Stochastic transmission in epidemiological models

Albani, Vinicius V. L.; Zubelli, Jorge P.

doi:10.1007/s00285-023-02042-z

Cited by 3 publications

(1 citation statement)

References 48 publications

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“…Since the outbreak of the COVID-19 epidemic, a large number of models have been proposed to describe, simulate, and forecast its transmission rule. Some models are individualbased [9] or multi-scale [10], some models are based on cells and viruses [11] or stochastic processes [12,13], and others are developments of classical SIR and SEIR models [14][15][16][17][18][19][20]. On the other hand, there are a lot of studies about control measures.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters

2024

Mathematics

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The coronavirus disease 2019 (COVID-19) pandemic disrupted public health and economies worldwide. In this paper, we investigate an optimal control problem to simultaneously minimize the epidemic size and control costs associated with intervention strategies based on official data. Considering people with undetected infections, we establish a control system of COVID-19 with time-varying parameters. To estimate these parameters, a parameter identification scheme is adopted and a mixed algorithm is constructed. Moreover, we present an optimal control problem with two objectives that involve the newly increased number of infected individuals and the control costs. A numerical scheme is conducted, simulating the epidemic data pertaining to Shanghai during the period of 2022, caused by the Omicron variant. Coefficient combinations of the objectives are obtained, and the optimal control measures for different infection peaks are indicated. The numerical results suggest that the identification variables obtained by using the constructed mixed algorithm to solve the parameter identification problem are feasible. Optimal control measures for different epidemic peaks can serve as references for decision-makers.

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Section: Introductionmentioning

confidence: 99%

Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters

2024

Mathematics

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Mathematical modeling and stability analysis of the novel fractional model in the Caputo derivative operator: A case study

Saadeh,

Abdoon,

Qazza

et al. 2024

Heliyon

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Modeling and Optimal Control of Infectious Diseases

Lefebvre

2024

Mathematics

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We propose a stochastic model of infectious disease transmission that is more realistic than those found in the literature. The model is based on jump-diffusion processes. However, it is defined in such a way that the number of people susceptible to be infected decreases over time, which is the case for a population of fixed size. Next, we consider the problem of finding the optimal control of the proposed model. The dynamic programming equation satisfied by the value function is derived. Estimators of the various model parameters are obtained.

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Stochastic transmission in epidemiological models

Cited by 3 publications

References 48 publications

Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters

Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters

Mathematical modeling and stability analysis of the novel fractional model in the Caputo derivative operator: A case study

Modeling and Optimal Control of Infectious Diseases

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