Optimal control for SIRC epidemic outbreak

Iacoviello, Daniela; Stasio, Nicolino

doi:10.1016/j.cmpb.2013.01.006

Cited by 47 publications

(41 citation statements)

References 21 publications

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“…Por considerar esta imunidade parcial, a qual existe em uma série de doenças que sofrem mutações, o modelo SIRC apresenta uma divisão compartimental mais apropriada do que o modelo SIR, apresentando uma modelagem mais precisa para descrever doenças como a Influenza A e outras, e.g., (IACOVIELLO;STASIO, 2013 …”

Section: Modelo Compartimental Sircunclassified

Um estudo sobre a memória epidemiológica: modelo SIRC fracionário

Cezaro¹,

Gomes²

2017

C.Q.D.

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Um estudo sobre a memória epidemiológica:modelo SIRC fracionárioOn a epidemiological memory framework: fractional SIRC model Resumo Nesta versão, apresentamos uma maneira de introduzir um retardo de fase que pode ser interpretado como um processo de memória do sistema, no modelo compartimental SIRC utilizando as derivadas de ordem fracionária do tipo Caputo, por ser mais simples de serem interpretadas as condições inicias do sistema dinâmico em termos biológicos. O diferencialé que tal processo de memóriaé introduzido de maneira natural no sistema, dadas as propriedades dos operadores fracionários. Estaé uma expanção do trabalho (GOMES; DE CEZARO, 2017) apresentada no Encontro Regional de Matemática Aplicada e Computacional (ERMAC), onde apresentamos uma análise teórica mais completa, bem como exploramos melhor os resultados numéricos. Discutimos os resultados para várias ordens de derivada fracionária em comparação com o modelo de ordem inteira, demonstrando que a introdução das derivadas de ordem fracionária apresentam um retardo na dinâmica do sistema, o qual pode ser interpretado como memória epidemiológica. Palavras-chave: Modelo Fracionário SIRC. Cálculo Fracionário e Aplicações AbstractIn this version, we present a way to introduces an phase delay, that can be interpreted as a memory process in the compartmental SIRC model using the fractional derivatives of Caputo's type, since the initial conditions for the fractional dynamics have a more clear interpretation in terms of biological applications. The novelty of our proposal is that the memory process is naturally introduced in the system, given the properties of fractional operators. This is an expansion of (GOMES; DE CEZARO, 2017) presented at (ERMAC). In this version we present a more complete theoretical analysis of the fractional SIRC model, as well as we improve the numerical results. We discuss further the results for the the results for several orders of fractional derivative in comparison with the standard model with derivative of order one. We show that the introduction of fractional order derivatives in the model induces a phase delay in the dynamics of the system that can be interpreted as an epidemiological memory effect. Keywords: Fractional SIRC model. Fractional calculus and Applications. IntroduçãoO interesse por estudar epidemias causadas por doenças infecciosasé muito antigo, e.g., (BERNOULLI, 1760) e referências. Uma das motivações desse estudo reside no fato de que doenças infecciosas afetam populações humanas, animais e vegetais há muito tempo, causando custos aos cofres públicos e até mesmo devastando populações. Conforme (HETHCOTE, 2000), tais motivações não são coisas do passado, pois, epidemias ainda são apontadas como causas preocupantes de mortalidade nos países em desenvolvimento.No Brasil, pesquisadores apontam a necessidade desses estudos, tanto naárea biomédica, para o desenvolvimento de vacinas, quanto baseadas em populações para auxiliar na tomada de decisões em políticas públicas (BARRETO et. al, 2011).Em uma breve pesqu...

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Section: Modelo Compartimental Sircunclassified

Um estudo sobre a memória epidemiológica: modelo SIRC fracionário

Cezaro¹,

Gomes²

2017

C.Q.D.

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“…In the last few years, the importance of epidemic modeling and control has increased in respect of their capability to describe infectious disease and proposing suitable control strategies [1][2][3][4][5][6][7][8]; moreover, the power of epidemic modeling has been used also in different fields, such as to study the propagation effects of a virus outbreak on a network [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…By taking into account the conditions (29) and (30), 2 8 cases are possible, but they are reduced by eliminating the contrasting conditions. The control equations with conditions (29) and (30), along with the costate and the state equations, yield the expressions for the controls:…”

Section: With the Introduction Of The Costate Vectormentioning

confidence: 99%

Optimal Resource Allocation to Reduce an Epidemic Spread and Its Complication

Giamberardino

Iacoviello

2019

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Mathematical modeling represents a useful instrument to describe epidemic spread and to propose useful control actions, such as vaccination scheduling, quarantine, informative campaign, and therapy, especially in the realistic hypothesis of resources limitations. Moreover, the same representation could efficiently describe different epidemic scenarios, involving, for example, computer viruses spreading in the network. In this paper, a new model describing an infectious disease and a possible complication is proposed; after deep-model analysis discussing the role of the reproduction number, an optimal control problem is formulated and solved to reduce the number of dead patients, minimizing the control effort. The results show the reasonability of the proposed model and the effectiveness of the control action, aiming at an efficient resource allocation; the model also describes the different reactions of a population with respect to an epidemic disease depending on the economic and social original conditions. The optimal control theory applied to the proposed new epidemic model provides a sensible reduction in the number of dead patients, also suggesting the suitable scheduling of the vaccination control. Future work will be devoted to the identification of the model parameters referring to specific epidemic disease and complications, also taking into account the geographic and social scenario.

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“…The author gave a brief description of the deterministic SIRC model and calculated the basic regeneration number [8]. In 2013,Iacoviello and Stasio studied the SIRC model more closely [9], and discussed the optimal control method in the case of the outbreak of the SIRC model based on the mathematical results.…”

mentioning

confidence: 99%

“…Iacoviello and Stasio studied the SIRC model more closely [9], and discussed the optimal control method in the case of the outbreak of the SIRC model based on the mathematical results.…”

mentioning

confidence: 99%

Threshold Dynamics of the Stochastic SIRC Epidemic Model

Zhang¹

2018

JAMP

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In this paper, we discuss the dynamics of a stochastic SIRC epidemic model with infection rate affected by white noise. We prove that this stochastic model has a unique nonnegative solution globally. A threshold is identified. When the noise is small, the solution of the stochastic model converges to the disease-free equilibrium point of the deterministic model if 0 1 s R < , which means the basic reproductive number of the stochastic model. And if 0 1 s R > , the solution of the stochastic model fluctuates around the epidemic equilibrium of the deterministic model. When the noise is large, the disease tends to extinction. The results are illustrated by computer simulations. relationships between groups in these models are different. The SI model is suitable for the disease without recurrent seizures. The SIS model can describe the patient getting sick repeatedly. The SIR model is used when the patient are immunized after infection. Other descriptions may include the presence of subjects in the quarantine state (Q) and in this situation SIRQ models are analyzed [6]. The models are more and more complex with the development of epidemiology. Recently the class of cross-immune individuals (C) in the population has been introduced [7]: it is an intermediate state between the fully susceptible state (S) and the fully protected one (R). The obtained SIRC model takes temporary partial immunity into account. The author gave a brief description of the deterministic SIRC model and calculated the basic regeneration number [8]. In 2013,Iacoviello and Stasio studied the SIRC model more closely [9], and discussed the optimal control method in the case of the outbreak of the SIRC model based on the mathematical results.

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Optimal control for SIRC epidemic outbreak

Cited by 47 publications

References 21 publications

Um estudo sobre a memória epidemiológica: modelo SIRC fracionário

Um estudo sobre a memória epidemiológica: modelo SIRC fracionário

Optimal Resource Allocation to Reduce an Epidemic Spread and Its Complication

Threshold Dynamics of the Stochastic SIRC Epidemic Model

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