Modelling of surface reactions and diffusion mediated by bulk diffusion.

We develop a continuum framework applicable to solid-state hydrogen storage, cell biology and other scenarios where the diffusion of a single constituent within a bulk region is coupled via adsorption/desorption to reactions and diffusion on the boundary of the region. We formulate content balances for all relevant constituents and develop thermodynamically consistent constitutive equations. The latter encompass two classes of kinetics for adsorption/desorption and chemical reactions-fast and Marcelin-De Donder, and the second class includes mass action kinetics as a special case. We apply the framework to derive a system consisting of the standard diffusion equation in bulk and FitzHugh-Nagumo type surface reaction-diffusion system of equations on the boundary. We also study the linear stability of a homogeneous steady state in a spherical region and establish sufficient conditions for the occurrence of instabilities driven by surface diffusion. These findings are verified through numerical simulations which reveal that instabilities driven by diffusion lead to the emergence of steady-state spatial patterns from random initial conditions and that bulk diffusion can suppress spatial patterns, in which case temporal oscillations can ensue. We include an extension of our framework that accounts for mechanochemical coupling when the bulk region is occupied by a deformable solid. This article is part of the theme issue 'Foundational issues, analysis and geometry in continuum mechanics'.

Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network.

The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction-diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction-diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction-diffusion model for describing local dynamics.

State Estimation for Coupled Reaction-Diffusion PDE Systems Using Modulating Functions.

Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online.

Coupled mathematical modeling of cisplatin electroporation.

The use of electrochemotherapy (ECT) is a well-established technique to increase the cellular uptake of cytotoxic agents within certain cancer treatment strategies. The study of the mechanisms that take part in this complex process is of high interest to gain a deeper knowledge of it, enabling the improvement of these strategies. In this work, we present a coupled multi-physics electroporation model based on a related previous one, to describe the effect of a set of electric pulses on cisplatin transport across the plasma membrane. The model applies a system of partial differential equations that includes Poisson's equation for the electric field, Nernst-Planck's equation for species transport, Maxwell's tensor and mechanical equilibrium equation for membrane deformation and Smoluchowski's equation for pore creation dynamics. Our numerical results were compared with previous numerical and experimental published data with good qualitative and quantitative agreement. These results indicate that pore aperture is favored at the cell poles by the electric field and mechanical stress forces, giving support to the dominant hypothesis of hydrophilic pore creation as the main mechanism of drug entry during an ECT treatment.

A reaction-diffusion model of spatial propagation of A[Formula: see text] oligomers in early stage Alzheimer's disease.

The misconformation and aggregation of the protein Amyloid-Beta (A[Formula: see text]) is a key event in the propagation of Alzheimer's Disease (AD). Different types of assemblies are identified, with long fibrils and plaques deposing during the late stages of AD. In the earlier stages, the disease spread is driven by the formation and the spatial propagation of small amorphous assemblies called oligomers. We propose a model dedicated to studying those early stages, in the vicinity of a few neurons and after a polymer seed has been formed. We build a reaction-diffusion model, with a Becker-Döring-like system that includes fragmentation and size-dependent diffusion. We hereby establish the theoretical framework necessary for the proper use of this model, by proving the existence of solutions using a fixed point method.

Estimation of the expected number of cases of microcephaly in Brazil as a result of Zika.

In this paper we have adapted a delayed dengue model to Zika. By assuming that the epidemic starts by a single infected individual entering a disease-free population at some initial time t0 we have used the least squares parameter estimation technique in R to estimate the initial time t0 using observed Zika data from Brazil as well as the transmission probabilities of Zika in Brazil between humans and mosquitoes and vice-versa. Different values of Aedes aegypti (A. aegypti) biting rate are used throughout the paper. We have estimated the value of the basic reproduction number for Zika in Brazil and calculated the expected number of cases of microcephaly in newborns as a result of women infected with Zika during pregnancy. We started off with a non-age-structured model then introduced age-structure into the model. However in reality seasonality, in particular temperature and rainfall, have a great impact on the population size of A. aegypti. Hence we repeat both the non-age-structured and age-structured analyses introducing seasonality into the A. aegypti birth function to model the effect of these environmental factors.

Optimal control of vaccination in a vector-borne reaction-diffusion model applied to Zika virus.

Zika virus has acquired worldwide concern after a recent outbreak in Latin America that started in Brazil, with associated neurological conditions such as microcephaly in newborns from infected mothers. The virus is transmitted mainly by Aedes aegypti mosquitoes, but direct (sexual) transmission has been documented. We formulate a reaction diffusion model that considers spatial movement of humans and vectors, with local contact transmission of Zika virus. Vaccination is introduced as a control variable, giving immunity to susceptible humans, in order to characterize an optimal vaccination strategy that minimizes the costs associated with infections and vaccines. The optimal control characterization is obtained in terms of state and adjoint equations. Parameter estimation and numerical simulations are carried out using data for the initial 2015 Zika outbreak in the state of Rio Grande do Norte in Brazil. Several scenarios are considered and analyzed in terms of number of new infections and costs, showing that the optimal control application is successful, significantly reducing these quantities.

On the controlling of temperature: A proposal for a real-time controller in broiler houses

Environmental conditions in broiler houses, specifically temperature, are key factors that should be controlled to ensure appropriate environment for broiler rearing. In countries with tropical/subtropical climate, like Brazil, high temperatures produce heat stress to animals, affecting the production process. This research proposes a real-time model to control temperature inside broiler houses. The controller is a self-correcting model that makes real-time decisions on the ventilation system operation (exhaust fans) together with temperature prediction at the facility. The model involves partial differential equations (PDE) whose parameters are updated according to data registered in real-time. Some experiments were carried out at a pilot farm in the municipality of Jundiaí, São Paulo State, Brazil, for different periods during winter and summer. The results based on simulations in comparison with the current automatic ventilation system show that the model is consistent to keep temperature under control for an efficient production. The model achieved a bias of 0.6 °C on average in comparison with the ideal temperature, whereas the automatic controller measured a bias of 3.3 °C, respectively. Future lines suggest that this approach could be useful in many other situations that involve environmental control for livestock production.(AU)

Numerical modeling of mosquito population dynamics of Aedes aegypti.

BACKGROUND: The global incidences of dengue virus have increased the interest in studying and understanding the mosquito population dynamics. It is predominantly spread by Aedes aegypti in the tropical and sub-tropical countries in the world. Understanding these dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. For this reason, a new model has been proposed to investigate the population dynamics of mosquitoes in a city. METHODS: The present paper discusses the numerical modeling of population dynamics of Ae. aegypti mosquitoes in an urban neighborhood of a city using the finite volume method. The model describes how populations spread through the city assisted by the wind. This model allows incorporating external factors (wind and chemical insecticides) and topography data (streets, building blocks, parks, forests and beach). The proposed model has been successfully tested in examples involving two Brazilian cities (City center, Juiz de Fora and Copacabana Beach, Rio de Janeiro). RESULTS: Invasion phenomena of Ae. aegypti mosquitoes have been observed in each of the simulations. It was observed that, inside the blocks, the growth of the population for both winged and aquatic phase causes an infestation of Ae. aegypti in a short time. Within the blocks the mosquito population was concentrated and diffused slowly. In the streets, there was a long-distance spread, which was influenced by wind and diffusion with a low concentration of mosquito population. The model was also tested taking into account chemical insecticides spread in two different configurations. It has been observed that the insecticides have a significant effect on the mosquito population for both winged and aquatic phases when the chemical insecticides spread more uniformly along all the streets in a neighborhood of a city. CONCLUSIONS: The presented methodology can be employed to evaluate and to understand the epidemic risks in a specific region of the city. Moreover the model allows an increase in efficiency of the existing mosquito population control techniques and to theoretically test new methods before involving the human population.

On the controlling of temperature: A proposal for a real-time controller in broiler houses

ABSTRACT: Environmental conditions in broiler houses, specifically temperature, are key factors that should be controlled to ensure appropriate environment for broiler rearing. In countries with tropical/subtropical climate, like Brazil, high temperatures produce heat stress to animals, affecting the production process. This research proposes a real-time model to control temperature inside broiler houses. The controller is a self-correcting model that makes real-time decisions on the ventilation system operation (exhaust fans) together with temperature prediction at the facility. The model involves partial differential equations (PDE) whose parameters are updated according to data registered in real-time. Some experiments were carried out at a pilot farm in the municipality of Jundiaí, São Paulo State, Brazil, for different periods during winter and summer. The results based on simulations in comparison with the current automatic ventilation system show that the model is consistent to keep temperature under control for an efficient production. The model achieved a bias of 0.6 °C on average in comparison with the ideal temperature, whereas the automatic controller measured a bias of 3.3 °C, respectively. Future lines suggest that this approach could be useful in many other situations that involve environmental control for livestock production.

On the controlling of temperature: A proposal for a real-time controller in broiler houses

ABSTRACT: Environmental conditions in broiler houses, specifically temperature, are key factors that should be controlled to ensure appropriate environment for broiler rearing. In countries with tropical/subtropical climate, like Brazil, high temperatures produce heat stress to animals, affecting the production process. This research proposes a real-time model to control temperature inside broiler houses. The controller is a self-correcting model that makes real-time decisions on the ventilation system operation (exhaust fans) together with temperature prediction at the facility. The model involves partial differential equations (PDE) whose parameters are updated according to data registered in real-time. Some experiments were carried out at a pilot farm in the municipality of Jundiaí, São Paulo State, Brazil, for different periods during winter and summer. The results based on simulations in comparison with the current automatic ventilation system show that the model is consistent to keep temperature under control for an efficient production. The model achieved a bias of 0.6 °C on average in comparison with the ideal temperature, whereas the automatic controller measured a bias of 3.3 °C, respectively. Future lines suggest that this approach could be useful in many other situations that involve environmental control for livestock production.