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Due to the facts that epidemic-related parameters vary significantly in different stages of infectious diseases and are relatively stable within the same stage, infectious disease models should be switch-type models. However, research on switch-type infectious disease models is scarce due to the complexity and intricate design of switching rules. This scarcity has motivated the writing of this paper. By assuming that switching instants and impulse times occur at different moments, this paper proposes switch rules suitable for impulse control and derives synchronization criteria for reaction–diffusion switch-type infectious disease systems under impulse control. The effectiveness of this method is validated through numerical simulations. It is important to mention that, based on the information available to us, this paper is currently the sole study focusing on switch-type reaction–diffusion models for infectious diseases. [ABSTRACT FROM AUTHOR]

This paper enhances the agent model of ordinary individuals by incorporating the roles of places in the transmission, prevention, and control in the process, establishing a fundamental connection between these two types of agents through individual travel rules. The impact of real-world prevention and control measures on regional epidemic transmission is studied based on this model. Firstly, based on the analysis of place elements in typical cases of major infectious diseases, we give the classification of places. Secondly, the resident agent and the place agent are constructed and rules are established to form an agent-based major infectious disease transmission model considering the place. Then, the simulation process is established and an ideal regional environment is constructed to simulate overall changes in major infectious disease scale and spread speed. Additionally, evolutionary simulations are conducted for individual isolation intensity and place control time during emergency management stages to compare infection outcomes, and we analyze different roles and application scenarios of specific prevention and control measures. Finally, simulation results from real major infectious disease cases in Yangzhou, China, validate the effectiveness of this model in predicting major infectious disease development trends as well as evaluating prevention and control measure effects. [ABSTRACT FROM AUTHOR]

COVID-19 is a contagious disease that poses a serious risk to public health worldwide. To reduce its spread, people need to adopt preventive behaviours such as wearing masks, maintaining physical distance, and isolating themselves if they are infected. However, the effectiveness of these measures may depend on various factors that differ across countries. This paper investigates how some factors, namely outsiders' effect, life expectancy, population density, smoker percentage, and temperature, influence the transmission and death rate of COVID-19 in ninety-five top-affected countries. We collect and analyse the data of COVID-19 cases and deaths using statistical tests. We also use fuzzy logic to model the chances of COVID-19 based on the results of the statistical tests. Unlike the conventional uniform weighting of the rule base in fuzzy logic, we propose a novel method to calculate the weights of the rule base according to the significance of the factors. This study aims to provide a comprehensive and comparative analysis of the factors of COVID-19 transmission and death rates among different countries. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic is still ongoing, even if the emergency is over, and we now have enough data to analyze the outbreak over a long timeline. There is evidence that the outbreak alternates periods of high and low infections. Retrospectively, this can help in understanding the nature of an appropriate mathematical model for this dramatic infection. The periodic behavior may be the consequence of time-dependent coefficients related to seasonal effects and specific political actions, or an intrinsic feature of the model. The present paper relies on the assumption that the periodic spikes are an intrinsic feature of the disease, and, as such, it should be properly reflected in the mathematical model. Based on the concept of waning immunity proposed for other pathologies, we introduce a new model with (i) a compartment for weakly immune people subject to immunity booster, represented by a non-linear term; (ii) discrimination between individuals infected/vaccinated for the first time, and individuals already infected/vaccinated, undergoing to new infections/doses. We analyze some preliminary properties of our model, called SIRW2, and provide a proof-of-concept that it is capable of reproducing qualitatively the long-term oscillatory behavior of COVID-19 infection. [ABSTRACT FROM AUTHOR]

In this paper, we establish a random epidemic model with double vaccination and spontaneous variation of the virus. Firstly, we prove the global existence and uniqueness of positive solutions for a stochastic epidemic model. Secondly, we prove the threshold R 0 * can be used to control the stochastic dynamics of the model. If R 0 * < 0 , the disease will be extinct with probability 1; whereas if R 0 * > 0 , the disease can almost certainly continue to exist, and there is a unique stable distribution. Finally, we give some numerical examples to verify our theoretical results. Most of the existing studies prove the stochastic dynamics of the model by constructing Lyapunov functions. However, the construction of a Lyapunov function of higher-order models is extremely complex, so this method is not applicable to all models. In this paper, we use the definition method suitable for more models to prove the stationary distribution. Most of the stochastic infectious disease models studied now are second-order or third-order, and cannot accurately describe infectious diseases. In order to solve this kind of problem, this paper adopts a higher price five-order model. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model based on COVID-19 is developed to study and manage disease outbreaks. The effect of vaccination with regard to its efficacy and percentage of population vaccinated in a closed population is investigated. To study virus transmission, the system employs six nonlinear ordinary differential equations with susceptible–exposed–asymptomatic–infected–vaccinated–recovered populations and the basic reproduction number are calculated. The proposed model describes for highly infectious diseases (such as COVID-19) in a closed containment area with no migration. This paper considers that the percentage of vaccinated population has a significant impact on the number of COVID-19 positive cases during the pandemic wave and examines how the pandemic rise time is delayed. Numerical simulation to investigate disease outbreaks when the community is undergoing vaccination is performed, taking the efficacy rate of the vaccine into account. Sensitivity Index values are calculated for the reproduction number and their relations with few other parameters are depicted. [ABSTRACT FROM AUTHOR]

Significant and composite indices for infectious disease can have implications for developing interventions and public health. This paper presents an investment for developing access to further analysis of the incidence of individual and multiple diseases. This research mainly comprises two steps: first, an automatic and reproducible procedure based on functional data analysis techniques was proposed for analyzing the dynamic properties of each disease; second, orthogonal transformation was adopted for the development of composite indices. Between 2000 and 2019, nineteen class B notifiable diseases in China were collected for this study from the National Bureau of Statistics of China. The study facilitates the probing of underlying information about the dynamics from discrete incidence rates of each disease through the procedure, and it is also possible to obtain similarities and differences about diseases in detail by combining the derivative features. There has been great success in intervening in the majority of notifiable diseases in China, like bacterial or amebic dysentery and epidemic cerebrospinal meningitis, while more efforts are required for some diseases, like AIDS and virus hepatitis. The composite indices were able to reflect a more complex concept by combining individual incidences into a single value, providing a simultaneous reflection for multiple objects, and facilitating disease comparisons accordingly. For the notifiable diseases included in this study, there was superior management of gastro-intestinal infectious diseases and respiratory infectious diseases from the perspective of composite indices. This study developed a methodology for exploring the prevalent properties of infectious diseases. The development of effective and reliable analytical methods provides special insight into infectious diseases' common dynamics and properties and has implications for the effective intervention of infectious diseases. [ABSTRACT FROM AUTHOR]

Vaccination strategies remain one of the most effective and feasible preventive measures in combating infectious diseases, particularly during the COVID-19 pandemic. With the passage of time, continuous long-term lockdowns became impractical, and the effectiveness of contact-tracing procedures significantly declined as the number of cases increased. This paper presents a mathematical assessment of the dynamics and prevention of COVID-19, taking into account the constant and time-varying optimal COVID-19 vaccine with multiple doses. We attempt to develop a mathematical model by incorporating compartments with individuals receiving primary, secondary, and booster shots of the COVID-19 vaccine in a basic epidemic model. Initially, the model is rigorously studied in terms of qualitative analysis. The stability analysis and mathematical results are presented to demonstrate that the model is asymptotically stable both locally and globally at the COVID-19-free equilibrium state. We also investigate the impact of multiple vaccinations on the COVID-19 model's results, revealing that the infection risk can be reduced by administrating the booster vaccine dose to those individuals who already received their first vaccine doses. The existence of backward bifurcation phenomena is studied. A sensitivity analysis is carried out to determine the most sensitive parameter on the disease incidence. Furthermore, we developed a control model by introducing time-varying controls to suggest the optimal strategy for disease minimization. These controls are isolation, multiple vaccine efficacy, and reduction in the probability that different vaccine doses do not develop antibodies against the original virus. The existence and numerical solution to the COVID-19 control problem are presented. A detailed simulation is illustrated demonstrating the population-level impact of the constant and time-varying optimal controls on disease eradication. Using the novel concept of human awareness and several vaccination doses, the elimination of COVID-19 infections could be significantly enhanced. [ABSTRACT FROM AUTHOR]

Under the background of double carbon, it is important to study forest pests and diseases to improve forest carbon sink. In this paper, we establish a delayed model associated with the larvae and adults of Saperda populnea, susceptible poplars, and infected poplars. First, we analyze the existence and stability of the equilibrium of the model. Second, we study the existence of Hopf bifurcation near the equilibrium and obtain the normal form of Hopf bifurcation by the multiple time scales method. Then, we analyze the direction and stability of Hopf bifurcating periodic solutions. Third, we analyze and conjecture some parameter values based on official data, and carry out numerical simulations to verify our results. Finally, we give some suggestions on the prevention and control of Saperda populnea. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the pattern dynamics of an SI epidemic model caused by spatial dependency, which is represented by self- and cross-diffusion terms. Cross-diffusion of the susceptible represents a tendency of the susceptible to stay away from the infected. Meanwhile, cross-diffusion of the infected represents their movement to the location with a high density of the susceptible. This study focuses on the presence of the effects of cross-diffusion terms on the Turing instability. This study applies Turing analysis to yield the Turing space and Turing patterns corresponding to the model by involving the infection rate as the bifurcation parameter. The results show that the presence of cross-diffusion terms narrows the Turing space depending on the magnitude of the cross-diffusion coefficients itself. Dynamical behaviors of the model are then investigated through a series of numerical simulations that successfully perform five types of patterns, i.e., spots, spots–stripes, stripes, stripes–holes, and holes. Those patterns give a description of the spread of an infectious disease. The holes denote an outbreak situation in a region, whereas the non-outbreak situation is emphasized by the spots pattern. Further, the decreasing of the ratio of recruitment and death rates indicates that the increasing of the infection rate triggers an outbreak. The present study confirms that cross-diffusion terms have a significant role in infectious disease transmission, spatially. [ABSTRACT FROM AUTHOR]

From the moment a patient is admitted to the hospital, monitoring begins, and specific information is collected. The continuous flow of parameters, including clinical and analytical data, serves as a significant source of information. However, there are situations in which not all values from medical tests can be obtained. This paper aims to predict the medical test values of COVID-19 patients in the intensive care unit (ICU). By retrieving the missing medical test values, the model provides healthcare professionals with an additional tool and more information with which to combat COVID-19. The proposed approach utilizes a customizable deep learning model. Three types of neural networks, namely Multilayer Perceptron (MLP), Long/Short-Term Memory (LSTM), and Gated Recurrent Units (GRU), are employed. The parameters of these neural networks are configured to determine the model that delivers the optimal performance. Evaluation of the model's performance is conducted using metrics such as Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute Error (MAE). The application of the proposed model achieves predictions of the retrieved medical test values, resulting in RMSE = 7.237, MAPE = 5.572, and MAE = 4.791. Moreover, the article explores various scenarios in which the model exhibits higher accuracy. This model can be adapted and utilized in the diagnosis of future infectious diseases that share characteristics with Coronavirus Disease 2019 (COVID-19). [ABSTRACT FROM AUTHOR]

Prediction of the infectious disease is a potential research area from the decades. With the progress in medical science, early anticipation of the disease spread becomes more meaningful when the resources are limited. Also spread prediction with limited data pose a deadly challenge to the practitioners. Hence, the paper presents a case study of the Corona virus (COVID-19). COVID-19 has hit the major parts of the world and implications of this virus, is life threatening. Research community has contributed significantly to understand the spread of virus with time, along with meteorological conditions and other parameters. Several forecasting techniques have already been deployed for this. Considering the fact, the paper presents a proposal of two Rolling horizon based Cubic Grey Models (RCGMs). First, the mathematical details of Cubic Polynomial based simple grey model is presented than two models based on time series rolling are proposed. The models are developed with the time series data of different locations, considering diverse overlap period and rolling values. It is observed that the proposed models yield satisfactory results as compared with the conventional and advanced grey models. The comparison of the performance has been carried out with calculation of standard error indices. At the end, some recommendations are also framed for the authorities, that can be helpful for decision making in tough time. [ABSTRACT FROM AUTHOR]

Based on China's summary of three years of experience and measures in the prevention and control of the COVID-19 epidemic, we have built a COVID-19 prevention and control model integrating health and medical detection, big data information technology to track the trend of the epidemic throughout the whole process, isolation of key epidemic areas, and dynamic prevention and control management throughout the whole process. This model provides a simple, feasible, and theoretically reliable prevention and control model for future large-scale infectious disease prevention and control. The Lyapnov functional method is replaced by the global exponential attractor theory, which provides a new mathematical method for studying the global stability of the multi parameter, multi variable infectious disease prevention and control system. We extracted mathematical methods and models suitable for non-mathematical infectious disease researchers from profound and difficult to understand mathematical theories. Using the results of the global exponential Attractor theory obtained in this paper, we studied the global dynamics of the COVID-19 model with an epidemiological investigation. The results demonstrated that the non-constant disease-free equilibrium is globally asymptotically stable when λ * < 0 , and the COVID-19 epidemic is persisting uniformly when λ * > 0 . In order to understand the impact of the epidemiological investigation under different prevention and control stages in China, we compare the control effects of COVID-19 under different levels of epidemiological investigation policies. We visually demonstrate the global stability and global exponential attractiveness of the COVID-19 model with transferors between regions and epidemiological investigation in a temporal-spatial heterogeneous environment with the help of numerical simulations. We find that the epidemiological investigation really has a significant effect on the prevention and control of the epidemic situation, and we can also intuitively observe the relationship between the flow of people (including tourism, shopping, work and so on) and epidemiological investigation policies. Our model is adapted to different stages of prevention and control; the emergency "circuit breaker" mechanism of the model is also consistent with actual prevention and control. [ABSTRACT FROM AUTHOR]

Most biological processes take time to occur. In infectious diseases, such as malaria or chikungunya, there is a period of time between when a susceptible individual gets bitten by the vector, and when the individual develops the disease. These times are commonly modeled by introducing delays or by adding exposed as a new population class. Given a model based on differential equations, delays can be introduced in different forms. In this paper, we study different ways of introducing the delays and, alternatively, using exposed populations. We also analyze their steady solutions and stability, and establish the conditions under which the studied models predict an epidemic. Results and conclusions are presented. [ABSTRACT FROM AUTHOR]

Nowadays, a lot of research papers are concentrating on the diffusion dynamics of infectious diseases, especially the most recent one: COVID-19. The primary goal of this work is to explore the stability analysis of a new version of the S E I R model formulated with incommensurate fractional-order derivatives. In particular, several existence and uniqueness results of the solution of the proposed model are derived by means of the Picard–Lindelöf method. Several stability analysis results related to the disease-free equilibrium of the model are reported in light of computing the so-called basic reproduction number, as well as in view of utilising a certain Lyapunov function. In conclusion, various numerical simulations are performed to confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we explore two modeling approaches to understanding the dynamics of infectious diseases in the population: equation-based modeling (EBM) and agent-based modeling (ABM). To achieve this, a comparative study of these approaches was conducted and we highlighted their advantages and disadvantages. Two case studies on the spread of the COVID-19 pandemic were carried out using both approaches. The results obtained show that differential equation-based models are faster but still simplistic, while agent-based models require more machine capabilities but are more realistic and very close to biology. Based on these outputs, it seems that the coupling of both approaches could be an interesting compromise. [ABSTRACT FROM AUTHOR]

The consideration of infectious diseases from a mathematical point of view can reveal possible options for epidemic control and fighting the spread of infection. However, predicting and modeling the spread of a new, previously unexplored virus is still difficult. The present paper examines the possibility of using a new approach to predicting the statistical indicators of the epidemic of a new type of virus based on the example of COVID-19. The important result of the study is the description of the principle of dynamic balance of epidemiological processes, which has not been previously used by other researchers for epidemic modeling. The new approach is also based on solving the problem of predicting the future dynamics of precisely random values of model parameters, which is used for defining the future values of the total number of: cases (C); recovered and dead (R); and active cases (I). Intelligent heuristic algorithms are proposed for calculating the future trajectories of stochastic parameters, which are called the percentage increase in the total number of confirmed cases of the disease and the dynamic characteristics of epidemiological processes. Examples are given of the application of the proposed approach for making forecasts of the considered indicators of the COVID-19 epidemic, in Russia and European countries, during the first wave of the epidemic. [ABSTRACT FROM AUTHOR]

Environmental disturbances have a strong impact on cholera transmission. Stochastic differential equations are an effective tool for characterizing environmental perturbations. In this paper, a stochastic infectious disease model for cholera is established and investigated. The dynamics of the stochastic cholera model are discussed. Firstly, the existence and uniqueness of the positive solution are proven. Then, the asymptotical stability of the disease-free equilibrium of the system is investigated. Furthermore, the asymptotical stability of the endemic equilibrium of the deterministic system corresponding to the stochastic system is obtained. Then, the theoretical results are verified by some numerical simulations. Finally, the optimal problem is considered as the theoretical basis for the control of cholera. Both theoretical and numerical results indicate that the random perturbations may make the model more realistic, which provides theoretical assessment for the control of cholera transmission. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid SEIAM model for infectious disease with a continuous age structure is established, where combined dynamic effects of media coverage and multi-staged infected progression on threshold dynamics are discussed. Sufficient conditions for uniform persistence of the solution are studied by using the basic reproduction number. By constructing appropriate Lyapunov functions, the global stability analysis of endemic equilibrium is investigated based on Lyapunov–LaSalle's stability theorem. In order to minimize costs incurred due to applied controls and infectious disease burden, an optimal cost-effective control strategy associated with disease treatment and media coverage is discussed. Numerical simulations are carried out to show consistency with theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the author proposes a new SEIRS model that generalizes several classical deterministic epidemic models (e.g., SIR and SIS and SEIR and SEIRS) involving the relationships between the susceptible S, exposed E, infected I, and recovered R individuals for understanding the proliferation of infectious diseases. As a way to incorporate the most important features of the previous models under the assumption of homogeneous mixing (mass-action principle) of the individuals in the population N, the SEIRS model utilizes vital dynamics with unequal birth and death rates, vaccinations for newborns and non-newborns, and temporary immunity. In order to determine the equilibrium points, namely the disease-free and endemic equilibrium points, and study their local stability behaviors, the SEIRS model is rescaled with the total time-varying population and analyzed according to its epidemic condition R0 for two cases of no epidemic (R0 ≤ 1) and epidemic (R0 > 1) using the time-series and phase portraits of the susceptible s, exposed e, infected i, and recovered r individuals. Based on the experimental results using a set of arbitrarily-defined parameters for horizontal transmission of the infectious diseases, the proportional population of the SEIRS model consisted primarily of the recovered r (0.7-0.9) individuals and susceptible s (0.0-0.1) individuals (epidemic) and recovered r (0.9) individuals with only a small proportional population for the susceptible s (0.1) individuals (no epidemic). Overall, the initial conditions for the susceptible s, exposed e, infected i, and recovered r individuals reached the corresponding equilibrium point for local stability: no epidemic (DFE XDFE) and epidemic (EE XEE). [ABSTRACT FROM AUTHOR]

This paper analyses an SIRS epidemic model with the vaccination of susceptible individuals and treatment of infectious ones. Both actions are governed by a designed control system whose inputs are the subpopulations of the epidemic model. In addition, the vaccination of a proportion of newborns is considered. The control reproduction number R c of the controlled epidemic model is calculated, and its influence in the existence and stability of equilibrium points is studied. If such a number is smaller than a threshold value R ¯ c , then the model has a unique equilibrium point: the so-called disease-free equilibrium point at which there are not infectious individuals. Furthermore, such an equilibrium point is locally and globally asymptotically stable. On the contrary, if R c > R ¯ c , then the model has two equilibrium points: the referred disease-free one, which is unstable, and an endemic one at which there are infectious individuals. The proposed control strategy provides several free-design parameters that influence both values R c and R ¯ c . Then, such parameters can be appropriately adjusted for guaranteeing the non-existence of the endemic equilibrium point and, in this way, eradicating the persistence of the infectious disease. [ABSTRACT FROM AUTHOR]

Networks and graphs offer a suitable and powerful framework for studying the spread of infection in human and animal populations. In the case of a heterogeneous population, the social contact network has a pivotal role in the analysis of directly transmitted infectious diseases. The literature presents several works where network-based models encompass realistic features (such as contacts networks or host–pathogen biological data), but analytical results are nonetheless scarce. As a significant example, in this paper, we develop a multi-group version of the epidemiological SEIR population-based model. Each group can represent a social subpopulation with the same habits or a group of geographically localized people. We consider also heterogeneity in the weighting of contacts between two groups. As a simple application, we propose a simple control algorithm in which we optimize the connection weights in order to minimize the combination between an economic cost and a social cost. Some numerical simulations are also provided. [ABSTRACT FROM AUTHOR]

At the end of 2019, an outbreak of the novel coronavirus (COVID-19) made a profound impact on the country's production and people's daily lives. Up until now, COVID-19 has not been fully controlled all over the world. Based on the clinical research progress of infectious diseases, combined with epidemiological theories and possible disease control measures, this paper establishes a Susceptible Infected Recovered (SIR) model that meets the characteristics of the transmission of the new coronavirus, using the least square estimation (LSE) method to estimate the model parameters. The simulation results show that quarantine and containment measures as well as vaccine and drug development measures can control the spread of the epidemic effectively. As can be seen from the prediction results of the model, the simulation results of the epidemic development of the whole country and Nanjing are in agreement with the real situation of the epidemic, and the number of confirmed cases is close to the real value. At the same time, the model's prediction of the prevention effect and control measures have shed new light on epidemic prevention and control. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model to describe the spread of an infectious disease on a farm is developed. To analyze the evolution of the infection, the direct transmission from infected individuals and the indirect transmission from the bacteria accumulated in the enclosure are considered. A threshold value of population is obtained to assure the extinction of the disease. When this size of population is exceeded, two control procedures to apply at each time are proposed. For each of them, a maximum number of steps without control and reducing the prevalence of disease is obtained. In addition, a criterion to choose between both procedures is established. Finally, the results are numerically simulated for a hypothetical outbreak on a farm. [ABSTRACT FROM AUTHOR]

Many infectious diseases are deadly to humans. The Aedes aegypi mosquito is the principal vector of infectious diseases that include chikungunya, dengue, yellow fever, and zika. Some factors such as survival time and aging are vital in its development and capacity to transmit the pathogens, which in turn are affected by environmental factors such as temperature. In this paper, we consider aging as the biological wear and tear presented in some mosquito populations over time, whereas survival is considered as the maximum time that a mosquito lives. We propose statistical methods that are commonly used in engineering for reliability analysis to compare transmission riskiness among different mosquitoes. We conducted a case study in three Colombian cities: Bello, Riohacha, and Villavicencio. In this study, we detected that the Aedes aegypi female mosquitoes in Bello live longer than in Riohacha and Villavicencio, and the females in Riohacha live longer than those in Villavicencio. Regarding aging, the females from Riohacha age slower than in Villavicencio and the latter age slower than in Bello. Mosquito populations that age slower are considered young and the other ones are old. In addition, we detected that the females from Bello in the temperature range of 27 ∘ C–28 ∘ C age slower than those in Bello at higher temperatures. In general, a young female has a higher risk of transmitting a disease to humans than an old female, regardless of its survival time. These findings have not been previously reported in studies of this type of infectious diseases and contributed to new knowledge in biomedicine. [ABSTRACT FROM AUTHOR]

This paper presents an evolutionary algorithm that simulates simplified scenarios of the diffusion of an infectious disease within a given population. The proposed evolutionary epidemic diffusion (EED) computational model has a limited number of variables and parameters, but is still able to simulate a variety of configurations that have a good adherence to real-world cases. The use of two space distances and the calculation of spatial 2-dimensional entropy are also examined. Several simulations demonstrate the feasibility of the EED for testing distinct social, logistic and economy risks. The performance of the system dynamics is assessed by several variables and indices. The global information is efficiently condensed and visualized by means of multidimensional scaling. [ABSTRACT FROM AUTHOR]

In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams–Bashforth–Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams–Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method. [ABSTRACT FROM AUTHOR]