Numerical optimal control applied to an epidemiological model

Schreppel, Christina; Chudej, Kurt

doi:10.1016/j.ifacol.2018.03.001

Cited by 5 publications

(4 citation statements)

References 6 publications

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“…Generally, the optimal control problems for real life applications found in the literature can only be solved numerically [91]. Using the Pontryagin Maximum Principle, the necessary optimality conditions for the existence are usually derived (see [113]).…”

Section: Parameter Estimation and Simulation Of An Epidemic Modelmentioning

confidence: 99%

Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation

Trejos

Valverde

Venturino

2021

Applied Mathematics and Nonlinear Sciences

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In this paper, the main biological aspects of infectious diseases and their mathematical translation for modeling their transmission dynamics are revised. In particular, some heterogeneity factors which could influence the fitting of the model to reality are pointed out. Mathematical tools and methods needed to qualitatively analyze deterministic continuous-time models, formulated by ordinary differential equations, are also introduced, while its discrete-time counterparts are properly referenced. In addition, some simulation techniques to validate a mathematical model and to estimate the model parameters are shown. Finally, we present some control strategies usually considered to prevent epidemic outbreaks and their implementation in the model.

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Section: Parameter Estimation and Simulation Of An Epidemic Modelmentioning

confidence: 99%

Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation

Trejos

Valverde

Venturino

2021

Applied Mathematics and Nonlinear Sciences

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“…Some authors who have worked on the incorporation of optimal controls to a generalized real-world diseases and its management include previous studies, [37][38][39][40][41][42][43][44] while numerical techniques like the shooting method, finite difference scheme, and forward-backward Runge-Kutta scheme used in the solution of optimal control problems can be seen in previous studies. [45][46][47][48][49][50][51][52][53][54][55][56][57][58] In view of the earlier studies, several works done on the modeling of onchocerciasis only considered microsimulation and deterministic models and the impact of ivermectin drug treatment only as a control in eradicating the disease annually or bi-annually. However, these authors did not consider dividing infectious humans into stages of infectious states and incorporate nonlinear form of treatment rate.…”

Section: Introductionmentioning

confidence: 99%

“…Many works have been done in applying different control interventions to stop the spread of several human, animal, and crop diseases. Some authors who have worked on the incorporation of optimal controls to a generalized real‐world diseases and its management include previous studies, 37–44 while numerical techniques like the shooting method, finite difference scheme, and forward–backward Runge–Kutta scheme used in the solution of optimal control problems can be seen in previous studies 45–58 …”

Section: Introductionmentioning

confidence: 99%

Bifurcation, sensitivity, and optimal control analysis of onchocerciasis disease transmission model with two groups of infectives and saturated treatment function

Ogunmiloro

Idowu

2022

Math Methods in App Sciences

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A model depicting the transmission of onchocerciasis disease in human host community with two distinct groups of infected humans exhibiting low and high microfilariae (mf) output with saturated treatment function is developed and analyzed. The model equilibrium solutions are obtained, and it is found that the model exhibits forward bifurcation and the effective basic reproduction number governing the spread of the disease is computed by the use of the next generation matrix method. The sensitivity results of model parameters reveal that the rates describing the recruitment of humans, blackflies, onchocerciasis disease transmission, and the biting rate of blackflies are positively sensitive to , which necessitate the need for controls to be implemented in order to curtail the infectious contact between humans and blackflies in the host environment. To this effect, the model is further transformed into an optimal control problem by applying control strategies of personal protection of using treated bednets and wearing of permethrin‐treated cloths , surgical care for humans with body deformation and impaired vision , education campaign , and the use of insecticide , respectively. The existence and uniqueness of the optimal control model are established, and the Pontryagin maximum principle (PMP) is employed to characterize the controls. The optimal control model is solved using the Runge–Kutta numerical scheme via MATLAB, and the simulations under different control combinations show that each of the controls have its own effect in minimizing onchocerciasis transmission, but the combined effects of the four control strategies proved to be more beneficial towards the elimination of the disease in human and blackfly host community. Also, the simulations of the control profiles reveal that each of these controls are sustained at maximum until 3 months before gradually declining to zero in terminal time of 12 months.

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“…The study of DHF associated with changes in temperature and rainfall was done by [2], [3]. The consider of DFH related with control variables was carried out by [11], [12], [13], [14], [15]. All of these studies use mathematical models and take case studies in a particular place.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model of Dengue Control With Control of Mosquito Larvae and Mosquito Affected by Climate Change

Wartono

Soleh

Muda

2021

BAREKENG: J. Il. Mat. & Ter.

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Consider a SIR model for the spread of dengue hemorrhagic fever involving three populations, mosquito eggs, mosquitoes, and humans. The parameters of the SIR model were estimated using rainfall data and air temperature for the cities of Pekanbaru and Solok. The main aim of this paper is to determine the effect of mosquito larvae and adult mosquito control on the spread of the dengue virus. Numerical solutions were also presented by using the Runge-Kutta method of order 4. Based on the results, the SIR model was obtained by involving the control parameters of mosquito larvae and adult mosquitoes. Besides, the mosquito population is affected by changes in temperature, rainfall, and fog. Numerical simulations illustrate that the number of infected mosquitoes and infected humans is influenced by the parameters of the percentage of mortality of mosquito larvae and adult mosquitoes.

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Numerical optimal control applied to an epidemiological model

Cited by 5 publications

References 6 publications

Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation

Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation

Bifurcation, sensitivity, and optimal control analysis of onchocerciasis disease transmission model with two groups of infectives and saturated treatment function

Mathematical Model of Dengue Control With Control of Mosquito Larvae and Mosquito Affected by Climate Change

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