Uncertainty quantification for the random HIV dynamical model driven by drug adherence.

In HIV drug therapy, the high variability of CD4+ T cells and viral loads brings uncertainty to the determination of treatment options and the ultimate treatment efficacy, which may be the result of poor drug adherence. We develop a dynamical HIV model coupled with pharmacokinetics, driven by drug adherence as a random variable, and systematically study the uncertainty quantification, aiming to construct the relationship between drug adherence and therapeutic effect. Using adaptive generalized polynomial chaos, stochastic solutions are approximated as polynomials of input random parameters. Numerical simulations show that results obtained by this method are in good agreement, compared with results obtained through Monte Carlo sampling, which helps to verify the accuracy of approximation. Based on these expansions, we calculate the time-dependent probability density functions of this system theoretically and numerically. To verify the applicability of this model, we fit clinical data of four HIV patients, and the goodness of fit results demonstrate that the proposed random model depicts the dynamics of HIV well. Sensitivity analyses based on the Sobol index indicate that the randomness of drug effect has the greatest impact on both CD4+ T cells and viral loads, compared to random initial values, which further highlights the significance of drug adherence. The proposed models and qualitative analysis results, along with monitoring CD4+ T cells counts and viral loads, evaluate the influence of drug adherence on HIV treatment, which helps to better interpret clinical data with fluctuations and makes several contributions to the design of individual-based optimal antiretroviral strategies.

From economic threshold to economic injury level: Modeling the residual effect and delayed response of pesticide application.

Integrated Pest Management (IPM) poses a challenge in determining the optimal timing of pesticide sprays to ensure that pest populations remain below the Economic Injury Level (EIL), due to the long-term residual effects of many pesticides and the delayed responses of pest populations to pesticide sprays. To address this issue, a specific pesticide kill-rate function is incorporated into a deterministic exponential growth model and a subsequent stochastic model. The findings suggest the existence of an optimal pesticide spraying cycle that can periodically control pests below the EIL. The results regarding stochasticity indicate that random fluctuations promote pest extinction and ensure that the pest population, under the optimal cycle, does not exceed the EIL on average, even with a finite number of IPM strategies. All those confirm that the modeling approach can accurately reveal the intrinsic relationship between the two key indicators Economic Threshold and EIL in the IPM strategy, and further realize the precise characterization of the residual effect and delayed response of pesticide application.

Model analysis and data validation of structured prevention and control interruptions of emerging infectious diseases.

The design of optimized non-pharmaceutical interventions (NPIs) is critical to the effective control of emergent outbreaks of infectious diseases such as SARS, A/H1N1 and COVID-19 and to ensure that numbers of hospitalized cases do not exceed the carrying capacity of medical resources. To address this issue, we formulated a classic SIR model to include a close contact tracing strategy and structured prevention and control interruptions (SPCIs). The impact of the timing of SPCIs on the maximum number of non-isolated infected individuals and on the duration of an infectious disease outside quarantined areas (i.e. implementing a dynamic zero-case policy) were analyzed numerically and theoretically. These analyses revealed that to minimize the maximum number of non-isolated infected individuals, the optimal time to initiate SPCIs is when they can control the peak value of a second rebound of the epidemic to be equal to the first peak value. More individuals may be infected at the peak of the second wave with a stronger intervention during SPCIs. The longer the duration of the intervention and the stronger the contact tracing intensity during SPCIs, the more effective they are in shortening the duration of an infectious disease outside quarantined areas. The dynamic evolution of the number of isolated and non-isolated individuals, including two peaks and long tail patterns, have been confirmed by various real data sets of multiple-wave COVID-19 epidemics in China. Our results provide important theoretical support for the adjustment of NPI strategies in relation to a given carrying capacity of medical resources.

Clustering analysis for the evolutionary relationships of SARS-CoV-2 strains.

To explore the differences and relationships between the available SARS-CoV-2 strains and predict the potential evolutionary direction of these strains, we employ the hierarchical clustering analysis to investigate the evolutionary relationships between the SARS-CoV-2 strains utilizing the genomic sequences collected in China till January 7, 2023. We encode the sequences of the existing SARS-CoV-2 strains into numerical data through k-mer algorithm, then propose four methods to select the representative sample from each type of strains to comprise the dataset for clustering analysis. Three hierarchical clustering algorithms named Ward-Euclidean, Ward-Jaccard, and Average-Euclidean are introduced through combing the Euclidean and Jaccard distance with the Ward and Average linkage clustering algorithms embedded in the OriginPro software. Experimental results reveal that BF.28, BE.1.1.1, BA.5.3, and BA.5.6.4 strains exhibit distinct characteristics which are not observed in other types of SARS-CoV-2 strains, suggesting their being the majority potential sources which the future SARS-CoV-2 strains' evolution from. Moreover, BA.2.75, CH.1.1, BA.2, BA.5.1.3, BF.7, and B.1.1.214 strains demonstrate enhanced abilities in terms of immune evasion, transmissibility, and pathogenicity. Hence, closely monitoring the evolutionary trends of these strains is crucial to mitigate their impact on public health and society as far as possible.

Valuation and comparison of the actual and optimal control strategy in an emerging infectious disease: Implication from a COVID-19 transmission model.

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.

Non-smooth dynamics of a SIR model with nonlinear state-dependent impulsive control.

The classic SIR model is often used to evaluate the effectiveness of controlling infectious diseases. Moreover, when adopting strategies such as isolation and vaccination based on changes in the size of susceptible populations and other states, it is necessary to develop a non-smooth SIR infectious disease model. To do this, we first add a non-linear term to the classical SIR model to describe the impact of limited medical resources or treatment capacity on infectious disease transmission, and then involve the state-dependent impulsive feedback control, which is determined by the convex combinations of the size of the susceptible population and its growth rates, into the model. Further, the analytical methods have been developed to address the existence of non-trivial periodic solutions, the existence and stability of a disease-free periodic solution (DFPS) and its bifurcation. Based on the properties of the established Poincaré map, we conclude that DFPS exists, which is stable under certain conditions. In particular, we show that the non-trivial order-1 periodic solutions may exist and a non-trivial order-$ k $ ($ k\geq 1 $) periodic solution in some special cases may not exist. Moreover, the transcritical bifurcations around the DFPS with respect to the parameters $ p $ and $ AT $ have been investigated by employing the bifurcation theorems of discrete maps.

Free boundary problem for a nonlocal time-periodic diffusive competition model.

In this paper we consider a free boundary problem for a nonlocal time-periodic competition model. One species is assumed to adopt nonlocal dispersal, and the other one adopts mixed dispersal, which is a combination of both random dispersal and nonlocal dispersal. We first prove the global well-posedness of solutions to the free boundary problem with more general growth functions, and then discuss the spreading and vanishing phenomena. Moreover, under the weak competition condition, we study the long-time behaviors of solutions for the spreading case.

Hormetic and synergistic effects of cancer treatments revealed by modelling combinations of radio - or chemotherapy with immunotherapy.

BACKGROUND: 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. METHODS: Interactions between effector cells, tumour cells and cytokines with pulsed radio/chemo-immunotherapy were modelled using a pulse differential system. RESULTS: 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. CONCLUSIONS: 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.

Combining the dynamic model and deep neural networks to identify the intensity of interventions during COVID-19 pandemic.

During the COVID-19 pandemic, control measures, especially massive contact tracing following prompt quarantine and isolation, play an important role in mitigating the disease spread, and quantifying the dynamic contact rate and quarantine rate and estimate their impacts remain challenging. To precisely quantify the intensity of interventions, we develop the mechanism of physics-informed neural network (PINN) to propose the extended transmission-dynamics-informed neural network (TDINN) algorithm by combining scattered observational data with deep learning and epidemic models. The TDINN algorithm can not only avoid assuming the specific rate functions in advance but also make neural networks follow the rules of epidemic systems in the process of learning. We show that the proposed algorithm can fit the multi-source epidemic data in Xi'an, Guangzhou and Yangzhou cities well, and moreover reconstruct the epidemic development trend in Hainan and Xinjiang with incomplete reported data. We inferred the temporal evolution patterns of contact/quarantine rates, selected the best combination from the family of functions to accurately simulate the contact/quarantine time series learned by TDINN algorithm, and consequently reconstructed the epidemic process. The selected rate functions based on the time series inferred by deep learning have epidemiologically reasonable meanings. In addition, the proposed TDINN algorithm has also been verified by COVID-19 epidemic data with multiple waves in Liaoning province and shows good performance. We find the significant fluctuations in estimated contact/quarantine rates, and a feedback loop between the strengthening/relaxation of intervention strategies and the recurrence of the outbreaks. Moreover, the findings show that there is diversity in the shape of the temporal evolution curves of the inferred contact/quarantine rates in the considered regions, which indicates variation in the intensity of control strategies adopted in various regions.

Transmission dynamics informed neural network with application to COVID-19 infections.

Since the end of 2019 the COVID-19 repeatedly surges with most countries/territories experiencing multiple waves, and mechanism-based epidemic models played important roles in understanding the transmission mechanism of multiple epidemic waves. However, capturing temporal changes of the transmissibility of COVID-19 during the multiple waves keeps ill-posed problem for traditional mechanism-based epidemic compartment models, because that the transmission rate is usually assumed to be specific piecewise functions and more parameters are added to the model once multiple epidemic waves involved, which poses a huge challenge to parameter estimation. Meanwhile, data-driven deep neural networks fail to discover the driving factors of repeated outbreaks and lack interpretability. In this study, aiming at developing a data-driven method to project time-dependent parameters but also merging the advantage of mechanism-based models, we propose a transmission dynamics informed neural network (TDINN) by encoding the SEIRD compartment model into deep neural networks. We show that the proposed TDINN algorithm performs very well when fitting the COVID-19 epidemic data with multiple waves, where the epidemics in the United States, Italy, South Africa, and Kenya, and several outbreaks the Omicron variant in China are taken as examples. In addition, the numerical simulation shows that the trained TDINN can also perform as a predictive model to capture the future development of COVID-19 epidemic. We find that the transmission rate inferred by the TDINN frequently fluctuates, and a feedback loop between the epidemic shifting and the changes of transmissibility drives the occurrence of multiple waves. We observe a long response delay to the implementation of control interventions in the four countries, while the decline of the transmission rate in the outbreaks in China usually happens once the implementation of control interventions. The further simulation show that 17 days' delay of the response to the implementation of control interventions lead to a roughly four-fold increase in daily reported cases in one epidemic wave in Italy, which suggest that a rapid response to policies that strengthen control interventions can be effective in flattening the epidemic curve or avoiding subsequent epidemic waves. We observe that the transmission rate in the outbreaks in China is already decreasing before enhancing control interventions, providing the evidence that the increasing of the epidemics can drive self-conscious behavioural changes to protect against infections.

Randomness accelerates the dynamic clearing process of the COVID-19 outbreaks in China.

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.

Prediction of the next major outbreak of COVID-19 in Mainland China and a vaccination strategy for it.

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.

Mathematical modeling the order of driver gene mutations in colorectal cancer.

Tumor heterogeneity is a large obstacle for cancer study and treatment. Different cancer patients may involve different combinations of gene mutations or the distinct regulatory pathways for inducing the progression of tumor. Investigating the pathways of gene mutations which can cause the formation of tumor can provide a basis for the personalized treatment of cancer. Studies suggested that KRAS, APC and TP53 are the most significant driver genes for colorectal cancer. However, it is still an open issue regarding the detailed mutation order of these genes in the development of colorectal cancer. For this purpose, we analyze the mathematical model considering all orders of mutations in oncogene, KRAS and tumor suppressor genes, APC and TP53, and fit it on data describing the incidence rates of colorectal cancer at different age from the Surveillance Epidemiology and End Results registry in the United States for the year 1973-2013. The specific orders that can induce the development of colorectal cancer are identified by the model fitting. The fitting results indicate that the mutation orders with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53 explain the age-specific risk of colorectal cancer with very well. Furthermore, eleven pathways of gene mutations can be accepted for the mutation order of genes with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53, and the alternation of APC acts as the initiating or promoting event in the colorectal cancer. The estimated mutation rates of cells in the different pathways demonstrate that genetic instability must exist in colorectal cancer with alterations of genes, KRAS, APC and TP53.

Statistical Analysis of Two-Compartment Pharmacokinetic Models with Drug Non-adherence.

Poor drug adherence is considered one of major barriers to achieving the clinical and public health benefits of many pharmacotherapies. In the current paper, we aim to investigate the impact of dose omission on the plasma concentrations of two-compartment pharmacokinetic models with two typical routes of drug administration, namely the intravenous bolus and extravascular first-order absorption. First, we reformulate the classical two-compartment pharmacokinetic models with a new stochastic feature, where a binomial random model of dose intake is integrated. Then, we formalize the explicit expressions of expectation and variance for trough concentrations and limit concentrations, with the latter proved of the existence and uniqueness for steady-state distribution. Moreover, we mathematically demonstrate the strict stationarity and ergodicity of trough concentrations as a Markov chain. In addition, we numerically simulate the impact of drug non-adherence to different extents on the variability and regularity of drug concentration and compare the drug pharmacokinetic preference between one and two compartment pharmacokinetic models. The results of sensitivity analysis also suggest the drug non-adherence as one of the most sensitive model parameters to the expectation of limit concentration. Our modelling and analytical approach can be integrated into the chronic disease models to estimate or quantitatively predict the therapy efficacy with drug pharmacokinetics presumably affected by random dose omissions.

Threshold conditions for curbing COVID-19 with a dynamic zero-case policy derived from 101 outbreaks in China.

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.

Lessons drawn from Shanghai for controlling highly transmissible SARS-CoV-2 variants: insights from a modelling study.

BACKGROUND: The continuous emergence of novel SARS-CoV-2 variants with markedly increased transmissibility presents major challenges to the zero-COVID policy in China. It is critical to adjust aspects of the policy about non-pharmaceutical interventions (NPIs) by searching for and implementing more effective ways. We use a mathematical model to mimic the epidemic pattern of the Omicron variant in Shanghai to quantitatively show the control challenges and investigate the feasibility of different control patterns in avoiding other epidemic waves. METHODS: We initially construct a dynamic model with a core step-by-step release strategy to reveal its role in controlling the spread of COVID-19, including the city-based pattern and the district-based pattern. We used the least squares method and real reported case data to fit the model for Shanghai and its 16 districts, respectively. Optimal control theory was utilized to explore the quantitative and optimal solutions of the time-varying control strength (i.e., contact rate) to suppress the highly transmissible SARS-CoV-2 variants. RESULTS: The necessary period for reaching the zero-COVID goal can be nearly 4 months, and the final epidemic size was 629,625 (95%CI: [608,049, 651,201]). By adopting the city-based pattern, 7 out of 16 strategies released the NPIs more or earlier than the baseline and ensured a zero-resurgence risk at the average cost of 10 to 129 more cases in June. By adopting the district-based pattern, a regional linked release can allow resumption of social activity to ~ 100% in the boundary-region group about 14 days earlier and allow people to flow between different districts without causing infection resurgence. Optimal solutions of the contact rate were obtained with various testing intensities, and higher diagnosis rate correlated with higher optimal contact rate while the number of daily reported cases remained almost unchanged. CONCLUSIONS: Shanghai could have been bolder and more flexible in unleashing social activity than they did. The boundary-region group should be relaxed earlier and more attention should be paid to the centre-region group. With a more intensive testing strategy, people could return to normal life as much as possible but still ensure the epidemic was maintained at a relatively low level.

Assessing the transmissibility of epidemics involving epidemic zoning.

BACKGROUND: Epidemic zoning is an important option in a series of measures for the prevention and control of infectious diseases. We aim to accurately assess the disease transmission process by considering the epidemic zoning, and we take two epidemics with distinct outbreak sizes as an example, i.e., the Xi'an epidemic in late 2021 and the Shanghai epidemic in early 2022. METHODS: For the two epidemics, the total cases were clearly distinguished by their reporting zone and the Bernoulli counting process was used to describe whether one infected case in society would be reported in control zones or not. Assuming the imperfect or perfect isolation policy in control zones, the transmission processes are respectively simulated by the adjusted renewal equation with case importation, which can be derived on the basis of the Bellman-Harris branching theory. The likelihood function containing unknown parameters is then constructed by assuming the daily number of new cases reported in control zones follows a Poisson distribution. All the unknown parameters were obtained by the maximum likelihood estimation. RESULTS: For both epidemics, the internal infections characterized by subcritical transmission within the control zones were verified, and the median control reproduction numbers were estimated as 0.403 (95% confidence interval (CI): 0.352, 0.459) in Xi'an epidemic and 0.727 (95% CI: 0.724, 0.730) in Shanghai epidemic, respectively. In addition, although the detection rate of social cases quickly increased to 100% during the decline period of daily new cases until the end of the epidemic, the detection rate in Xi'an was significantly higher than that in Shanghai in the previous period. CONCLUSIONS: The comparative analysis of the two epidemics with different consequences highlights the role of the higher detection rate of social cases since the beginning of the epidemic and the reduced transmission risk in control zones throughout the outbreak. Strengthening the detection of social infection and strictly implementing the isolation policy are of great significance to avoid a larger-scale epidemic.

The relative importance of key meteorological factors affecting numbers of mosquito vectors of dengue fever.

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.

Coupling an individual adaptive-decision model with a SIRV model of influenza vaccination reveals new insights for epidemic control.

Past seasonal influenza epidemics and vaccination experience may affect individuals' decisions on whether to be vaccinated or not, decisions that may be constantly reassessed in relation to recent influenza related experience. To understand the potentially complex interaction between experience and decisions and whether the vaccination rate is likely to reach a critical coverage level or not, we construct an adaptive-decision model. This model is then coupled with an influenza vaccination dynamics (SIRV) model to explore the interaction between individuals' decision-making and an influenza epidemic. Nonlinear least squares estimation is used to obtain the best-fit parameter values in the SIRV model based on data on new influenza-like illness (ILI) cases in Texas. Uncertainty and sensitivity analyses are then carried out to determine the impact of key parameters of the adaptive decision-making model on the ILI epidemic. The results showed that the necessary critical coverage rate of ILI vaccination could not be reached by voluntary vaccination. However, it could be reached in the fourth year if mass media reports improved individuals' memory of past vaccination experience. Individuals' memory of past vaccination experience, the proportion with histories of past vaccinations and the perceived cost of vaccination are important factors determining whether an ILI epidemic can be effectively controlled or not. Therefore, health authorities should guide people to improve their memory of past vaccination experience through media reports, publish timely data on annual vaccination proportions and adjust relevant measures to appropriately reduce vaccination perceived cost, in order to effectively control an ILI epidemic.