scholarly journals Optimal control problem arises from illegal poaching of southern white rhino mathematical model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dipo Aldila ◽  
Nadhira Azizah ◽  
Bevina D. Handari

Abstract In this paper, a novel dynamical population model of a southern white rhino with legal and illegal poaching activity is introduced. The model constructed is based on a predator–prey model with southern white rhinos as prey and humans (hunters) as predators. We divide the southern white rhino population into three classes based on their horn condition. We investigate the existence and the stability of the equilibrium points, which depend on some threshold functions. From an analytical result, it is trivial that arresting as many hunters as possible helps conserve white rhinos, but it comes at a high cost. Therefore, an optimal strategy is needed. The optimal control is then constructed using Pontryagin’s minimum principle and solved numerically with an iterative forward–backward method. Optimal control simulations are given to provide additional insight into the dynamics of the model. Analysis of the cost function effectiveness is conducted using the ACER (Average Cost–Effectiveness Ratio) and ICER (Incremental Cost–Effectiveness Ratio) indicator method. The results show that the hunter population can be more easily controlled with a time-dependent hunter arrest rate rather than by treating it as a constant.

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Stephen Edward ◽  
Nyimvua Shaban ◽  
Eunice Mureithi

In this paper, we apply optimal control theory to the model for shigellosis. It is assumed that education campaign, sanitation, and treatment are the main controls for this disease. The aim is to minimize the number of infections resulting from contact with careers, infectious population, and contaminated environments while keeping the cost of associated controls minimum. We achieve this aim through the application of Pontryagin’s Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth-order Runge-Kutta schemes. We simulate the model under different strategies to investigate which option could yield the best results. The findings show that the strategy combining all three control efforts (treatment, sanitation, and education campaign) proves to be more beneficial in containing shigellosis than the rest. On the other hand, cost-effectiveness analysis is performed via incremental cost-effectiveness ratio (ICER). The findings from the ICER show that a strategy incorporating all three controls (treatment, sanitation, and education campaign) is the most cost-effective of all strategies considered in the study.


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Cristiana J. Silva

<p style='text-indent:20px;'>In this paper, we propose a time-delayed HIV/AIDS-PrEP model which takes into account the delay on pre-exposure prophylaxis (PrEP) distribution and adherence by uninfected persons that are in high risk of HIV infection, and analyze the impact of this delay on the number of individuals with HIV infection. We prove the existence and stability of two equilibrium points, for any positive time delay. After, an optimal control problem with state and control delays is proposed and analyzed, where the aim is to find the optimal strategy for PrEP implementation that minimizes the number of individuals with HIV infection, with minimal costs. Different scenarios are studied, for which the solutions derived from the Minimum Principle for Multiple Delayed Optimal Control Problems change depending on the values of the time delays and the weights constants associated with the number of HIV infected individuals and PrEP. We observe that changes on the weights constants can lead to a passage from <i>bang-singular-bang</i> to <i>bang-bang</i> extremal controls.</p>


2020 ◽  
Vol 6 (1) ◽  
pp. 37-42
Author(s):  
Gulirano Khodjieva ◽  

This article is devoted to pharmacoeconomics and patients’ compliance to the therapy of iron deficiency anemia. These directions are relatively young in science and their importance often remains underestimated by most specialists. Pharmacoeconomics’ main goal is to determine the most optimal medicine for treating the disease’s cost-effectiveness ratio.


Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 785
Author(s):  
Hasan S. Panigoro ◽  
Agus Suryanto ◽  
Wuryansari Muharini Kusumawinahyu ◽  
Isnani Darti

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig–MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with power-law kernel) and the Atangana–Baleanu fractional derivative in the Caputo (ABC) sense (operator with Mittag–Leffler kernel). We take the same order of the fractional derivative in all equations for both senses to maintain the symmetry aspect. The existence and uniqueness of solutions of both eco-epidemic models (i.e., in the Caputo sense and in ABC sense) are established. Both models have the same equilibrium points, namely the trivial (origin) equilibrium point, the extinction of infected prey and predator point, the infected prey free point, the predator-free point and the co-existence point. For a model in the Caputo sense, we also show the non-negativity and boundedness of solution, perform the local and global stability analysis and establish the conditions for the existence of Hopf bifurcation. It is found that the trivial equilibrium point is a saddle point while other equilibrium points are conditionally asymptotically stable. The numerical simulations show that the solutions of the model in the Caputo sense strongly agree with analytical results. Furthermore, it is indicated numerically that the model in the ABC sense has quite similar dynamics as the model in the Caputo sense. The essential difference between the two models is the convergence rate to reach the stable equilibrium point. When a Hopf bifurcation occurs, the bifurcation points and the diameter of the limit cycles of both models are different. Moreover, we also observe a bistability phenomenon which disappears via Hopf bifurcation.


Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 566
Author(s):  
Julio Emilio Marco-Franco ◽  
Pedro Pita-Barros ◽  
Silvia González-de-Julián ◽  
Iryna Sabat ◽  
David Vivas-Consuelo

When exceptional situations, such as the COVID-19 pandemic, arise and reliable data is not available at decision-making times, estimation using mathematical models can provide a reasonable reckoning for health planning. We present a simplified model (static but with two-time references) for estimating the cost-effectiveness of the COVID-19 vaccine. A simplified model provides a quick assessment of the upper bound of cost-effectiveness, as we illustrate with data from Spain, and allows for easy comparisons between countries. It may also provide useful comparisons among different vaccines at the marketplace, from the perspective of the buyer. From the analysis of this information, key epidemiological figures, and costs of the disease for Spain have been estimated, based on mortality. The fatality rate is robust data that can alternatively be obtained from death registers, funeral homes, cemeteries, and crematoria. Our model estimates the incremental cost-effectiveness ratio (ICER) to be 5132 € (4926–5276) as of 17 February 2021, based on the following assumptions/inputs: An estimated cost of 30 euros per dose (plus transport, storing, and administration), two doses per person, efficacy of 70% and coverage of 70% of the population. Even considering the possibility of some bias, this simplified model provides confirmation that vaccination against COVID-19 is highly cost-effective.


Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 336
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko

This article presents a study devoted to the emerging method of synthesized optimal control. This is a new type of control based on changing the position of a stable equilibrium point. The object stabilization system forces the object to move towards the equilibrium point, and by changing its position over time, it is possible to bring the object to the desired terminal state with the optimal value of the quality criterion. The implementation of such control requires the construction of two control contours. The first contour ensures the stability of the control object relative to some point in the state space. Methods of symbolic regression are applied for numerical synthesis of a stabilization system. The second contour provides optimal control of the stable equilibrium point position. The present paper provides a study of various approaches to find the optimal location of equilibrium points. A new problem statement with the search of function for optimal location of the equilibrium points in the second stage of the synthesized optimal control approach is formulated. Symbolic regression methods of solving the stated problem are discussed. In the presented numerical example, a piece-wise linear function is applied to approximate the location of equilibrium points.


2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.


Analysis ◽  
2020 ◽  
Vol 40 (3) ◽  
pp. 127-150
Author(s):  
Tania Biswas ◽  
Sheetal Dharmatti ◽  
Manil T. Mohan

AbstractIn this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary conditions of optimality via the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.


2019 ◽  
Vol 40 (Supplement_1) ◽  
Author(s):  
J King ◽  
S Bhat ◽  
L J Heath ◽  
C G Derington ◽  
Z Yu ◽  
...  

Abstract Background Direct oral anticoagulants (DOACs) are at least as effective as low-molecular weight heparins (LMWH) at preventing recurrence after cancer-associated venous thromboembolism (CA-VTE). DOACs are also oral and far less costly, but they may confer a higher bleeding risk than LMWH. Purpose To estimate the cost-effectiveness of DOACs and LMWHs for CA-VTE. Methods We developed a health state transition model to estimate recurrent VTE, bleeding events, quality-adjusted life years (QALY), and direct healthcare costs (2018 United States dollars) associated with DOACs vs. LMWH use. The model had four states: (1) long-term anticoagulation (first 3 months after VTE), (2) extended anticoagulation (more than 3 months after VTE), (3) off anticoagulants, and (4) death. We used a United States healthcare sector perspective, 3-month cycle length, and 1-year time horizon. Event probabilities were derived from the Hokusai Cancer VTE trial and other literature. Event and medication costs were obtained from national sources. We used a threshold of less than $50,000 per QALY gained to define cost-effectiveness. Results Compared to LMWH, DOACs were less costly (mean costs: $8,477 vs. $33,917 per year) and similarly effective (mean QALY: 0.616 vs. 0.622). The incremental cost-effectiveness ratio was $4,479,374 per QALY gained with LMWH, indicating that DOACs are cost-effective (Table 1). In threshold analyses, LMWH therapy only became cost-effective when DOAC recurrent VTE risk increased to at least 72% (relative risk vs. LMWH, 6.19) or DOAC clinically relevant bleeding increased to at least 39% (relative risk vs. LMWH, 10.09). Scenarios Recurrent VTE, % Major bleed, % Mean difference DOAC − LMW ICER DOAC LMWH Relative Risk DOAC LMWH Relative Risk Cost QALY Base case 8.1 11.6 0.71 6.8 4.0 1.75 −$25,440 (−26,496, −24,274) −0.006 (−0.019, 0.008) $4,479,374 DOAC outcome rate threshold at which LMWH becomes cost-effective*   Recurrent VTE 71.5 11.7 6.19 – – – −$6,064 (−7,534, −4,627) −0.121 (−0.136, −0.108) $49,886   Major Bleed – – – 38.9 4.0 10.09 −$2,192 (−3,400, −704) −0.044 (−0.056, −0.030) $49,878 DOAC = direct oral anticoagulant, ICER = incremental cost-effectiveness ratio, LMWH = low-molecular-weight heparin, VTE = venous thromboembolism. Values are mean (95% Uncertainty Interval). Uncertainty was derived from 1,000 stochastic model iterations. *Represents the minimum increased risk with DOAC that would result in LMWH achieving an ICER <$50K per QALY gained. Conclusion In this simulation study, DOACs were a cost-effective oral alternative to LMWH for the treatment of CA-VTE. For LMWH to be cost-effective, DOAC event rates needed to be far higher than what is likely to be observed in clinical practice. Acknowledgement/Funding Agency for Health Research and Quality R18HS026156


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