Narrow Results

Rumor is an unauthenticated statement that gives significant changes in the social life of the people, financial markets (stocks and trades), etc. By incorporating the dissemination of rumor through groups in social, mobile networks and by considering the people’s cognitive factor (hesitate and forget), a new model on the rumor spreading process is presented in this paper. The spreading dynamics of rumor in homogeneous and heterogeneous networks is analyzed by using mean-field theory. The reproduction number is obtained by using the next-generation matrix. The global stability of the rumor-free equilibrium for the homogeneous and heterogeneous model is proved elaborately. An optimal control problem is developed to minimize the hesitators and infected persons and the existence of optimality is shown using Pontryagin’s Minimum Principle. The hesitating and forgetting mechanism has a great impact on the model and is similar to the real-life. Further, the control parameters work superior in controlling the spreading of rumors. Finally, the numerical results are verified by the analytical results.

The city of Rio de Janeiro is one of the biggest cities in Brazil. Drug gangs and paramilitary groups called milícias control some regions of the city where the government is not present, specially in the slums. Due to the characteristics of such two distinct groups, it was observed that the evolution of COVID-19 is different in those two regions, in comparison with the regions controlled by the government. In order to understand qualitatively those observations, we divided the city in three regions controlled by the government, by the drug gangs and by the milícias, respectively, and we consider a Susceptible-Infected-Recovered-Dead (SIRD)-like epidemic model where the three regions are coupled. Considering different levels of exposure, the model is capable to reproduce qualitatively the distinct evolution of the COVID-19 disease in the three regions, suggesting that the organized crime shapes the COVID-19 evolution in the city of Rio de Janeiro. This case study suggests that the model can be used in general for any metropolitan region with groups of people that can be categorized by their level of exposure.

We present a five-variable compartmental model for the spread of Trypanosoma brucei gambiense, the parasite responsible for the transmission (through tsetse flies) of sleeping sickness in Central Africa. The model’s equilibrium points depend on two “summary parameters”: g_r, the proportion removed among human infectives, and R₀, the basic reproduction rate. Stability results are obtained for the origin but not for other equilibrium points. A two-variable simplified version of the model is presented and the stability of all its equilibrium points can be investigated analytically. Both models are applied to the Niari focus of Central Africa and used to test the impact of a vector control strategy. The models’ results are in agreement with the extinction of the epidemic that was brought about by a fifty percent decrease in vector density.

Methods of comparing discrete and continuous cable models of single neurons and dynamical phenomena observed in neurobiology can be described with infinite-coupled systems of semilinear parabolic differential-functional equations of the reaction-diffusion-convection type or infinite systems of ordinary integro-differential equations. It is known that numerous problems in computational neuroscience use finite systems of equations based on the so-called compartmental model. It seems a natural idea to extend the results obtained in the theory of finite systems onto infinite systems. However, this requires stringent assumptions to be adopted to achieve compatibility. In most instances the dynamics of infinite systems behave differently to their finite-dimensional projections. The truncation method applied to infinite systems of equations and presented herein yields a truncated system consisting of the first N equations of the infinite system in N unknown functions. A solution of infinite system is defined as the limit when N → ∞ of the sequence of approximations {z_N}_N=1,2,…, where are defined as solutions of suitable finite truncated systems with corresponding initial-boundary conditions. Geometrically, it may be described as the projection of an infinite system of differential equations considered in a function abstract space of infinite dimension (such as Banach or Hilbert space) onto its finite-dimensional subspaces.

As a potential source of consciousness, the brain's endogenous electromagnetic (EM) field has much to commend it. Difficulties connecting EM phenomena and consciousness have been exacerbated by the lack of a specific conclusive biophysically realistic mechanism originating the EM field, its form and dynamics. This work explores a potential mechanism: the spatial and temporal coherent action of transmembrane ion channel currents which simultaneously produce electric and magnetic fields that dominate all other field sources. Ion channels, as tiny current filaments, express, at a distance, the electric and magnetic fields akin to those of a short (transmembrane) copper wire. Following assembly of appropriate formalisms from EM field theory, the paper computationally explores the scalar electric potential produced by the current filaments responsible for an action potential (AP) in a realistic hippocampus CA1 pyramidal neuron. It reveals that AP signaling can impress a highly structured, focused and directed "sweeping-lighthouse beam" that "illuminates" neighbors at mm scales. Ion channel currents thereby provide a possible explanation for both EEG/MEG origins and recently confirmed functional EM coupling effects. Finally, a physically plausible EM field decomposition is posited. It reveals objective and subjective perspectives intrinsic to the membrane-centric field dynamics. Perceptual "fields" can be seen to operate as the collective action of virtual EM-boson composites (called qualeons) visible only by "being" the fields, yet objectively appear as the familiar EM field activity. This explains the problematic evidence presentation and offers a physically plausible route to a solution to the "hard problem".

A compartmental model is established for schistosomiasis infection in Qianzhou and Zimuzhou, two islets in the center of Yangtzi River near Nanjing, P. R. China. The model consists of five differential equations about the susceptible and infected subpopulations of mammalian Rattus norvegicus and Oncomelania snails. We calculate the basic reproductive number R₀ and discuss the global stability of the disease free equilibrium and the unique endemic equilibrium when it exists. The dynamics of the model can be characterized in terms of the basic reproductive number. The parameters in the model are estimated based on the data from the field study of the Nanjing Institute of Parasitic Diseases. Our analysis shows that in a natural isolated area where schistosomiasis is endemic, killing snails is more effective than killing Rattus norvegicus for the control of schistosomiasis.

On March 12, 2020, the WHO declared the COVID-19 pandemic, in response to widespread infections and thousands of fatalities resulting from the outbreak. Researchers worldwide have paid close attention to this pandemic. This situation has been aided by mathematical models that guide public policy. In Rwanda, this problem involves uncertainty and incomplete information, and a stochastic approach is appropriate for capturing a broad range of possible outcomes. However, many epidemiological models do not account for preventive measures using a stochastic approach to analyze COVID-19 in Rwanda. Therefore, the aim of the paper is to build and analyze a COVID-19 pandemic stochastic model with preventive measures implemented in Rwanda. A deterministic model is formulated and transformed into stochastic equations. The numerical solutions of both models were computed and compared. The stochastic model is considered to be the best to use in the Rwanda context because of the model’s fluctuations, which capture even the residuals and uncertainties. The results indicate that the pandemic could spread faster if awareness-raising strategies are not effectively implemented, and preventive actions for the pandemic are considered crucial tools for effective control and mitigation.

In this chapter, we discuss how medical image analysis can take advantage of computational modeling. First, a general framework of model-based approach is presented, whose objective is enabling to relate external descriptions to internal processes, which originate them. Two coupled models i.e. model of an organ under study and model of an imaging modality, constitute the main components of this framework. Then, a few applications of the presented approach are described. Two vital abdominal organs, namely liver and kidney, are considered and their typical pathological processes connected with significant vascular modifications are analyzed. Resulting patterns are observed by means of dynamic Computed Tomography, when contrast material injection and propagation are simulated. Texture features are extracted from regions of interest defined in simulated images in different acquisition conditions. Studying evolution of features allows us to better understand both advantages and limitations of texture analysis and is very helpful in proper medical image interpretation.

A linear time invariant state space model is proposed for the production and decay of two epimers (R) and (S) of a hopane released from oil bearing rock during laboratory pyrolysis. Concentrations of R and S are measured over time. The parameters to be estimated are: the initial amounts of precursors X, for R, and Y, for S; the rate constants for the production of R and S; the rate constants for the decay of R and S; and the rate constants for the two-way epimerization between both X and Y and R and S. It is shown that the model is locally identifiable. The parameters are estimated by numerical integration of the rate equations, alternated with a derivative free least squares constrained, optimisation routine. Asymptotic standard errors and covariances of parameters are given and compared with those obtained from a resampling approach (parametric bootstrap). An alternative fitting procedure, based on estimating derivatives of the concentrations of R and S by fitting splines, is implemented and compared with that based on integration of the rate equations. The rate constants are important for elucidation of the reaction pathways, and the estimates of initial concentrations of X and Y have potential for inferring the yields of oil bearing rock.

In developing neuromimetic engineering systems, the choice of neuron-like element is critical, because this element determines the functional ability of the system. According to recent neuroscience research, a neuron is expected to perform sophisticated information processing, making use of the complex physiological properties of its dendrites. In this chapter, the computational function of neuronal dendrites is explored based on mathematical models. Theoretical analyses show that a passive dendrite is capable of complex logic operations by means of nonlinear synaptic interactions. Computer simulations show that active dendrites integrate synaptic inputs locally and then hierarchically according to synaptic organization and dendritic geometry. Based on these results, a formal neuron is proposed which simply and sufficiently describes the actual properties of the dendrites. This model is therefore suitable for constructing a large-scale network without the loss of the active dendrites' essential responsiveness. These modeling studies provide novel perspectives on the computation in a single neuron with a complex dendritic tree.

As a potential source of consciousness, the brain's endogenous electromagnetic (EM) field has much to commend it. Difficulties connecting EM phenomena and consciousness have been exacerbated by the lack of a specific conclusive biophysically realistic mechanism originating the EM field, its form and dynamics. This work explores a potential mechanism: the spatial and temporal coherent action of transmembrane ion channel currents which simultaneously produce electric and magnetic fields that dominate all other field sources. Ion channels, as tiny current filaments, express, at a distance, the electric and magnetic fields akin to those of a short (transmembrane) copper wire. Following assembly of appropriate formalisms from EM field theory, the chapter computationally explores the scalar electric potential produced by the current filaments responsible for an action potential (AP) in a realistic hippocampus CA1 pyramidal neuron. It reveals that AP signaling can impress a highly structured, focused and directed “sweeping-lighthouse beam” that “illuminates” neighbors at mm scales. Ion channel currents thereby provide a possible explanation for both EEG/MEG origins and recently confirmed functional EM coupling effects. Finally, a physically plausible EM field decomposition is posited. It reveals objective and subjective perspectives intrinsic to the membrane-centric field dynamics. Perceptual “fields” can be seen to operate as the collective action of virtual EM-boson composites (called qualeons) visible only by “being” the fields, yet objectively appear as the familiar EM field activity. This explains the problematic evidence presentation and offers a physically plausible route to a solution to the “hard problem.”