Threshold interventions are essential for the targeted control of infectious diseases, but their effectiveness can be strongly influenced by vector preference, which is often neglected in existing non-smooth dynamic models. Accordingly, this study investigates the impact of vector preference on threshold control strategies. We develop a Filippov model with vector preference and a joint threshold policy, where interventions are triggered when the combined proportion of susceptible and infected hosts exceeds a critical level. We theoretically analyze the existence of sliding regions, the existence and stability of regular equilibria and pseudo-equilibria, as well as discontinuity-induced bifurcation phenomena. Our results reveal that vector preference can induce diverse equilibrium states. In particular, preference for susceptible hosts allows the coexistence of up to five equilibria, leading to various bistability and possible tristability. Numerical simulations further show that without preference the threshold level directly determines whether early intervention is triggered. Preference for susceptible hosts markedly increases threshold sensitivity and readily induces multistability, allowing disease persistence even when the basic reproduction number is below one; thus, effective control requires targeting the critical threshold rather than merely lowering it. In contrast, preference for infected hosts yields a more monotonic response and facilitates stable disease suppression over a broader range of threshold values. These results indicate that precise threshold setting is essential for effective disease control across different host preference patterns.

This study aims at exploring a general and adaptive control strategy to confront the rapid evolution of an emerging infectious disease ('Disease X'), drawing lessons from the management of COVID-19 in China. We employ a dynamic model incorporating age structures and vaccination statuses, which is calibrated using epidemic data. We therefore estimate the cumulative infection rate (CIR) during the first epidemic wave of Omicron variant after China relaxed its zero-COVID policy to be 82.9% (95% CI: 82.3%, 83.5%), with a case fatality rate (CFR) of 0.25% (95% CI: 0.248%, 0.253%). We further show that if the zero-COVID policy had been eased in January 2022, the CIR and CFR would have decreased to 81.64% and 0.205%, respectively, due to a higher level of immunity from vaccination. However, if we ease the zero-COVID policy during the circulation of Delta variant from June 2021, the CIR would decrease to 74.06% while the CFR would significantly increase to 1.065%. Therefore, in the face of a 'Disease X', the adaptive strategies should be guided by multiple factors, the 'zero-COVID-like' policy could be a feasible and effective way for the control of a variant with relative low transmissibility. However, we should ease the strategy as the virus matures into a new variant with much higher transmissibility, particularly when the population is at a high level of immunity.

The quantitative relationship between rainfall and the frequency of dengue outbreaks remains poorly understood, with rainfall's contribution often overlooked or mischaracterized. Taking Guangzhou as the case, we develop a dynamic model to identify the optimal rainfall range for mosquito population development. Using mosquito surveillance and meteorological data, we estimate the optimal weekly rainfall range as 131.2-212.8 mm. Additionally, we use the distributed lag nonlinear model to analyse the correlation between rainfall and local cases, providing cross-validation. We consequently introduce a novel rainfall index to quantify its causal effects on dengue burden and use a hurdle regularization model to assess the interplay between imported cases, rainfall and temperature in shaping dengue outbreaks. The cases in 2014 and 2015 are predicted by fitting the model to epidemic data between 2006 and 2013. Our proposed rainfall index outperforms existing indices in both model fitting and prediction accuracy. Additionally, switching 2014 and 2015 index values shows a significantly larger 2015 outbreak and smaller 2014 wave, unlike adjustments to temperature or imported case data, highlighting rainfall's dominant role in shaping Guangzhou dengue outbreaks. Although the parameters and the results are restricted to Guangzhou, the fundamental framework can be widely applied to any other region by including the specific data.

Previous studies have identified various factors affecting dengue fever, but most focus on correlations within specific regions, not establishing causality. This study uses Convergent Cross Mapping (CCM) to explore the causal relationships between nine meteorological factors and reported dengue fever cases in 14 Chinese provinces with the highest incidence. Results show that temperature and pressure have causal links with case numbers in more provinces. In Guangdong, which has the most reported cases, Partial Cross Mapping (PCM) reveals a direct causal relationship only between GDP and reported dengue fever cases, while meteorological factors influence dengue fever via their impact on mosquito populations. Principal Component Analysis (PCA) from 30 provinces further confirms the importance of temperature and pressure. Given the significant negative correlation between temperature and pressure, separate models were developed for each province using the Distributed Lag Nonlinear Model (DLNM) combined with the Generalized Additive Model (GAM), with GDP as a covariate. The results indicate that the Relative Risk (RR) increases significantly under high temperatures and low pressure within a shorter lag period. GDP significantly promotes case numbers in all provinces.

In this paper, we propose an susceptible-infectious-hospitalized-recovered (SIHR) epidemic model with a nonlinear hospitalization rate depending on the number of unoccupied hospital beds. Note that the number of all hospital beds is used as a measure of all available medical resources. The basic reproduction number is calculated using the next-generation matrix method. We analyze the existence of endemic equilibria and discuss the global stability of the disease-free equilibrium. Existence and stability of endemic equilibria indicate possible occurrences of bifurcations. We confirm the appearance of backward bifurcation, saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation using normal form theory and central manifold theory. Numerical simulations show that the dynamic behavior of the model undergoes a transition from forward bifurcation to backward bifurcation and saddle-node bifurcation when the number of total hospital beds is reduced. Our findings suggest that when the number of total hospital beds falls below a threshold, backward bifurcation will occur, meaning that the disease cannot be eliminated even if the basic reproduction number is below unity. Therefore, the number of hospital beds should be increased beyond the bed threshold during an outbreak of a disease, which has important implications for disease control.

Aedes mosquitoes, known as vectors of mosquito-borne diseases, pose significant risks to public health and safety. Modeling the population dynamics of Aedes mosquitoes requires comprehensive approaches due to the complex interplay between biological mechanisms and environmental factors. This study developed a model that couples differential equations with a neural network to simulate the dynamics of mosquito population, and explore the relationships between oviposition rate, temperature, and precipitation. Data from nine cities in Guangdong Province spanning four years were used for model training and parameter estimation, while data from the remaining three cities were reserved for model validation. The trained model successfully simulated the mosquito population dynamics across all twelve cities using the same set of parameters. Correlation coefficients between simulated results and observed data exceeded 0.7 across all cities, with some cities surpassing 0.85, demonstrating high model performance. The coupled neural network in the model effectively revealed the relationships among oviposition rate, temperature, and precipitation, aligning with biological patterns. Furthermore, symbolic regression was used to identify the optimal functional expression for these relationships. By integrating the traditional dynamic model with machine learning, our model can adhere to specific biological mechanisms while extracting patterns from data, thus enhancing its interpretability in biology. Our approach provides both accurate modeling and an avenue for uncovering potential unknown biological mechanisms. Our conclusions can provide valuable insights into designing strategies for controlling mosquito-borne diseases and developing related prediction and early warning systems.

To effectively combat emerging infectious diseases like COVID-19, it is crucial to adopt strict prevention and control measures promptly to effectively contain the spread of the epidemic. In this paper, we propose a transmission model to investigate the influence of two control strategies: reducing contact numbers and improving medical resources. We examine these strategies in terms of constant control and time-varying control. Through sensitivity analysis on two reproduction numbers of the model with constant control, we demonstrate that reducing contact numbers is more effective than improving medical resources. Furthermore, these two constant controls significantly influence the peak values and timing of infections. Specifically, intensifying control measures can reduce peak values, albeit at the expense of delaying the peak time. In the model with time-varying control, we initially explore the corresponding optimal control problem and derive the characteristic expression of optimal control. Subsequently, we utilize real data from January 10th to April 12th, 2020, in Wuhan city as a case study to perform parameter estimation by using our proposed improved algorithm. Our findings illustrate that implementing optimal control measures can effectively reduce infections and deaths, and shorten the duration of the epidemic. Then, we numerically explore that implementing control measures promptly and increasing intensity to reduce contact numbers can make actual control be more closer to optimized control. Finally, we utilize the real data from October 31st to November 18th, 2021, in Hebei province as a second case study to validate the feasibility of our proposed suggestions.

Accurate prediction of epidemics is pivotal for making well-informed decisions for the control of infectious diseases, but addressing heterogeneity in the system poses a challenge. In this study, we propose a novel modelling framework integrating the spatio-temporal heterogeneity of susceptible individuals into homogeneous models, by introducing a continuous recruitment process for the susceptibles. A neural network approximates the recruitment rate to develop a Universal Differential Equations (UDE) model. Simultaneously, we pre-set a specific form for the recruitment rate and develop a mechanistic model. Data from a COVID Omicron variant outbreak in Shanghai are used to train the UDE model using deep learning methods and to calibrate the mechanistic model using MCMC methods. Subsequently, we project the attack rate and peak of new infections for the first Omicron wave in China after the adjustment of the dynamic zero-COVID policy. Our projections indicate an attack rate and a peak of new infections of 80.06% and 3.17% of the population, respectively, compared with the homogeneous model’s projections of 99.97% and 32.78%, thus providing an 18.6% improvement in the prediction accuracy based on the actual data. Our simulations demonstrate that heterogeneity in the susceptibles decreases herd immunity for ~37.36% of the population and prolongs the outbreak period from ~30 days to ~70 days, also aligning with the real case. We consider that this study lays the groundwork for the development of a new class of models and new insights for modelling heterogeneity.

The COVID-19 epidemic we have experienced is unprecedented in scale and duration. The interaction of multiple factors has led to a complex pattern in the development of the epidemic, which has also brought significant challenges to the control of the epidemic. We focus on age heterogeneity, the dynamics of individual behavioural changes, and vaccinations during the spread of COVID-19 and propose a multi-scale age structure model to explore the impact of the interaction of these factors on disease transmission. We use game theory to depict whether individuals take normal behaviours or protective measures due to changes in fear of disease infection. Taking the cross-infection of two age groups as an example, we calculated the explicit expression of the reproductive number to explore the threshold of disease outbreak and extinction. Our results reveal that dynamic switching of behavioural changes result in multi-wave patterns. Under the interaction of multiple factors, we found several interesting phenomenon by exploring the disease dynamics. Thresholds for behavioural change in old people and young people have opposite effects on reducing the peak number of disease infections. Older people’s high alertness to diseases may increase the peak infection rate for each age group. Whilst fixing other parameters, we found a critical value of the old people’s attention to infective cases, at which the infection peak of the elderly can be minimised. If the vaccine is ineffective in reducing the infection rate, as the ratio of vaccination increases, the cumulative number of mild infections will increase instead.

After the widespread prevalence of COVID-19 at the end of 2022 in Mainland China, a major concern is when will the second major outbreak occur and with what prevalence and fatality rates will it be associated with, as peoples' immunity from natural infection subsides. To address this, we established an age-structured model considering vaccine and infection-derived immunity, fitted an immunity-waning curve, and calibrated the model using the epidemic and vaccination data from Hong Kong in 2022. The model and the situation of the first major epidemic in Mainland China were then used to predict the prevalence rate, fatality rate and peak time of the second wave. In addition, the controlling effects of different vaccination strategies on the second major outbreak are discussed. Finally, a characterization indicator for the level of population immunity was provided. We conclude that if the prevalence of the first major epidemic was 80%, the prevalence rate of the second major outbreak would be about 37.64%, and the peak time would have been July 2 2023. Strengthening vaccination can effectively delay the peak of the second wave of the epidemic and reduce the prevalence.

Radio/chemotherapy and immune systems provide examples of hormesis, as tumours can be stimulated (or reduced) at low radio/chemical or antibody doses but inhibited (or stimulated) by high doses. Interactions between effector cells, tumour cells and cytokines with pulsed radio/chemo-immunotherapy were modelled using a pulse differential system. Our results show that radio/chemotherapy (dose) response curves (RCRC) and/or immune response curves (IRC) or a combination of both, undergo homeostatic changes or catastrophic shifts revealing hormesis in many parameter regions. Some mixed response curves had multiple humps, posing challenges for interpretation of clinical trials and experimental design, due to a fuzzy region between an hormetic zone and the toxic threshold. Mixed response curves from two parameter bifurcation analyses demonstrated that low-dose radio/chemotherapy and strong immunotherapy counteract side-effects of radio/chemotherapy on effector cells and cytokines and stimulate effects of immunotherapy on tumour growth. The implications for clinical applications were confirmed by good fits to our model of RCRC and IRC data. The combination of low-dose radio/chemotherapy and high-dose immunotherapy is very effective for many solid tumours. The net benefit and synergistic effect of combined therapy is conducive to the treatment and inhibition of tumour cells.

By 31 May 2022, original/Alpha, Delta and Omicron strains induced 101 outbreaks of COVID-19 in mainland China. Most outbreaks were cleared by combining non-pharmaceutical interventions (NPIs) with vaccines, but continuous virus variations challenged the dynamic zero-case policy (DZCP), posing questions of what are the prerequisites and threshold levels for success? And what are the independent effects of vaccination in each outbreak? Using a modified classic infectious disease dynamic model and an iterative relationship for new infections per day, the effectiveness of vaccines and NPIs was deduced, from which the independent effectiveness of vaccines was derived. There was a negative correlation between vaccination coverage rates and virus transmission. For the Delta strain, a 61.8% increase in the vaccination rate (VR) reduced the control reproduction number (CRN) by about 27%. For the Omicron strain, a 20.43% increase in VR, including booster shots, reduced the CRN by 42.16%. The implementation speed of NPIs against the original/Alpha strain was faster than the virus's transmission speed, and vaccines significantly accelerated the DZCP against the Delta strain. The CRN ([Formula: see text]) during the exponential growth phase and the peak time and intensity of NPIs were key factors affecting a comprehensive theoretical threshold condition for DZCP success, illustrated by contour diagrams for the CRN under different conditions. The DZCP maintained the [Formula: see text] of 101 outbreaks below the safe threshold level, but the strength of NPIs was close to saturation especially for Omicron, and there was little room for improvement. Only by curbing the rise in the early stage and shortening the exponential growth period could clearing be achieved quickly. Strengthening China's vaccine immune barrier can improve China's ability to prevent and control epidemics and provide greater scope for the selection and adjustment of NPIs. Otherwise, there will be rapid rises in infection rates and an extremely high peak and huge pressure on the healthcare system, and a potential increase in excess mortality.

During the implementation of strong non-pharmaceutical interventions (NPIs), more than one hundred COVID-19 outbreaks induced by different strains in China were dynamically cleared in about 40 days, which presented the characteristics of small scale clustered outbreaks with low peak levels. To address how did randomness affect the dynamic clearing process, we derived an iterative stochastic difference equation for the number of newly reported cases based on the classical stochastic SIR model and calculate the stochastic control reproduction number (SCRN). Further, by employing the Bayesian technique, the change points of SCRNs have been estimated, which is an important prerequisite for determining the lengths of the exponential growth and decline phases. To reveal the influence of randomness on the dynamic zeroing process, we calculated the explicit expression of the mean first passage time (MFPT) during the decreasing phase using the relevant theory of first passage time (FPT), and the main results indicate that random noise can accelerate the dynamic zeroing process. This demonstrates that powerful NPI measures can rapidly reduce the number of infected people during the exponential decline phase, and enhanced randomness is conducive to dynamic zeroing, i.e. the greater the random noise, the shorter the average clearing time is. To confirm this, we chose 26 COVID-19 outbreaks in various provinces in China and fitted the data by estimating the parameters and change points. We then calculated the MFPTs, which were consistent with the actual duration of dynamic zeroing interventions.

Although single factors such as rainfall are known to affect the population dynamics of Aedes albopictus, the main vector of dengue fever in Eurasia, the synergistic effects of different meteorological factors are not fully understood. To address this topic, we used meteorological data and mosquito-vector association data including Breteau and ovitrap indices in key areas of dengue outbreaks in Guangdong Province, China, to formulate a five-stage mathematical model for Aedes albopictus population dynamics by integrating multiple meteorological factors. Unknown parameters were estimated using a genetic algorithm, and the results were analyzed by k-Shape clustering, random forest and grey correlation analysis. In addition, the population density of mosquitoes in 2022 was predicted and used for evaluating the effectiveness of the model. We found that there is spatiotemporal heterogeneity in the effects of temperature and rainfall and their distribution characteristics on the diapause period, the numbers of peaks in mosquito densities in summer and the annual total numbers of adult mosquitoes. Moreover, we identified the key meteorological indicators of the mosquito quantity at each stage and that rainfall (seasonal rainfall and annual total rainfall) was more important than the temperature distribution (seasonal average temperature and temperature index) and the uniformity of rainfall annual distribution (coefficient of variation) for most of the areas studied. The peak rainfall during the summer is the best indicator of mosquito population development. The results provide important theoretical support for the future design of mosquito vector control strategies and early warnings of mosquito-borne diseases.

COVID-19 epidemics exhibited multiple waves regionally and globally since 2020. It is important to understand the insight and underlying mechanisms of the multiple waves of COVID-19 epidemics in order to design more efficient non-pharmaceutical interventions (NPIs) and vaccination strategies to prevent future waves. We propose a multi-scale model by linking the behaviour change dynamics to the disease transmission dynamics to investigate the effect of behaviour dynamics on COVID-19 epidemics using game theory. The proposed multi-scale models are calibrated and key parameters related to disease transmission dynamics and behavioural dynamics with/without vaccination are estimated based on COVID-19 epidemic data (daily reported cases and cumulative deaths) and vaccination data. Our modeling results demonstrate that the feedback loop between behaviour changes and COVID-19 transmission dynamics plays an essential role in inducing multiple epidemic waves. We find that the long period of high-prevalence or persistent deterioration of COVID-19 epidemics could drive almost all of the population to change their behaviours and maintain the altered behaviours. However, the effect of behaviour changes fades out gradually along the progress of epidemics. This suggests that it is essential to have not only persistent, but also effective behaviour changes in order to avoid subsequent epidemic waves. In addition, our model also suggests the importance to maintain the effective altered behaviours during the initial stage of vaccination, and to counteract relaxation of NPIs, it requires quick and massive vaccination to avoid future epidemic waves.

本文考虑目前国内实施的跟踪隔离和筛查措施,以及南京关联疫情外溢情况,基于全国和江苏省疫情报告数据以及百度人口迁徙数据,构建了考虑中国大陆31个省、自治区和直辖市的新冠肺炎传播复杂网络模型.旨在研究疫情发展趋势、防控措施的有效性以及突发性疫情外溢传播风险.首先基于确诊病例、跟踪隔离密切接触者以及外溢省份数量等数据拟合模型,估计了本次疫情的发展趋势和感染规模,探讨了常规防控和应急响应措施对疫情发展态势和防控效果的影响.其次重点研究了给定初始暴发区域时其余地区的外溢感染风险,给出了外溢高风险区域识别方法,以及高风险区域排序.通过与2020年武汉、北京和辽宁疫情外溢情况对比,验证了方法的可靠性,并以此发布各省份高风险输入预警,为后期的突发疫情防控以及外溢风险提供早期预警.

We conducted a comparative study of the COVID-19 epidemic in three different settings: mainland China, the Guangdong province of China and South Korea, by formulating two disease transmission dynamics models which incorporate epidemic characteristics and setting-specific interventions, and fitting the models to multi-source data to identify initial and effective reproduction numbers and evaluate effectiveness of interventions. We estimated the initial basic reproduction number for South Korea, the Guangdong province and mainland China as 2.6 (95% confidence interval (CI): (2.5, 2.7)), 3.0 (95%CI: (2.6, 3.3)) and 3.8 (95%CI: (3.5,4.2)), respectively, given a serial interval with mean of 5 days with standard deviation of 3 days. We found that the effective reproduction number for the Guangdong province and mainland China has fallen below the threshold 1 since February 8th and 18th respectively, while the effective reproduction number for South Korea remains high until March 2nd Moreover our model-based analysis shows that the COVID-19 epidemics in South Korean is almost under control with the cumulative confirmed cases tending to be stable as of April 14th. Through sensitivity analysis, we show that a coherent and integrated approach with stringent public health interventions is the key to the success of containing the epidemic in China and especially its provinces outside its epicenter. In comparison, we find that the extremely high detection rate is the key factor determining the success in controlling the COVID-19 epidemics in South Korea. The experience of outbreak control in mainland China and South Korea should be a guiding reference for the rest of the world.

Objective: To fit and predict the trend of COVID-19 epidemics in the United States (USA) and the United Kingdom (UK), and analyze the effect of vaccination. Methods: Based on the SEIR dynamic model, considering the presymptomatic infections, isolation measures, vaccine vaccination coverage, etc., we developed a SEIR with vaccine inoculation, Presymptomatic infectious, unconfirmed infectious, hospital isolation and domiciliary isolation dynamics model. The publicly released incidence data of COVID-19 from November 6, 2020 to January 31, 2021 in USA and from November 23, 2020 to January 31, 2021 in UK were used to fit the model and the publicly released incidence data of COVID-19 from February 1, 2021 to April 1 were used to evaluate the predicting power of the model by software R 4.0.3 and predict changes in the daily new cases in the context of different vaccination coverage. Results: According to the cumulative confirmed cases, the fitting bias and the predicting bias of the SVEPIUHDR model for USA and UK were less than 5%, respectively. From the model prediction results, the cumulative cases after COVID-19 vaccination in USA in early April reached 31 864 970. If there had not had such vaccination, the cumulative cases of COVID-19 would have reached to 35 317 082, with a gap of more than 3.4 million cases. In UK, the cumulative cases of COVID-19 after the vaccination was estimated to be 4 195 538 in early April, compared with 4 268 786 cases if no COVID-19 vaccination had been provided, there would have heen a gap of more than 70 000 cases. Conclusion: SVEPIUHDR model shows a good prediction effect on the epidemic of COVID-19 in both USA and UK.

Background The COVID-19 pandemic is complex and is developing in different ways according to the country involved. Methods To identify the key parameters or processes that have the greatest effects on the pandemic and reveal the different progressions of epidemics in different countries, we quantified enhanced control measures and the dynamics of the production and provision of medical resources. We then nested these within a COVID-19 epidemic transmission model, which is parameterized by multi-source data. We obtained rate functions related to the intensity of mitigation measures, the effective reproduction numbers and the timings and durations of runs on medical resources, given differing control measures implemented in various countries. Results Increased detection rates may induce runs on medical resources and prolong their durations, depending on resource availability. Nevertheless, improving the detection rate can effectively and rapidly reduce the mortality rate, even after runs on medical resources. Combinations of multiple prevention and control strategies and timely improvement of abilities to supplement medical resources are key to effective control of the COVID-19 epidemic. A 50% reduction in comprehensive control measures would have led to the cumulative numbers of confirmed cases and deaths exceeding 590,000 and 60,000, respectively, by 27 March 2020 in mainland China. Conclusions Multiple data sources and cross validation of a COVID-19 epidemic model, coupled with a medical resource logistic model, revealed the key factors that affect epidemic progressions and their outbreak patterns in different countries. These key factors are the type of emergency medical response to avoid runs on medical resources, especially improved detection rates, the ability to promote public health measures, and the synergistic effects of combinations of multiple prevention and control strategies. The proposed model can assist health authorities to predict when they will be most in need of hospital beds and equipment such as ventilators, personal protection equipment, drugs, and staff.

Background : The global outbreak of COVID-19 has caused worrying concern amongst the public and health authorities. The first and foremost problem that many countries face is a shortage of medical resources. The experience of Wuhan, China, in fighting against COVID-19 provides a model for other countries to learn from. Methods : We formulated a piecewise smooth model to describe the limitation of hospital beds, based on the transmission progression of COVID-19, and the strengthening prevention and control strategies implemented in Wuhan, China. We used data of the cumulative numbers of confirmed cases, cured cases and deaths in Wuhan city from 10 January to 20 March, 2020 to estimate unknown parameters and the effective reproduction number. Sensitivity analysis was conducted to investigate the impact of a shortage of hospital beds on the COVID-19 outbreak. Results : Even with strong prevention and control measures in Wuhan, slowing down of the supply rate, reducing the maximum capacity and delaying the intervention time of supplementing hospital beds aggravated the outbreak severity by magnifying the cumulative numbers of confirmed cases and deaths, prolonging the period of the outbreak in Wuhan, enlarging the value of the effective reproduction number during the outbreak and postponing the time when the threshold value is reduced to 1. Conclusions : The quick establishment of the Huoshenshan and Leishenshan Hospitals in a short time and the deployment of mobile cabin hospitals played important roles in containing the COVID-19 outbreak in Wuhan, providing a model for other countries to provide more hospital beds for COVID-19 patients faster and earlier.