A SIQRB delayed model for cholera and optimal control treatment

Lemos-Paião, Ana P.; Maurer, Helmut; Silva, Cristiana J.; Torres, Delfim F. M.

doi:10.1051/mmnp/2022027

Cited by 6 publications

(6 citation statements)

References 37 publications

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“…On the other hand, a cluster of bacteria, 𝐵 𝑎 (𝑡), is also considered, reflecting the bacteria concentration at time-𝑡. The initial conditions and parameters used in the SIQRB model can be shown in Table 1 [2], [3]. This study proposes optimal control, namely a treatment for infected individuals by cholera through quarantine and water sanitation, into the dynamic cholera model.…”

Section: Mathematical Model Formulation Of Choleramentioning

confidence: 99%

“…where 𝑢 1 (𝑡) is the treatment for cholera-infected individuals through quarantine, with 0 ≤ 𝑢 1 (𝑡) ≤ 1 [2], and 𝑢 2 (𝑡) is water sanitation, with 0 ≤ 𝑢 2 (𝑡) ≤ 0.1 [24]. Equation ( 1) is a dynamical system of cholera spreading model modified from [2], [3] by considering water sanitation as the additional optimal control strategy.…”

Section: Mathematical Model Formulation Of Choleramentioning

confidence: 99%

“…In this simulation, the parameters used can be seen in Table 1. To compare the simulation results on individuals infected by cholera and the concentration of bacteria with and without control, the sub-model from Equation (1) can be written as follows [2], [3]: where the sub-model is an interpretation of the cholera mathematical model without optimal control and quarantine which assumes that 𝜔 = 𝛿 = 𝜀 = 𝛾 2 = 𝑄 𝑢 (0) = 𝑅 𝑒 (0) = 0. A comparison of submodel simulations, optimal control strategy with treatment (𝑢 1 ) and optimal control strategy with treatment (𝑢 1 ) and water sanitation (𝑢 2 ) can be seen in Figure 2.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…Individuals who are susceptible to infection can become infected individuals if they come into contact with these individuals. Individuals at an elevated risk for infection can transmit the disease to others who cohabitate with them via storage containers for food and water [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

“…The complex problem for analyzing cholera outbreaks discussing stochastic model, age-structured cholera transmission, and choleraschistosomiasis coinfection can be observed in [21][22][23]. In a previous study [2], [3], a SIQRB (Susceptible-Infectious-Quarantined-Recovered-Bacterium) model was proposed, in which it was assumed that infected individuals were quarantined during the treatment period, while research conducted by Posny et al, 2015 [24] where the optimal control strategy used is water sanitation with the SVIRB (Susceptible-Vaccinated-Infectious-Recovered-Bacterium) type model modified from [25].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Optimal Control with Treatment and Water Sanitation for Cholera Epidemic Model

Purnawan

Faroh

Wahyudi

et al. 2023

EKSAKTA

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This paper proposes a mathematical model for cholera using optimal control of treatment through quarantine and water sanitation. Cholera is acute diarrhoea caused by Vibrio cholera bacteria infecting the intestinal tract. The analysis related to the spread of this disease is carried out through a mathematical approach. The constructed mathematical model is demonstrated epidemiologically. The proposed optimal control is the treatment of infected individuals during the quarantine period and sanitation, namely environmental hygiene, especially water. This strategy aims to suppress the number of infected individuals and reduce the concentration of bacteria due to cholera disease. To solve the optimal control problem, we employ the 4th-order forward-backward Runge-Kutta method. Based on the simulation results, the number of individuals infected by cholera and the concentration of bacteria decreased significantly. Moreover, the proposed method can transfer infected to recovered individuals faster than an optimal control treatment.

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Section: Mathematical Model Formulation Of Choleramentioning

confidence: 99%

Section: Mathematical Model Formulation Of Choleramentioning

confidence: 99%

Section: Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal Control with Treatment and Water Sanitation for Cholera Epidemic Model

Purnawan

Faroh

Wahyudi

et al. 2023

EKSAKTA

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Mathematical modeling of cholera dynamics with intrinsic growth considering constant interventions

Brhane,

Ahmad,

Hina

et al. 2024

Sci Rep

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A mathematical model that describes the dynamics of bacterium vibrio cholera within a fixed population considering intrinsic bacteria growth, therapeutic treatment, sanitation and vaccination rates is developed. The developed mathematical model is validated against real cholera data. A sensitivity analysis of some of the model parameters is also conducted. The intervention rates are found to be very important parameters in reducing the values of the basic reproduction number. The existence and stability of equilibrium solutions to the mathematical model are also carried out using analytical methods. The effect of some model parameters on the stability of equilibrium solutions, number of infected individuals, number of susceptible individuals and bacteria density is rigorously analyzed. One very important finding of this research work is that keeping the vaccination rate fixed and varying the treatment and sanitation rates provide a rapid decline of infection. The fourth order Runge–Kutta numerical scheme is implemented in MATLAB to generate the numerical solutions.

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Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise

Ain,

Din,

Qiang

et al. 2024

Fractal Fract

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In this study, we develop a comprehensive mathematical model to analyze the dynamics of epidemic cholera, characterized by acute diarrhea due to pathogen overabundance in the human body. The model is first developed from a deterministic point of view, and then it is modified to include the randomness by stochastic differential equations. The study selected Lévy noise above other well-known types of noise, emphasizing its importance in epidemic modeling. Besides presenting a biological justification for the stochastic system, we demonstrate that the equivalent deterministic model exhibits possible equilibria. The introduction is followed by theoretical analysis of the model. Through rigorous analysis, we establish that the stochastic model ensures a unique global solution. Lyapunov function theory is applied to construct necessary conditions, which on average, guarantee the model’s stability for R0s>1. Our findings suggest the likelihood of eradicating the disease when Rs is below one, a significant insight supported by graphical simulations of the model. Graphical illustrations were generated from simulating the model in order to increase the analytical results’ robustness. This work provides a strong theoretical framework for a thorough comprehension of a range of such diseases. This research not only provides a deeper understanding of cholera dynamics but also offers a robust theoretical framework applicable to a range of similar diseases, alongside a novel approach for constructing Lyapunov functions for nonlinear models with random disturbances.

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A SIQRB delayed model for cholera and optimal control treatment

Cited by 6 publications

References 37 publications

Optimal Control with Treatment and Water Sanitation for Cholera Epidemic Model

Optimal Control with Treatment and Water Sanitation for Cholera Epidemic Model

Mathematical modeling of cholera dynamics with intrinsic growth considering constant interventions

Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise

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