to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Chaotic Krill Herd algorithm

This study proposes a novel chaotic cuckoo search (CCS) optimization method by incorporating chaotic theory into cuckoo search (CS) algorithm. In CCS, chaos characteristics are combined with the CS with the intention of further enhancing its performance. Further, the elitism scheme is incorporated into CCS to preserve the best cuckoos. In CCS method, 12 chaotic maps are applied to tune the step size of the cuckoos used in the original CS method. Twenty-seven benchmark functions and an engineering case are utilized to investigate the efficiency of CCS. The results clearly demonstrate that the performance of CCS together with a suitable chaotic map is comparable as well as superior to that of the CS and other metaheuristic algorithms.

Chaotic cuckoo search

Coronaviruses are a large family of viruses that cause different symptoms, from mild cold to severe respiratory distress, and they can be seen in different types of animals such as camels, cattle, cats and bats. Novel coronavirus called COVID-19 is a newly emerged virus that appeared in many countries of the world, but the actual source of the virus is not yet known. The outbreak has caused pandemic with 26,622,706 confirmed infections and 874,708 reported deaths worldwide till August 31, 2020, with 17,717,911 recovered cases. Currently, there exist no vaccines officially approved for the prevention or management of the disease, but alternative drugs meant for HIV, HBV, malaria and some other flus are used to treat this virus. In the present paper, a fractional-order epidemic model with two different operators called the classical Caputo operator and the Atangana–Baleanu–Caputo operator for the transmission of COVID-19 epidemic is proposed and analyzed. The reproduction number $${{\mathcal {R}}}_0$$
 is obtained for the prediction and persistence of the disease. The dynamic behavior of the equilibria is studied by using fractional Routh–Hurwitz stability criterion and fractional La Salle invariant principle. Special attention is given to the global dynamics of the equilibria. Moreover, the fitting of parameters through least squares curve fitting technique is performed, and the average absolute relative error between COVID-19 actual cases and the model’s solution for the infectious class is tried to be reduced and the best fitted values of the relevant parameters are achieved. The numerical solution of the proposed COVID-19 fractional-order model under the Caputo operator is obtained by using generalized Adams–Bashforth–Moulton method, whereas for the Atangana–Baleanu–Caputo operator, we have used a new numerical scheme. Also, the treatment compartment is included in the population which determines the impact of alternative drugs applied for treating the infected individuals. Furthermore, numerical simulations of the model and their graphical presentations are performed to visualize the effectiveness of our theoretical results and to monitor the effect of arbitrary-order derivative.

/pdf/modeling-and-analysis-of-covid-19-epidemics-with-treatment-1ns0dd8na3.pdf

Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan

https://www.tandfonline.com/doi/pdf/10.1080/16583655.2020.1741943

Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations

In this paper, we establish exact solutions for complex nonlinear equations. The He's semi-inverse and the (G^'G)-expansion methods are used to construct exact solutions of these equations. We apply He's semi-inverse method to establish a variational theory for the coupled Higgs equation and Maccari system. Based on this formulation, a solitary solution can be easily obtained using the Ritz method. The (G^'G)-expansion method is used to seek more general exact solutions of the coupled Higgs equation and the Maccari system. As a result, hyperbolic function solutions, trigonometric function solutions and rational function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions are also derived from the traveling wave solutions. Moreover, it is observed that the suggested technique is compatible with the physical nature of such problems.

Exact solutions of the coupled Higgs equation and the Maccari system using He's semi-inverse method and (G'G)-expansion method

Exponential synchronization of chaotic system and application in secure communication

Stability analysis of a fractional order model for the HIV/AIDS epidemic in a patchy environment

In this paper, we present a general formulation for a fractional optimal control problem (FOCP), in which the state and co-state equations are given in terms of the left fractional derivatives. We ...

Optimal control of a fractional-order model for the HIV/AIDS epidemic

In this paper, we present a fractional model for transmission dynamics of HIV/AIDS with random testing and contact tracing and incorporate into the model the control parameters of condom use and antiretroviral therapy (ART) aimed at controlling the spread of HIV/AIDS epidemic. The stability of equilibria of the model is discussed using the stability theorem and using the fractional La-Salle invariance principle for fractional differential equations. The effect of the fractional derivative order $$\alpha $$
 (
 $$ 0.6\le \alpha <1 $$
 ) on the HIV/AIDS epidemic model is investigated. The numerical results show that the derivative order $$\alpha $$
 can play the role of precautionary measures against infection transmission, treatment of infection and delay in accepting HIV test. We give a general formulation for a fractional optimal control problem, in which the state and co-state equations are given in terms of the left fractional derivatives. We develop the Forward–Backward sweep method using the Adams-type predictor–corrector method to solve the fractional optimal control of the model. The results show that implementing the ART treatment control of diagnosed HIV-infected people together with contact tracing results in a significant decrease in the number of undiagnosed HIV-infected population and AIDS people. Also, implementing all the control efforts decreases significantly the number of diagnosed and undiagnosed HIV-infected population and AIDS people. In addition, the values of the controls are reduced when the fractional derivative order $$\alpha $$
 limits to 1 (
 $$ 0< \alpha < 1$$
 ).

Hossein Kheiri

Papers

Exact solutions of the coupled Higgs equation and the Maccari system using He's semi-inverse method and (G'G)-expansion method

Exponential synchronization of chaotic system and application in secure communication

Stability analysis of a fractional order model for the HIV/AIDS epidemic in a patchy environment

Optimal control of a fractional-order model for the HIV/AIDS epidemic

Fractional optimal control of an HIV/AIDS epidemic model with random testing and contact tracing