in isolation.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":"11 2","pages":"Pages 549-559"},"PeriodicalIF":2.5,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-19DOI: 10.1016/j.idm.2025.11.007
Jingze Ma, Yan Wang
This study investigates a stochastic model of Chikungunya virus (CHIKV) infection that incorporates a general incidence rate along with B-cell and CTL immune responses. Stochasticity is modeled through a log-normal Ornstein-Uhlenbeck process. We first establish the existence of a unique and globally positive solution. Then, the solution's dynamic behavior around the two steady states is examined, and it is shown that the stochastic model's dynamics at the steady state generalizes the global asymptotic stability of the deterministic model. We prove the existence of the stationary distribution by constructing suitable Lyapunov functions when the stochastic reproduction number is greater than one. The probability density function near the quasi-steady state is subsequently derived. Sufficient conditions for CHIKV extinction are provided by spectral radius analysis. Furthermore, we conduct uncertainty and sensitivity analyses to investigate the effects of key parameters on each population and the value of the stochastic reproduction number. Finally, numerical simulations are carried out to explore the impact of noise intensity and the average incidence rate on the dynamic behavior of the model.
{"title":"Stochastic dynamics of Chikungunya virus infection model incorporating general incidence rate and immune responses","authors":"Jingze Ma, Yan Wang","doi":"10.1016/j.idm.2025.11.007","DOIUrl":"10.1016/j.idm.2025.11.007","url":null,"abstract":"<div><div>This study investigates a stochastic model of Chikungunya virus (CHIKV) infection that incorporates a general incidence rate along with B-cell and CTL immune responses. Stochasticity is modeled through a log-normal Ornstein-Uhlenbeck process. We first establish the existence of a unique and globally positive solution. Then, the solution's dynamic behavior around the two steady states is examined, and it is shown that the stochastic model's dynamics at the steady state generalizes the global asymptotic stability of the deterministic model. We prove the existence of the stationary distribution by constructing suitable Lyapunov functions when the stochastic reproduction number is greater than one. The probability density function near the quasi-steady state is subsequently derived. Sufficient conditions for CHIKV extinction are provided by spectral radius analysis. Furthermore, we conduct uncertainty and sensitivity analyses to investigate the effects of key parameters on each population and the value of the stochastic reproduction number. Finally, numerical simulations are carried out to explore the impact of noise intensity and the average incidence rate on the dynamic behavior of the model.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":"11 2","pages":"Pages 438-476"},"PeriodicalIF":2.5,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145658880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-17DOI: 10.1016/j.idm.2025.09.007
Florian Lecorvaisier, Dominique Pontier, Frank Sauvage, David Fouchet
Since the 20th century, it has been widely recognized that the emergence of new pathogens is closely linked to human activities such as global travel and environmental exploitation. In addition, the widespread use of antibiotics and vaccines has contributed to the evolution and dissemination of new pathogen variants. However, the role of environmental and socio-demographic cofactors on the dynamics of pathogen spread remains insufficiently explored. In this study, we argue that such influences are best captured using mixed logistic regression models that incorporate temporally autocorrelated random effects, in order to reflect the complex and time-dependent nature of strain invasion processes. To address the statistical challenges of this framework, we compared two approaches: (i) a simplified model with independent random effects and frequentist inference, and (ii) a full model accounting for temporal autocorrelation, estimated using Bayesian inference. Our results show that the simplified model, although commonly used in longitudinal analyses, substantially underestimates the probability of detecting false-positive associations (i.e., it underestimates the Type I error rate), leading to potentially misleading conclusions. In contrast, the full Bayesian model avoids this bias and offers a more robust alternative. We applied this approach to a dataset monitoring the emergence of vaccine-escape Bordetella pertussis strains in the United States between 2007 and 2017. Among the eight cofactors tested, only temperature was significantly associated with the rate of strain invasion. Further simulation-based analyses revealed that the current dataset has limited statistical power to detect such associations. However, our results suggest that increasing the temporal resolution of data collection could substantially improve the model's ability to detect meaningful associations – without increasing surveillance costs.
{"title":"Comparing frequentist and Bayesian methods to identify drivers of pathogen strain invasion: A temporal case study of pertussis in the United States","authors":"Florian Lecorvaisier, Dominique Pontier, Frank Sauvage, David Fouchet","doi":"10.1016/j.idm.2025.09.007","DOIUrl":"10.1016/j.idm.2025.09.007","url":null,"abstract":"<div><div>Since the 20th century, it has been widely recognized that the emergence of new pathogens is closely linked to human activities such as global travel and environmental exploitation. In addition, the widespread use of antibiotics and vaccines has contributed to the evolution and dissemination of new pathogen variants. However, the role of environmental and socio-demographic cofactors on the dynamics of pathogen spread remains insufficiently explored. In this study, we argue that such influences are best captured using mixed logistic regression models that incorporate temporally autocorrelated random effects, in order to reflect the complex and time-dependent nature of strain invasion processes. To address the statistical challenges of this framework, we compared two approaches: (i) a simplified model with independent random effects and frequentist inference, and (ii) a full model accounting for temporal autocorrelation, estimated using Bayesian inference. Our results show that the simplified model, although commonly used in longitudinal analyses, substantially underestimates the probability of detecting false-positive associations (i.e., it underestimates the Type I error rate), leading to potentially misleading conclusions. In contrast, the full Bayesian model avoids this bias and offers a more robust alternative. We applied this approach to a dataset monitoring the emergence of vaccine-escape <em>Bordetella pertussis</em> strains in the United States between 2007 and 2017. Among the eight cofactors tested, only temperature was significantly associated with the rate of strain invasion. Further simulation-based analyses revealed that the current dataset has limited statistical power to detect such associations. However, our results suggest that increasing the temporal resolution of data collection could substantially improve the model's ability to detect meaningful associations – without increasing surveillance costs.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":"11 2","pages":"Pages 389-406"},"PeriodicalIF":2.5,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145658881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-15DOI: 10.1016/j.idm.2025.11.004
Jianrong Wang , Xue Yan , Xinghua Chang , Maoxing Liu
With the frequent emergence and spread of new infectious diseases, poses severe threats to public health, and the government often relies on non-pharmaceutical interventions to cope. Meanwhile, the impact of media information on public behavior and health awareness is increasingly significant, becoming an indispensable factor in epidemic prevention and control. This paper constructs an SVEIR-M infectious disease model integrating age structure and media coverage mechanisms, depicting the differences in individuals’ acceptance of media information and the effectiveness of vaccination at different age stages. The model introduces complex factors such as immune waning, latent development age, and media information dissemination, and systematically analyzes the existence and stability of disease-free and endemic equilibrium points using partial differential equations and Volterra integral tools. It is proved that the basic reproduction number R0 plays a threshold role in characterizing the dynamical properties of the system, and the global stability of equilibrium points under different conditions is demonstrated by constructing Lyapunov functions. In addition, the uniform persistence of the system is analyzed, and the correctness of the theoretical analysis is verified through numerical simulations, discussing the impact of different intervention measures on epidemic development. The research results show that media publicity and vaccination can significantly reduce the infection and mortality rates, and their combination can more effectively control the spread of the epidemic.
{"title":"Dynamical analysis of the SVEIR-M epidemic model with age structure under media coverage","authors":"Jianrong Wang , Xue Yan , Xinghua Chang , Maoxing Liu","doi":"10.1016/j.idm.2025.11.004","DOIUrl":"10.1016/j.idm.2025.11.004","url":null,"abstract":"<div><div>With the frequent emergence and spread of new infectious diseases, poses severe threats to public health, and the government often relies on non-pharmaceutical interventions to cope. Meanwhile, the impact of media information on public behavior and health awareness is increasingly significant, becoming an indispensable factor in epidemic prevention and control. This paper constructs an SVEIR-M infectious disease model integrating age structure and media coverage mechanisms, depicting the differences in individuals’ acceptance of media information and the effectiveness of vaccination at different age stages. The model introduces complex factors such as immune waning, latent development age, and media information dissemination, and systematically analyzes the existence and stability of disease-free and endemic equilibrium points using partial differential equations and Volterra integral tools. It is proved that the basic reproduction number <em>R</em><sub>0</sub> plays a threshold role in characterizing the dynamical properties of the system, and the global stability of equilibrium points under different conditions is demonstrated by constructing Lyapunov functions. In addition, the uniform persistence of the system is analyzed, and the correctness of the theoretical analysis is verified through numerical simulations, discussing the impact of different intervention measures on epidemic development. The research results show that media publicity and vaccination can significantly reduce the infection and mortality rates, and their combination can more effectively control the spread of the epidemic.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":"11 2","pages":"Pages 477-498"},"PeriodicalIF":2.5,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-12DOI: 10.1016/j.idm.2025.11.003
Ge Zhang , Zhihao Wang , Zhiming Li , Shenglong Chen , Qiaoling Chen
Understanding and predicting real-world epidemic dynamics has consistently posed a formidable challenge. This study addresses an age-structured stochastic SIR model incorporating a general incidence rate, high-order white noise, and Lévy jump perturbations. By employing Lyapunov function method, we establish the existence and uniqueness of a global positive solution. Furthermore, we derive a stochastic threshold that delineates the conditions for disease persistence and extinction. Moreover, the existence and uniqueness of a stationary distribution are proven by applying an improved version of Hasminskii's theory. Numerical simulations based on the positivity- and boundedness-preserving Euler–Maruyama scheme corroborate the theoretical results, showing that reducing the amplitude of higher-order noise amplifies the infection burden, whereas increasing the age-structure parameters ϑ and ς markedly suppresses transmission. Finally, the efficacy of physics-informed neural network based on stochastic SIR model (PINN-SIR), is demonstrated through its application to the fitting and forecasting of COVID-19 case in Zhejiang, China. The method shows promise for extension to more complex dynamical systems and diseases.
{"title":"Dynamics and forecasting of an age-structured stochastic SIR model with Lévy perturbations via physics-informed neural networks","authors":"Ge Zhang , Zhihao Wang , Zhiming Li , Shenglong Chen , Qiaoling Chen","doi":"10.1016/j.idm.2025.11.003","DOIUrl":"10.1016/j.idm.2025.11.003","url":null,"abstract":"<div><div>Understanding and predicting real-world epidemic dynamics has consistently posed a formidable challenge. This study addresses an age-structured stochastic SIR model incorporating a general incidence rate, high-order white noise, and Lévy jump perturbations. By employing Lyapunov function method, we establish the existence and uniqueness of a global positive solution. Furthermore, we derive a stochastic threshold that delineates the conditions for disease persistence and extinction. Moreover, the existence and uniqueness of a stationary distribution are proven by applying an improved version of Hasminskii's theory. Numerical simulations based on the positivity- and boundedness-preserving Euler–Maruyama scheme corroborate the theoretical results, showing that reducing the amplitude of higher-order noise amplifies the infection burden, whereas increasing the age-structure parameters <em>ϑ</em> and <em>ς</em> markedly suppresses transmission. Finally, the efficacy of physics-informed neural network based on stochastic SIR model (PINN-SIR), is demonstrated through its application to the fitting and forecasting of COVID-19 case in Zhejiang, China. The method shows promise for extension to more complex dynamical systems and diseases.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":"11 2","pages":"Pages 407-427"},"PeriodicalIF":2.5,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145658882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-11DOI: 10.1016/j.idm.2025.11.001
Wenjun Liu , Guohua Zou , Qin Bao , Shouyang Wang
The large-scale outbreaks of novel infectious diseases threaten public health, while strict intervention measures might slow down the economic activity. The effective prevention and control measures should balance cost and benefit. This study aims to explore the optimal intervention strategy for the infectious diseases by proposing a dynamic model with economic cost based on the modified SEIR model. Seven compartments were expanded as QSEAIRD model according to China's real practice in COVID-19. The parameters were estimated by minimizing the prediction error, and the GDP loss coefficients were introduced to quantify the economic costs of different measures. Thereafter, we formulated a corresponding algorithm to solve for the optimal prevention policies, which could control the epidemic within a specified time with minimized economic loss. Using Shanghai as a case study, we simulated the epidemic trends from March 2022 under different policy scenarios. We found that the government interventions effectively shortened the peak time by 60 % and significantly reduced its magnitude by 90 %. Without these measures, we predicted that Shanghai would reach the peaks of the first and second waves of infections at the end of 2022 and in June 2023, respectively, with the number of infections during the second peak being about 1/7 of that during the first. These results demonstrate that the government's prevention and control measures were effective in containing the epidemic. If relatively loose measures were adopted, the epidemic would not be controlled within one month, which would prolong the implementation of the prevention measures and increase economic loss. By conducting a cost-effectiveness analysis, the proposed model and algorithm can be flexibly applied to optimize the design of infectious disease prevention and control schemes under different scenarios, systematically enhancing the capacity to respond to the novel infectious diseases.
{"title":"Optimal prevention and control strategy of infectious disease: Cost-effectiveness analysis based on a modified dynamic model with economic loss","authors":"Wenjun Liu , Guohua Zou , Qin Bao , Shouyang Wang","doi":"10.1016/j.idm.2025.11.001","DOIUrl":"10.1016/j.idm.2025.11.001","url":null,"abstract":"<div><div>The large-scale outbreaks of novel infectious diseases threaten public health, while strict intervention measures might slow down the economic activity. The effective prevention and control measures should balance cost and benefit. This study aims to explore the optimal intervention strategy for the infectious diseases by proposing a dynamic model with economic cost based on the modified SEIR model. Seven compartments were expanded as QSEAIRD model according to China's real practice in COVID-19. The parameters were estimated by minimizing the prediction error, and the GDP loss coefficients were introduced to quantify the economic costs of different measures. Thereafter, we formulated a corresponding algorithm to solve for the optimal prevention policies, which could control the epidemic within a specified time with minimized economic loss. Using Shanghai as a case study, we simulated the epidemic trends from March 2022 under different policy scenarios. We found that the government interventions effectively shortened the peak time by 60 % and significantly reduced its magnitude by 90 %. Without these measures, we predicted that Shanghai would reach the peaks of the first and second waves of infections at the end of 2022 and in June 2023, respectively, with the number of infections during the second peak being about 1/7 of that during the first. These results demonstrate that the government's prevention and control measures were effective in containing the epidemic. If relatively loose measures were adopted, the epidemic would not be controlled within one month, which would prolong the implementation of the prevention measures and increase economic loss. By conducting a cost-effectiveness analysis, the proposed model and algorithm can be flexibly applied to optimize the design of infectious disease prevention and control schemes under different scenarios, systematically enhancing the capacity to respond to the novel infectious diseases.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":"11 1","pages":"Pages 377-388"},"PeriodicalIF":2.5,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145568709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-10DOI: 10.1016/j.idm.2025.11.005
Li Geng , Jun He , Ping Liu
The rapid antigenic drift of influenza A/H3N2 compromises the durability of vaccine-induced protection, underscoring the need for accurate antigenic assessment to evaluate vaccine efficacy and guide vaccine updates. Although the hemagglutination inhibition (HI) assay remains the gold standard for antigenic characterization, its labor-intensive and time-consuming procedures hinder large-scale application. Sequence-based computational approaches have therefore emerged as high-throughput and cost-effective complements to the HI assay. However, most existing methods insufficiently exploit differences in the intrinsic properties of amino acids across sequence positions, constraining advances in antigenicity prediction. To address this limitation, we propose FluAttn, an attention-based feature mining framework that automatically identifies and integrates antigenicity-relevant features from various amino acid property datasets. FluAttn not only allows for customizable feature scales but also simultaneously quantifies the differential contributions of these features during the mining process, thereby facilitating synergistic feature integration and enabling high-precision prediction of antigenic distances between A/H3N2 influenza viruses. Evaluation on datasets covering the periods 1963–2003 and 2003–2025 demonstrates that FluAttn significantly outperforms existing methods in both accuracy and robustness, providing a cost-effective and reliable framework for early antigenic characterization and vaccine candidate screening.
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Pub Date : 2025-11-05DOI: 10.1016/j.idm.2025.11.002
Xiang Chen, Paula Moraga
Background
Dengue fever is a major global health concern, with Brazil experiencing recurrent and severe outbreaks due to its favorable climate factors, socio-environmental conditions, and increasing human mobility. Accurate forecasting of dengue cases and outbreak risk is essential for early warning systems and effective public health interventions. Traditional forecasting models primarily rely on historical case data and climate variables, often neglecting the role of human movement in virus transmission. This study addresses this gap by incorporating human mobility data into a deep learning-based dengue forecasting framework.
Method
An LSTM-based model was developed to forecast weekly dengue cases and detect outbreaks across selected Brazilian cities. The model integrates historical dengue cases, lagged climate variables (temperature and humidity), and human mobility-adjusted imported cases to capture both temporal trends and spatial transmission dynamics. Its performance was evaluated against three alternative models: (1) an LSTM using only dengue case data, (2) an LSTM incorporating climate variables, and (3) an LSTM integrating climate and geographic neighborhood effects. Forecasting accuracy was assessed using Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Continuous Ranked Probability Score (CRPS), while outbreak classification was evaluated using accuracy, sensitivity, specificity, and the F1 score.
Results
The proposed mobility-enhanced LSTM model consistently outperformed all baselines in both dengue case forecasting and outbreak detection. Across all cities, it achieved lower MAE and MAPE values, indicating improved accuracy, while also demonstrating superior CRPS performance, reflecting well-calibrated uncertainty estimates. In outbreak classification, the model achieved the highest sensitivity and F1 scores, highlighting its effectiveness in detecting outbreak periods compared to models that relied solely on case trends, climate variables, or geographic proximity. The results underscore the importance of integrating mobility data in dengue forecasting, particularly in urban centers with high population movement.
Conclusion
By incorporating human mobility dynamics into deep learning-based forecasting, this study presents a scalable and adaptable framework for enhancing dengue early warning systems. The proposed model provides more accurate case predictions and outbreak classifications, offering actionable insights for public health planning and resource allocation. Beyond dengue, this approach can be extended to other vector-borne diseases influenced by mobility and climate factors, supporting more effective epidemic preparedness strategies worldwide.
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