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Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever
Issue:
Volume 7, Issue 2, April 2019
Pages:
37-48
Received:
13 April 2019
Accepted:
28 May 2019
Published:
26 June 2019
Abstract: The author developed a deterministic mathematical model for Typhoid fever disease dynamics that accounts for Vaccination and relapse of treatment. Three control strategies (vaccination, treatment of infection, screening and treatment of carriers) are applied to investigate the optimal intervention strategy of controlling Typhoid disease transmission. The aim of this study is to determine the optimal combination strategy of vaccination, treatment of infection, screening and treatment of carriers that will minimize the cost of those strategies and the number of Infective and Carriers. The author used Pontryagin’s maximum principle to characterize the optimal level of those three strategies. The result is simulated numerically using Runge-Kutta fourth order method through MATLAB software. Numerical results showed that implementation of all controls or a combination of vaccination, treatment of invectives as well as screening and treatment of carriers is the best strategy to eradicate the disease at an optimal level with minimum cost of interventions.
Abstract: The author developed a deterministic mathematical model for Typhoid fever disease dynamics that accounts for Vaccination and relapse of treatment. Three control strategies (vaccination, treatment of infection, screening and treatment of carriers) are applied to investigate the optimal intervention strategy of controlling Typhoid disease transmissio...
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Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method
Ayrin Aktar,
Md Mashiur Rahhman,
Kamalesh Chandra Roy
Issue:
Volume 7, Issue 2, April 2019
Pages:
49-57
Received:
21 April 2019
Accepted:
13 June 2019
Published:
27 June 2019
Abstract: This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.
Abstract: This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. ...
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Strong Matching Preclusion for Augmented Butterfly Networks
Jinyu Zou,
Yan Sun,
Chengfu Ye
Issue:
Volume 7, Issue 2, April 2019
Pages:
58-62
Received:
24 May 2019
Accepted:
27 June 2019
Published:
9 July 2019
Abstract: The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. The strong matching preclusion number (or simply, SMP number) smp(G) of a graph G is the minimum number of vertices and/or edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem and has been introduced by Park and Ihm. Butterfly Networks are interconnection networks which form the back bone of distributed memory parallel architecture. One of the current interests of researchers is Butterfly graphs, because they are studied as a topology of parallel machine architecture. Butterfly network has many weaknesses. It is non-Hamiltonian, not pancyclic and its toughness is less than one. But augmented butterfly network retains most of the favorable properties of the butterfly network. In this paper, we determine the strong matching preclusion number of the Augmented Butterfly networks.
Abstract: The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. The strong matching preclusion number (or simply, SMP number) smp(G) of a graph G is the minimum number of vertices and/or edges whose deletion results in a graph that has neithe...
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Mathematical Models of the Effect of Colloidal Surfactants on the Strength of Alkaline Concrete
Аlexander Shishkin,
Alexandra Shishkina
Issue:
Volume 7, Issue 2, April 2019
Pages:
63-69
Received:
14 June 2019
Accepted:
5 July 2019
Published:
17 July 2019
Abstract: Under certain conditions, an increase in the rate of hydration of the binding substance increases the strength of concrete at compression. This is especially true for the reactive powder concretes. We studied the effect of surface-active substances, capable of forming micelles, on the rate of formation and the resulting magnitude of strength at compression of the alkaline reactive powder concretes. A particular feature of our research was studying the simultaneous action of surface-active substance that forms micelles and a reactive powder or a filler on the change in the strength of concretes. It was found that the specified micellar solutions and reaction powders change the character of formation of strength of the alkaline reactive powder concretes. The rate of strength formation over the early stages increases due to the micellar catalysis of hydration of blast-furnace granular slag, while their enhanced compressive strength is maintained at the late stages of hardening. Strength of the alkaline reactive powder concretes, when applying the surface-active substances that form micelles, reaches 260% of the strength of such concretes without any additives. It was proved that the micellar catalysis could be used to control the hardening processes of a binding substance, consisting of blast-furnace granular slag and an alkaline component, and to form the strength of the resulting artificial stone. That shortens the time required for concrete to achieve the designed strength and improves the absolute magnitude of the compressive strength of such concretes at the age of 28 days.
Abstract: Under certain conditions, an increase in the rate of hydration of the binding substance increases the strength of concrete at compression. This is especially true for the reactive powder concretes. We studied the effect of surface-active substances, capable of forming micelles, on the rate of formation and the resulting magnitude of strength at com...
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