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Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies
Issue:
Volume 9, Issue 6, December 2020
Pages:
101-108
Received:
29 January 2020
Accepted:
9 March 2020
Published:
11 November 2020
Abstract: This paper proposes and analyses a basic deterministic mathematical model to investigate Simulation for controlling the spread of malaria Diseases Transmission dynamics. The model has seven non-linear differential equations which describe the control of malaria with two state variables for mosquito’s populations and five state variables for human’s population. To represent the classification of human population we have included protection and treatment compartments to the basic SIR epidemic model and extended it to SPITR model and to introduce the new SPITR modified model by adding vaccination for the transmission dynamics of malaria with four time dependent control measures in Ethiopia Insecticide treated bed nets (ITNS), Treatments, Indoor Residual Spray (IRs) and Intermittent preventive treatment of malaria in pregnancy (IPTP). The models are analyzed qualitatively to determine criteria for control of a malaria transmission dynamics and are used to calculate the basic reproduction R0. The equilibria of malaria models are determined. In addition to having a disease-free equilibrium, which is globally asymptotically stable when the R0<1, the basic malaria model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists (at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The results also designing the effects of some model parameters, the infection rate and biting rate. The numerical analysis and numerical simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of malaria were suggest using insecticide treated bed nets, indoor residual spraying, prompt effective diagnosis and treatment of infected individuals with vaccination is more effective for children.
Abstract: This paper proposes and analyses a basic deterministic mathematical model to investigate Simulation for controlling the spread of malaria Diseases Transmission dynamics. The model has seven non-linear differential equations which describe the control of malaria with two state variables for mosquito’s populations and five state variables for human’s...
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The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study
Molalegn Ayana,
Tsige Hailegiorgis,
Kassahun Getnet
Issue:
Volume 9, Issue 6, December 2020
Pages:
109-117
Received:
23 August 2020
Accepted:
18 September 2020
Published:
23 November 2020
Abstract: The COVID−19 pandemic is considered as the biggest global threat worldwide because of millions of confirmed infections, accompanied by hundred thousand deaths over the world. WHO is working with its networks of researchers and other experts to coordinate global work on surveillance, epidemiology, modeling, diagnostics, clinical care and treatment, and other ways to identify, manage the disease and limit onward transmission. Mathematical modeling has become an important tool in analyzing the epidemiological characteristics of infectious diseases. The present study describes the transmission pathways in the infection dynamics, and emphasizes the role of exposed (probably asymptomatic infected) and infected immigrants and the impact of self isolation techniques in the transmission and spread of covid−19 with no home to home check up to develop a mathematical model and show the impact of infected immigrants and self isolation on the dynamics and spread of covid-19. In our model we study the epidemic patterns of Covid−19, from a mathematical modeling perspective. The present model is developed making some reasonable modifications in the corresponding epidemic SCR model by considering symptomatic and asymptomatic infective immigrants as well as self isolation measures. Our numerical results indicate that the corona virus infection would remain pandemic, unless the responsible body takes Self isolation measure and intervention programs and introducing home to home check up of covid−19 to reduce the transmission of the disease from asymptomatic infected (exposed) individual to the susceptible individual. Among the model parameters the exposed and infected self isolation rate and exposed (probably asymptomatic infected) immigration rate are very sensitive parameters for the spread of the virus. Disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if R0<1, and unstable if it is R0>1. Simulation study is conducted using MATLAB ode45.
Abstract: The COVID−19 pandemic is considered as the biggest global threat worldwide because of millions of confirmed infections, accompanied by hundred thousand deaths over the world. WHO is working with its networks of researchers and other experts to coordinate global work on surveillance, epidemiology, modeling, diagnostics, clinical care and treatment, ...
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The Least-Energy Sign-Changing Solutions for Planar Schrödinger-Newton System with an Exponential Critical Growth
Wenbo Wang,
Wei Zhang,
Yongkun Li
Issue:
Volume 9, Issue 6, December 2020
Pages:
118-123
Received:
8 February 2020
Accepted:
8 September 2020
Published:
4 December 2020
Abstract: In 1990, the notion of critical growth in ℝ2 was introduced by Adimurthi and Yadava. Soon afterwards, de Figueiredo, Miyagaki and Ruf also studied the solvability of elliptic equations in dimension two. They treated the problems in the subcritical and the critical case. In 2019, Alves and Figueieredo proved the existence of a positive solution for a planar Schrodinger-Poisson system, where the nonlinearity is a continuous function with exponent critical growth. Also, in 2020, Chen and Tang investigated the planar Schrodinger-Poisson system with the critical growth nonlinearity. Under the axially symmetric assumptions, they obtained infinitely many pairs solutions and ground states. In this work, motivated by the works mentioned above and Z. Angew. Math. Phys., 66 (2015) 3267-3282, Z. Angew. Math. Phys., 67 (2016) 102, 18, we study the planar Schrödinger-Newton system with a Coulomb potential where the nonlinearity f is autonomous nonlinearity which belongs to C1 and satisfies super-linear at zero and exponential critical at infinity. Moreover, we need that f satisfies the Nehari type monotonic condition. We obtain a least-energy sign-changing solution via the variational method. To be more precise, we define the sign-changing Nehari manifold. And the least-energy sign-changing solution is obtained by minimizing the energy functional on the sign-changing Nehari manifold.
Abstract: In 1990, the notion of critical growth in ℝ2 was introduced by Adimurthi and Yadava. Soon afterwards, de Figueiredo, Miyagaki and Ruf also studied the solvability of elliptic equations in dimension two. They treated the problems in the subcritical and the critical case. In 2019, Alves and Figueieredo proved the existence of a positive solution for ...
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Annotations on the Relationship Among Discriminant Functions
Issue:
Volume 9, Issue 6, December 2020
Pages:
124-128
Received:
19 June 2020
Accepted:
20 July 2020
Published:
16 December 2020
Abstract: Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Ever since the emergence of the Linear Discriminant Function (LDF) by Fisher, several other classification statistics have emerged and violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). While the Best Linear Discriminant Function (BLDF) is referred to Best Sample Discriminant Function (BSDF) when the parameters are estimated from a sample and also optimal in the same sense as Quadratic Discriminant Function (QDF), Rao statistic is best for discriminating between options that are close each other. The relationships among the classification statistics examined were established: Among the methods of classification statistics considered, Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes n1 and n2 are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification.
Abstract: Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the origi...
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