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

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

doi:10.1007/s00285-021-01668-1

Cited by 9 publications

(7 citation statements)

References 44 publications

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“…To this end, inspired by the approach adopted in the papers (Bolzoni et al. 2021 ; Hansen and Day 2011 ), we assume that coincides with the end of the first epidemic wave, namely is the first time there is less than one infectious individual in the population: In other words, is the first time at which drops to . Of course, the presence of subsequent epidemic waves is not excluded, but for the sake of simplicity we focus here on just the first one.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…We want that the t f is a finite time with a reasonable epidemiological interpretation. To this end, inspired by the approach adopted in the papers (Bolzoni et al 2021;Hansen and Day 2011), we assume that t f coincides with the end of the first epidemic wave, namely t f is the first time there is less than one infectious individual in the population:…”

Section: Impact Of Viral Load On the Disease Dynamicsmentioning

confidence: 99%

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An SIR model with viral load-dependent transmission

2023

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The viral load is known to be a chief predictor of the risk of transmission of infectious diseases. In this work, we investigate the role of the individuals’ viral load in the disease transmission by proposing a new susceptible-infectious-recovered epidemic model for the densities and mean viral loads of each compartment. To this aim, we formally derive the compartmental model from an appropriate microscopic one. Firstly, we consider a multi-agent system in which individuals are identified by the epidemiological compartment to which they belong and by their viral load. Microscopic rules describe both the switch of compartment and the evolution of the viral load. In particular, in the binary interactions between susceptible and infectious individuals, the probability for the susceptible individual to get infected depends on the viral load of the infectious individual. Then, we implement the prescribed microscopic dynamics in appropriate kinetic equations, from which the macroscopic equations for the densities and viral load momentum of the compartments are eventually derived. In the macroscopic model, the rate of disease transmission turns out to be a function of the mean viral load of the infectious population. We analytically and numerically investigate the case that the transmission rate linearly depends on the viral load, which is compared to the classical case of constant transmission rate. A qualitative analysis is performed based on stability and bifurcation theory. Finally, numerical investigations concerning the model reproduction number and the epidemic dynamics are presented.

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Section: Numerical Simulationsmentioning

confidence: 99%

Section: Impact Of Viral Load On the Disease Dynamicsmentioning

confidence: 99%

An SIR model with viral load-dependent transmission

2023

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“…Mathematically, there have been numerous studies exploring the mechanisms by which anthropogenic factors influence the dynamics of infectious diseases. See, for instance, immunization, Gao et al [ 15 ], Starnini et al [ 16 ]; isolation, Te Vrugt et al [ 17 ], Bolzoni et al [ 18 ]; media coverage, Cai et al [ 19 ]; time delay, Agaba et al [ 20 , 21 ]. It is worth pointing out that in traditional mathematical modeling research on epidemics, medical conditions are usually considered as a fixed constant.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics of an SIS compartment model with resource constraints

Liu

Feng

2023

J. Appl. Math. Comput.

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This paper formulates a mathematical framework to describe the dynamics of SIS-type infectious diseases with resource constraints. We first define the basic reproduction number that determines disease prevalence and analyze the existence and local stability of the equilibria. Subsequently, we analyze the global dynamics of the model, excluding periodic solutions and heteroclinic orbits, using the compound matrix approach. The analysis implies that the model can undergo forward and backward bifurcations depending on critical parameters. In the former scenario, the disease persists when the basic reproduction number under resource constraints exceeds one. In the latter scenario, the backward bifurcation creates bistability dynamics in which the disease may persist or become extinct depending on the initial level of infected individuals and the resource abundance.

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“…One important attribute of the L 2 −formulation is that it is amenable to mathematical analysis in the sense that the optimal control problem (OCP) can be reduced to a two-point boundary value problem which can be easily solved by standard numerical methods [22]. This mathematical convenience is probably the main reason that the L 2 −formulation is so widespread in the literature [4,3,5,7,15,16,20,23,26,30,35,36,44,47]. Yet, for biomedical and epidemiological applications, the use of L 2 −objective functionals is frequently difficult to validate.…”

Section: Introductionmentioning

confidence: 99%

Optimal vaccination strategies for a heterogenous population using multiple objectives: The case of L1− and L2−formulations

Saldaña

Kebir

Camacho-Gutíerrez³

et al. 2023

Preprint

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The choice of the objective functional in optimization problems coming from biomedical and epidemiological applications plays a key role in optimal control outcomes. In this study, we investigate the role of the objective functional on the structure of the optimal control solution for an epidemic model that includes a core group with higher sexual activity levels than the rest of the population. An optimal control problem is formulated to find a targeted vaccination program able to control the spread of the infection with minimum vaccine deployment. Both $L_{1}-$ and $L_{2}-$objectives are considered as an attempt to explore the trade-offs between control dynamics and the functional form characterizing optimality. Our results show that the optimal vaccination policy for both the $L_{1}-$ and the $L_{2}-$formulation share one important qualitative property, that is, immunization of the core group should be prioritized by policymakers to achieve a fast reduction of the epidemic. Nevertheless, quantitative aspects of this result can be significantly affected depending on the objective weightings. Overall, our results suggest that the optimal control profiles are reasonably robust with respect to the $L_{1}-$ or $L_{2}-$formulation when the monetary cost of the vaccination policy is substantially lower than the cost associated with the disease burden but if this is not the case the optimal control profiles can be radically different for each formulation.

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

Cited by 9 publications

References 44 publications

An SIR model with viral load-dependent transmission

An SIR model with viral load-dependent transmission

Global dynamics of an SIS compartment model with resource constraints

Optimal vaccination strategies for a heterogenous population using multiple objectives: The case of L1− and L2−formulations

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