Distinguished from the existing HIV/AIDS epidemic models, we formulate a model by considering three-age-structured, spacial diffusion, viral load-dependent infection and conversion rates to study the ...global dynamical behaviors of HIV/AIDS transmission. The generation operator ℛ and the explicit expression of basic reproduction ratio R0 are introduced. The global stability of steady states and the uniform persistence of the disease are presented. Sensitivity analysis indicates that some parameters impact the value of R0 markedly and the intervening measure plays a crucial role in the intervention of HIV infection at population level. Furthermore, numerical simulations suggest that intervening measure at the individual and population levels is highly effective in controlling the transmission of the disease.
In this article we build a mathematical model for forest growth and we compare this model with a computer forest simulator named SORTIE. The main ingredient taken into account in both models is the ...competition for light between trees. The parameters of the mathematical model are estimated by using SORTIE model, when the parameter values of SORTIE model correspond to the ones previously evaluated for the Great Mountain Forest in USA. We see that the best fit of the parameters of the mathematical model is obtained when the competition for light influences only the growth rate of trees. We construct a size structured population dynamics model with one and two species and with spatial structure.
•A size-structured math model is proposed to describe the forest simulator SORTIE.•Comparisons with SORTIE are conducted by numerical simulations for single species.•A similar model for two-species case is proposed and similar comparisons are done.•A spatial math model is proposed to display the spread of forest.
The behaviour of statistical relational representations across differently sized domains has become a focal area of research from both a modelling and a complexity viewpoint. Recently, projectivity ...of a family of distributions emerged as a key property, ensuring that marginal probabilities are independent of the domain size. However, the formalisation used currently assumes that the domain is characterised only by its size. This contribution extends the notion of projectivity from families of distributions indexed by domain size to functors taking extensional data from a database. This makes projectivity available for the large range of applications taking structured input. We transfer key known results on projective families of distributions to the new setting. This includes a characterisation of projective fragments in different statistical relational formalisms as well as a general representation theorem for projective families of distributions. Furthermore, we prove a correspondence between projectivity and distributions on countably infinite domains, which we use to unify and generalise earlier work on statistical relational representations in infinite domains. Finally, we use the extended notion of projectivity to define a further strengthening, which we call σ-projectivity, and which allows the use of the same representation in different modes while retaining projectivity.
This paper deals with the numerical threshold stability of a nonlinear age-space structured heroin transmission model. A semi-discrete system is established by spatially domain discretization of the ...original nonlinear age-space structured model. A threshold value is proposed in stability analysis of the semi-discrete system and named as a numerical basic reproduction number. Besides the role it plays in numerical threshold stability analysis, the numerical basic reproduction number can preserve qualitative properties of the exact basic reproduction number and converge to the latter while stepsizes vanish. A fully discrete system is established via a time discretization of the semi-discrete system, in which an implicit-explicit technique is implemented to ensure the preservation of the biological meanings (such as positivity) without CFL restriction. Some numerical experiments are exhibited in the end to confirm the conclusions and explore the final state.
•A numerical scheme is constructed for nonlinear age-structured reaction-diffusion models.•A numerical stability threshold is proposed in numerical stability analysis.•The numerical stability threshold we proposed can preserve qualitative properties of the exact stability threshold.
Understanding human activity is very challenging even with the recently developed 3D/depth sensors. To solve this problem, this work investigates a novel deep structured model, which adaptively ...decomposes an activity instance into temporal parts using the convolutional neural networks. Our model advances the traditional deep learning approaches in two aspects. First, we incorporate latent temporal structure into the deep model, accounting for large temporal variations of diverse human activities. In particular, we utilize the latent variables to decompose the input activity into a number of temporally segmented sub-activities, and accordingly feed them into the parts (i.e. sub-networks) of the deep architecture. Second, we incorporate a radius–margin bound as a regularization term into our deep model, which effectively improves the generalization performance for classification. For model training, we propose a principled learning algorithm that iteratively (i) discovers the optimal latent variables (i.e. the ways of activity decomposition) for all training instances, (ii) updates the classifiers based on the generated features, and (iii) updates the parameters of multi-layer neural networks. In the experiments, our approach is validated on several complex scenarios for human activity recognition and demonstrates superior performances over other state-of-the-art approaches.
A multi-strain within-host model of HIV with age structure, which explicitly incorporates the loss of free viral particles due to absorption into target cells upon infection, and shedding into the ...environment is formulated and analyzed. In our model, a time delay between viral entry into a target cell and viral replication is incorporated, and multiple virus strains compete for a population of target cells. Control is incorporated into the model via strain-specific reverse transcriptase and protease inhibitors. An optimal control problem subject to multiple drug treatments is formulated and analyzed. Existence, characterization and uniqueness of optimal control is established. Using the forward-backward sweep numerical method, numerical simulations are presented. Simulations suggest that a combination of reverse transcriptase and protease inhibitors for each strain of the infected cells and free viruses results in a delay in initial peak in the populations of infected cells and free viruses, the absence of relapse phase within the entire time horizon of control, and a decrease in the number of infected cells and free viruses.
The numerical method for simulation of age-structured SIPCV epidemic model with age-structured sub-classes of susceptible, infectious, precancerous and cancer cells and unstructured population of ...human papilloma virus (HPV) dynamics with incubation period is developed. Convergence of the numerical approximations is studied both theoretically and numerically. We prove the stability and second rate of convergence of the approximate solutions to the exact solution of the SIPCV epidemic nonlinear system. The numerical experiments based on the grid refined method confirm and illustrate the second order of accuracy of the obtained numerical method and show the various dynamical regimes of population dynamics. Simulations for model parameters of the system reveal two unstable dynamical regimes of SIPCV population which correspond to the cancer tumor growth and formation of metastases in organism.
Brucellosis is a highly contagious zoonosis in the world caused by a group of bacteria from the genus brucella. It can infect both human and animals through eating contaminated food, breathing ...polluted air, and direct contact of the infected animals. The number of onset cases shows an increase tend in recent years, mainly in pastures and farms. To investigate the dynamics of brucellosis and capture the event of its spread, we propose a novel model that is an attempt for the first time ever to incorporate with both age-since-infection and spacial diffusion of the infection. We first analytically study the existence and uniqueness of the solution of the model, followed by positivity of the solutions. The location dependent reproduction number R(x) is explicitly calculated by a renewal process and the basic reproduction number R0 is defined by the spectral radius of R(x). The calculation method is novel and simple. It is shown that when R0<1 the infectious disease will die out; when R0>1 the disease will be prevalent. Parameter sensitivity analysis on the expression of R0 shows that certain parameters are more effective to impact the value of R0. Based on this analysis and our intensive numerical simulations, we recommend that the herdsmen should make efforts to keep the living environment of their animals clean, and eliminate infectious animals timely.
•We firstly propose a novel age–space structured brucellosis epidemic model.•We calculate an explicit formulation for the next generator operator R(x) by the renewal equation.•We give a general method to estimate the weighted coefficients for constructing Lyapunov functionals.•We show some effectively control strategies for herdsman by uncertainty analysis.
With the global spread of coronavirus disease 2019 (COVID-19), understanding the mechanisms and characteristics of epidemic waves has become necessary to control its spread. The sixth epidemic wave ...of COVID-19 in Sapporo, Japan, was analyzed using a new mathematical model called the SIUICICPRURC model. The main objectives are (1) introducing the SIUICICPRURC model, (2) introducing algorisms by which parameters and initial states were estimated, and (3) estimating values of parameters and initial states, and analyzing the epidemic wave.
Reported numbers of daily new confirmed infected cases, currently infected cases, and cumulative numbers of recovered or fatal cases were collected from the official website of the city of Sapporo. The SIUICICPRURC model, based on susceptible-infectious-removed and infection-period-structured models, was employed. Parameter values and initial states of variables were estimated using the least squares method, Visual Basic for Applications, and Solver in Microsoft Excel.
The peak time of transmission rate was estimated to be 5.8 to 6.0 days after infection, the peak time of infection confirmation rate was 8.0 to 8.1 days after infection, and the ultimate confirmation ratio of infection was 0.65 to 0.85. It was also estimated that almost all individuals in Sapporo were susceptible to the Omicron variant of the severe acute respiratory syndrome-coronavirus 2.
The sixth epidemic wave of COVID-19 was analyzed with the SIUICICPRURC model, with which crucial parameters and initial states were estimated. Furthermore, the results indicate that vaccination against the Wuhan strain and the previous infection were insufficient to induce a level of immunity required to prevent infection by the Omicron variant. Further improvement of mathematical modeling for infectious diseases is required to control emerging infectious diseases in the future, even if the threat of COVID-19 is overcome.
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Electricity price is a key influencer in the electricity market. Electricity market trades by each participant are based on electricity price. The electricity price adjusted with the change in supply ...and demand relationship can reflect the real value of electricity in the transaction process. However, for the power generating party, bidding strategy determines the level of profit, and the accurate prediction of electricity price could make it possible to determine a more accurate bidding price. This cannot only reduce transaction risk, but also seize opportunities in the electricity market. In order to effectively estimate electricity price, this paper proposes an electricity price forecasting system based on the combination of 2 deep neural networks, the Convolutional Neural Network (CNN) and the Long Short Term Memory (LSTM). In order to compare the overall performance of each algorithm, the Mean Absolute Error (MAE) and Root-Mean-Square error (RMSE) evaluating measures were applied in the experiments of this paper. Experiment results show that compared with other traditional machine learning methods, the prediction performance of the estimating model proposed in this paper is proven to be the best. By combining the CNN and LSTM models, the feasibility and practicality of electricity price prediction is also confirmed in this paper.
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