On the stabilization of reaction–diffusion systems modeling a class of man‐environment epidemics: A review

Aniţa, Sebastian; Capasso, Vincenzo

doi:10.1002/mma.1267

Cited by 16 publications

(13 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We shall find a sufficient condition for eradicability. For stabilizability results related to some reaction-diffusion systems in population dynamics, we refer to previous studies 16,17,22,[27][28][29][30][31][32][33] whilst for general distributed systems, see Lions. 34 When the costs of the controls to reduce the epidemic, of the damages produced by the disease and of the intervention in the subset in the time interval [0, T] are considered, then we get the total cost function:…”

Section: Definitionmentioning

confidence: 99%

“…As pointed out in Molineaux and Gramiccia, seasonality of the aggressivity to humans by the mosquito population might also be considered in the functional response h ; this has been a topic of the authors research program in other works …”

Section: Introduction and Setting Of The Problemsmentioning

confidence: 99%

“…We shall find a sufficient condition for eradicability. For stabilizability results related to some reaction‐diffusion systems in population dynamics, we refer to previous studies whilst for general distributed systems, see Lions…”

Section: Introduction and Setting Of The Problemsmentioning

confidence: 99%

“…As pointed out in Molineaux and Gramiccia, 5 seasonality of the aggressivity to humans by the mosquito population might also be considered in the functional response h; this has been a topic of the authors research program in other works. 17,[20][21][22] As far as the "local incidence" for mosquitoes, at point x ∈ Ω , and time t ≥ 0, as in previous models, 23 we assume that it is due to contagious bites to human infectives at any point x ′ ∈ Ω of the habitat, within a spatial neighborhood of…”

mentioning

confidence: 99%

See 3 more Smart Citations

Regional control for a spatially structured malaria model

Aniţa

Capasso

Dimitriu

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

A two‐component reaction‐diffusion system to describe the spread of malaria is considered. The model describes the dynamics of the infected mosquitoes and of the infected humans. The spread of the disease is controlled by three actions (controls) implemented in a subdomain of the habitat: killing mosquitoes, treating the infected humans, and reducing the contact rate mosquitoes‐humans. To start with, the problem of the eradicability of the disease is considered, while the cost of the controls is ignored. We prove that it is possible to decrease exponentially both the human and the vector infective population everywhere in the relevant habitat by acting only in a suitable subdomain. Later, the regional control problem of reducing the total cost of the damages produced by the disease, of the controls, and of the intervention in a certain subdomain is treated for the finite time horizon case. An iterative algorithm to decrease the total cost is proposed; apart from the three controls considered above, the logistic structure of the habitat is taken into account. The level set method is used as a key ingredient for describing the subregion of intervention. Some numerical simulations are given to illustrate the applicability of the theoretical results.

show abstract

Section: Definitionmentioning

confidence: 99%

Section: Introduction and Setting Of The Problemsmentioning

confidence: 99%

Section: Introduction and Setting Of The Problemsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Regional control for a spatially structured malaria model

Aniţa

Capasso

Dimitriu

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…As pointed out in [65], seasonality of the aggressivity to humans by the mosquito population might also be considered in the functional response h; this has been a topic of the authors research programme in [29], and [5], [4].…”

Section: Malariamentioning

confidence: 99%

Stabilization for a Reaction-Diffusion System in Epidemiology

Aniţa

Math Everywhere

Self Cite

View full text Add to dashboard Cite

A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion which depends upon the way the specific disease is communicated among different populations or subpopulations. Compartmental models describing a finite number of subpopulations can be described mathematically via systems of ordinary differential equations. The same is not possible for populations which exhibit some continuous structure, such as space location, age, etc. In particular when dealing with populations with space structure the relevant quantities are spatial densities, whose evolution in time requires now nonlinear partial differential equations, which are known as reaction-diffusion systems. In this chapter we are presenting an (historical) outline of mathematical epidemiology, paying particular attention to the role of spatial heterogeneity and dispersal in the population dynamics of infectious diseases. Two specific examples are discussed, which have been the subject of intensive research by the authors of the present chapter, i.e. man-environment-man epidemics, and malaria. In addition to the epidemiological relevance of these epidemics all over the world, their treatment requires a large amount of different sophisticate mathematical methods, and has even posed new non trivial mathematical problems, as one can realize from the list of references. One of the most relevant problems faced by the present authors, i.e. regional

show abstract