Robust viability analysis of a controlled epidemiological model

Autor: Lilian Sofia Sepulveda Salcedo, Michel De Lara
Přispěvatelé: Universidad Autónoma de Occidente (UAO), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC)
Rok vydání: 2019
Předmět:
0106 biological sciences
0301 basic medicine
Insecticides
Mosquito Control
Control vectorial
Colombia
Models
Biological
010603 evolutionary biology
01 natural sciences
Disease Outbreaks
Dengue
Reduction (complexity)
Epidemics control
03 medical and health sciences
[SDV.MHEP.MI]Life Sciences [q-bio]/Human health and pathology/Infectious diseases
parasitic diseases
Statistics
FOS: Mathematics
Animals
Humans
Mathematics - Optimization and Control
Ecology
Evolution
Behavior and Systematics
Mathematics
Stochastic Processes
Microbial Viability
Vector control
viability
uncertainty and robustness
Ross-Macdonald model
Uncertainty and robustness
Insect Vectors
3. Good health
Highly sensitive
Dengue outbreak
Culicidae
030104 developmental biology
Viability
Optimization and Control (math.OC)
Ross–Macdonald model
epidemics control
Kernel (statistics)
Female
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
[SDE.BE]Environmental Sciences/Biodiversity and Ecology
Zdroj: RED: Repositorio Educativo Digital UAO
Universidad Autónoma de Occidente
instacron:Universidad Autónoma de Occidente
Repositorio Institucional UAO
ISSN: 0040-5809
DOI: 10.1016/j.tpb.2019.02.003
Popis: Managing infectious diseases is a world public health issue, plagued by uncertainties. In this paper, we analyze the problem of viable control of a dengue outbreak under uncertainty. For this purpose, we develop a controlled Ross-Macdonald model in discrete time, with mosquito vector control by fumigation and with uncertainties affecting the dynamics. The robust viability kernel is the set of all initial states such that there exists at least a strategy of insecticide spraying which guarantees that the number of infected people remains below a threshold, for all times, and whatever the sequences of uncertainties (scenarios). Having chosen three nested subsets of uncertainties - a deterministic one (without uncertainty), a medium one and a large one - we can measure the incidence of the uncertainties on the size of the kernel, in particular on its reduction with respect to the de-terministic case. The numerical results show that the viability kernel without uncertainties is highly sensitive to the variability of parameters - here the biting rate, the probability of infection to mosquitoes and humans, and the proportion of female mosquitoes per person. So the robust viability kernel is a possible tool to reveal the importance of uncertainties regarding epidemics control.
Comment: arXiv admin note: text overlap with arXiv:1510.01055
Databáze: OpenAIRE
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