Dynamics of a metapopulation epidemic model with localized culling

Bolzoni, Luca; Marca, Rossella Della; Groppi, Maria; Gragnani, Alessandra

doi:10.3934/dcdsb.2020036

Cited by 3 publications

(3 citation statements)

References 43 publications

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“…The described scenario is similar to the case where the disease control is applied only when the number of infected (or new infections) exceeds a given threshold, which can be mathematically investigated through sliding models (Bolzoni et al. 2020 ; Qin et al. 2016 ).…”

Section: Discussionmentioning

confidence: 99%

“…the beginning and the end] of the epidemic may not be efficient, since several susceptible units would be screened/tested in the face of few infected ones. The described scenario is similar to the case where the disease control is applied only when the number of infected (or new infections) exceeds a given threshold, which can be mathematically investigated through sliding models (Bolzoni et al 2020;Qin et al 2016).…”

Section: Simulationsmentioning

confidence: 99%

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On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies

2021

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Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a major simplification consists in assuming that the infectious period is exponentially distributed, then implying that the chance of recovery is independent on the time since infection. Here, we first attempt to investigate the consequences of relaxing this assumption on the performances of time-variant disease control strategies by using optimal control theory. In the framework of a basic susceptible–infected–removed (SIR) model, an Erlang distribution of the infectious period is considered and optimal isolation strategies are searched for. The objective functional to be minimized takes into account the cost of the isolation efforts per time unit and the sanitary costs due to the incidence of the epidemic outbreak. Applying the Pontryagin’s minimum principle, we prove that the optimal control problem admits only bang–bang solutions with at most two switches. In particular, the optimal strategy could be postponing the starting intervention time with respect to the beginning of the outbreak. Finally, by means of numerical simulations, we show how the shape of the optimal solutions is affected by the different distributions of the infectious period, by the relative weight of the two cost components, and by the initial conditions.

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Section: Discussionmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies

2021

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“…They showed that strengthening the culling of mosquitoes together with protecting birds is a good choice in controlling the spread of West Nile virus. Bolzoni et al [24] studied a two-patches metapopulation mathematical model in wildlife diseases. They considered both proactive end reactive localized culling strategies.…”

Section: Introductionmentioning

confidence: 99%

Rich dynamics of a Filippov avian-only influenza model with a nonsmooth separation line

Yang

Wang

2021

Adv Differ Equ

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Depopulation of birds has been authenticated to be an effective measure in controlling avian influenza transmission. In this work, we establish a Filippov avian-only model incorporating a threshold policy control. We choose the index—the maximum between the infected threshold level $I_{T}$ I T and the product of the number of susceptible birds S and a ratio threshold value ξ—to decide on whether to trigger the control measures or not, which then leads to a discontinuous separation line and two pieces of sliding-mode domains. Meanwhile, one more sliding-mode domain gives birth to more complex dynamics. We investigate the global dynamical behavior of the Filippov model, including the real and/or virtual equilibria and the two sliding modes and their dynamics. The solutions will eventually stabilize at the real endemic equilibrium of the subsystem or the pseudoequilibria on the two sliding modes due to different threshold values. Therefore an effective and efficient threshold policy is essential to control the influenza by driving the number of infected birds below a certain level or at a previously given level.

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Bifurcation analysis of a sheep brucellosis model with testing and saturated culling rate

Nie

Sun

et al. 2022

MBE

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<abstract><p>Testing-culling is a very effective measure for the prevention and control of animal diseases. In this paper, based on sheep brucellosis control policies and animal testing characteristics and considering the limitation of culling resources, a dynamic model is established to study the impact of testing-culling measure. Theoretical analysis reveals that the model may have one or three positive equilibria. The equilibrium in the middle is always unstable, and the model shows saddle-node bifurcation, generalized Hopf bifurcation and Bogdanov-Takens bifurcation. Moreover, the theoretical results are verified via numerical analysis. These results reveal that testing and culling strategies can induce complex transmission dynamics that can help us develop appropriate prevention and control measures for animal brucellosis.</p></abstract>

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Dynamics of a metapopulation epidemic model with localized culling

Cited by 3 publications

References 43 publications

On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies

On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies

Rich dynamics of a Filippov avian-only influenza model with a nonsmooth separation line

Bifurcation analysis of a sheep brucellosis model with testing and saturated culling rate

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