The role of prostitution on HIV transmission with memory: A modeling approach

Naik, Parvaiz Ahmad; Yavuz, Mehmet; Zu, Jian

doi:10.1016/j.aej.2020.04.016

Cited by 78 publications

(45 citation statements)

References 42 publications

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“…An immediate sequel of the present work might cast equation (9a) in an explicit form by using curve fitting to experimental data [58][59][60]. Another direction of research is to apply Dimensional Analysis in epidemiological studies that mainly involve differential equations [61][62][63][64][65] and to the transmission or spread of pathogenic viruses (other than the present coronavirus one) such as the human immunodeficiency virus (HIV) [66], influenza virus [67], dengue virus [68], hepatitis C virus [69], Zika virus [70] and yellow fever virus [71]. Other interesting areas of research involve the comparison of the spread of pathogenic viruses and computer viruses [72][73][74] and supporting pathogenic research with other engineering tools such as the Karnaugh map [75] and probabilistic methods [76][77][78][79][80][81] Table 4 lists Equations (A4) in a dimensional-matrix form and then applies Gauss-Jordan elimination by performing elementary row operations to produce a 3 by 3 unit matrix under the symbols , and .…”

Section: Discussionmentioning

confidence: 99%

Modeling Coronavirus Spread Rate Utilizing Dimensional Analysis via an Irredundant Set of Fundamental Quantities

Rushdi

2020

IJPR

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The phenomenon of spread of a (pathogenic) virus involves many physical variables, and is not amenable to satisfactory analysis via conventional methods. Dimensional Analysis (DA) is singled out as a simple and accessible way that can determine (at least qualitatively) how virus spread is related to seven physical quantities that are thought to influence it. However, classical DA deduces four dimensionless products only, none of which incorporates temperature and humidity, despite the obvious relevance of these two meteorological factors. This paper proposes an alternative version of dimensional analysis using a novel irredundant set of three fundamental quantities only. This new DA version produces five dimensionless products, four of which are essentially a replication of the old ones, while the fifth is a novel product that relates both humidity and temperature to other influencing factors. Our novel DA solution is a significant contribution, since it provides a more realistic model for virus spread rate, and it does not ignore any of the essential influencing factors. Such a model might lead to a better understanding of the determinants of spread for the novel coronavirus SARS-CoV-2 that causes the ongoing COVID-19 fatal pandemic.

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Section: Discussionmentioning

confidence: 99%

Modeling Coronavirus Spread Rate Utilizing Dimensional Analysis via an Irredundant Set of Fundamental Quantities

Rushdi

2020

IJPR

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“…We conclude from the results of Equations (18) and (19) that the iterative process used is stable. The predictor corrector Adams Bashforth-Moulton method is now available for a system solution based on an equal (10) in References [40][41][42][43][44][45].…”

Section: Liouville-caputo Sensementioning

confidence: 99%

Modeling and numerical investigation of fractional‐order bovine babesiosis disease

Ahmad

Farman

Naik

et al. 2020

Numerical Methods Partial

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In this paper, analysis and modeling of bovine babesiosis disease are designed with fractional calculus. The solution for a bovine babesiosis disease and tick populations fractional order system is determined using the Caputo and Atangana-Baleanu-Caputo (ABC) fractional derivatives. Applying the homotopy analysis method and the Laplace transform with polynomial homotopy, the analytical solution of the bovine babesiosis disease has obtained. Furthermore, using an iterative scheme by the Laplace transform, and the Atangana-Baleanu fractional integral, special solutions of the model are obtained. Uniqueness and existence of the solutions by the fixed-point theorem and Picard-Lindel of approach are studied. Numerical simulation has been established for both Caputo and ABC fractional derivative of the proposed system is carried out. The numeric replications for diverse consequences are carried out, and data attained are in good agreement with theoretical outcomes, displaying a vital perception about the use of the set of fractional coupled differential equations to model babesiosis disease and tick populations.

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“…There are many variants of the SEIR and SIR models found in the literature [20] , [21] , [22] , [23] , [24] . Many other models and solutions based on differential equations are presented in recent literature [25] , [26] , [27] , [28] , [29] , [30] . Some of the authors also considered isolation and quarantine to reduce the spread of disease [31] , [32] , [33] .…”

Section: Introductionmentioning

confidence: 99%

A novel mathematical model for COVID-19 with remedial strategies

Javeed¹,

Anjum²,

Alimgeer³

et al. 2021

Results in Physics

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Coronavirus (COVID-19) outbreak from Wuhan, Hubei province in China and spread out all over the World. In this work, a new mathematical model is proposed. The model consists the system of ODEs. The developed model describes the transmission pathways by employing non constant transmission rates with respect to the conditions of environment and epidemiology. There are many mathematical models purposed by many scientists. In this model, “ and “ , transmission coefficients of the exposed cases to susceptible and infectious cases to susceptible respectively, are included. “ as a governmental action and restriction against the spread of coronavirus is also introduced. The RK method of order four (RK4) is employed to solve the model equations. The results are presented for four countries i.e., Pakistan, Italy, Japan, and Spain etc. The parametric study is also performed to validate the proposed model.

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The role of prostitution on HIV transmission with memory: A modeling approach

Cited by 78 publications

References 42 publications

Modeling Coronavirus Spread Rate Utilizing Dimensional Analysis via an Irredundant Set of Fundamental Quantities

Modeling Coronavirus Spread Rate Utilizing Dimensional Analysis via an Irredundant Set of Fundamental Quantities

Modeling and numerical investigation of fractional‐order bovine babesiosis disease

A novel mathematical model for COVID-19 with remedial strategies

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