In this paper, optimal control for a novel West Nile virus (WNV) model of fractional order derivative is presented. The proposed model is governed by a system of fractional differential equations (FDEs), where the fractional derivative is defined in the Caputo sense. An optimal control problem is formulated and studied theoretically using the Pontryagin maximum principle. Two numerical methods are used to study the fractional-order optimal control problem. The methods are, the iterative optimal control method (OCM) and the generalized Euler method (GEM). Positivity, boundedness and convergence of the IOCM are studied. Comparative studies between the proposed methods are implemented, it is found that the IOCM is better than the GEM.

In this paper, an optimal control for a novel fractional West Nile virus model with time delay is presented. The proposed model is governed by a system of fractional delay differential equations, where the fractional derivative is defined in the Grünwald-Letnikov sense. Stability analysis of fixed points is studied. Corresponding fractional optimal control problem, with time delays in both state and control variables, is formulated and studied. Two simple numerical methods are used to study the nonlinear fractional delay optimal control problem. The methods are standard finite difference method and nonstandard finite difference method. Comparative studies are implemented, it is found that the nonstandard finite difference method is better than the standard finite difference method.

No abstract

Objectives: This review article highlights the problem of an example of a drug that is used to control Hypertension (HTN). HTN: that is one of eight mortalities worldwide. Approximately one-third of the world's adult population suffers from hypertension (31.1 %, or 1.39 billion people). Hypertension prevalence varies. The World health organization (WHO) Region of Americans has the lowest prevalence of hypertension (18%) and the WHO African Region has the highest prevalence of hypertension (27%) overall. In Egypt, according to WHO, Egypt estimated the number of adult people suffering from hypertension in 2017 was (29.2%) and in 2020, the total percentage of death from hypertension (was 3.93%) of total death. Hypertension is described as a disturbance in the circulatory system accompanied by a sustained increase in systolic and diastolic blood pressure to a level that is likely to have negative effects. The most popular hypertension types in people are first and second hypertension which need to adjust the lifestyle and take medications when these types are not controlled. Several types of medications can be used to control HTN such as Diuretics, Angiotensin-converting enzymes inhibitors (ACEIs), Angiotensin receptor blockers (ARBs) calcium channel blockers (CCBs), and beta-blockers (BBs). All of them can be used individually or in combination with each other to control blood pressure. Beta-blockers (BBs) are one of these drugs that are used for HTN, classified as (first, second, and thirdgeneration). carvedilol (CAR) is one of the most popular drugs used in the third generation. It has additional advantages rather than first and second-generation that α1 -adrenergic receptors antagonist. CAR belongs to BBs but has some drawbacks such as low solubility, low bioavailability, and hepatic metabolism that makes it need to be taken several times a day. Methods: This review contains several articles on CAR nanocarriers application between 2014 to 2022, reviewed by many accepted scientific journals. Results: by application of several approaches of a nanocarrier delivery systems that were used to overcome CAR drawbacks, nano drug delivery can encapsulate CAR lipophilic drug in their core, deliver it to the site of action, sustain CAR release, and enhance the solubility and the bioavailability of this lipophilic drug. Conclusion:This review summarized all recent works that attempt to improve the solubility and the bioavailability of CAR. after the application of several nanocarriers approaches to overcome the drawbacks of CAR, each of these approaches can increase the solubility and the bioavailability of CAR but all of these nanocarriers need many challenges to be applied to be applicable in the market.