Mathematical Modelling and Applications最新文献_第2页

Modelling Transmission of Buruli Ulcer in the Central Region of Ghana 模拟布鲁里溃疡在加纳中部地区的传播

Mathematical Modelling and Applications Pub Date : 2020-12-31 DOI: 10.11648/J.MMA.20200504.13

N. Cynthia, Nyarko Peter Kwesi, Ampofi Isaac, Asante Emmanuel

{"title":"Modelling Transmission of Buruli Ulcer in the Central Region of Ghana","authors":"N. Cynthia, Nyarko Peter Kwesi, Ampofi Isaac, Asante Emmanuel","doi":"10.11648/J.MMA.20200504.13","DOIUrl":"https://doi.org/10.11648/J.MMA.20200504.13","url":null,"abstract":"The pathogen of Buruli Ulcer (BU) is known to be Mycobacterium Ulcerans whose mode of transmission is entirely not known, although the disease is recognised to be associated with contaminated water. The hypothesised transmission involves humans being bitten by the water bugs (vector) that prey on mollusks, snails and young ﬁshes. The hypothesised transmission also involves humans feeding on an infected fish or frog. This study seeks to contribute to the dynamics and analyses of the transmission mechanism of Buruli Ulcer in communities along Offin River in the Central Region of Ghana. The model equilibria were determined and conditions for the equilibria were also established. The basic reproduction number, was derived using the Next Generation approach and its estimated value was 1.20771. The result reveals that, is greater than 1, indicating a horizontal spread of the infection across the population. The transmission dynamics of Buruli Ulcer model of the Susceptible, Infected and Recovered (SIR) type also show that the disease will continue to spread at the study areas as long as the reservoir for Mycobacterium Ulcerans continue to sustain enough infected water bugs and infected fish or infected frog to contain the disease. The study further concludes that, the rate of spread of Buruli Ulcer in the affected communities continue to be high due to its mode of transmission. This study suggest that adequate control measures including mass education and prompt treatment to curb the spread should be emphasized.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123241938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Optimization of Parking Lot in the Forms of Parallelogram and Right Triangle for Cars and Motorbikes 汽车、摩托车平行四边形与直角三角形停车场优化设计

Mathematical Modelling and Applications Pub Date : 2019-12-30 DOI: 10.11648/J.MMA.20190404.12

Widiawati Putri, Ihda Hasbiyati, M. Gamal

{"title":"Optimization of Parking Lot in the Forms of Parallelogram and Right Triangle for Cars and Motorbikes","authors":"Widiawati Putri, Ihda Hasbiyati, M. Gamal","doi":"10.11648/J.MMA.20190404.12","DOIUrl":"https://doi.org/10.11648/J.MMA.20190404.12","url":null,"abstract":"Parking lots are elements that affect the transportation system. Placement of the wrong parking lot, such as on a roadside, causes congestion. One way to overcome this is to provide safe and efficient parking. This article discusses the optimization of parking lots in the form of parallelograms and right triangles for cars and motorbikes. The shape of the parallelogram land is formed in two ways namely directly and separately, the landform separately consists of the form of two right triangles and rectangles. The initial step in this discussion is to make a design on the parking lot and assumptions that correspond to the shape of the land. The design of parking lots in this article consists of three designs, namely land in the form of parallelograms, right triangles and rectangles. Furthermore, a mathematical model was built for each land design. The method used for the calculation of mathematical models for each design is the linear programming method and is calculated using LINGO software. The results obtained are the optimum number of car and motorbikes vehicles for each land design. In this article, the optimal results for car vehicles with land in the form of parallelograms formed directly are 1110 vehicles, furthermore the form of parallelograms formed separately are 1295 vehicles. These results indicate that the two forms are more optimal than the separated forms. Then, for the form of a right triangle gives optimal results 491 car vehicles. The next vehicle is a motorbikes, the optimal result for motorbikes with land in the form of a parallelogram that is formed directly is 11969 vehicles, then the shape of the parallelogram is formed separately there are 15440 vehicles. Then, to form a right triangle give optimal results 6163 motorbikes vehicles.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131651723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model 同伦分析法在求解SEIRS流行病模型中的应用

Mathematical Modelling and Applications Pub Date : 2019-09-03 DOI: 10.11648/J.MMA.20190403.11

Inyama Simeon Chioma, Ekeamadi Godsgift Ugonna, Uwagboe Osazee Michael, O. Andrew, Mbachu Hope Ifeyinwa, Uwakwe Joy Ijeoma

引用次数: 3

Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics 人口动态中避孕作为控制策略的影响建模

Mathematical Modelling and Applications Pub Date : 2019-08-16 DOI: 10.11648/J.MMA.20190402.12

K. Wesley, R. Titus

{"title":"Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics","authors":"K. Wesley, R. Titus","doi":"10.11648/J.MMA.20190402.12","DOIUrl":"https://doi.org/10.11648/J.MMA.20190402.12","url":null,"abstract":"The population size of every country or government is very important in planning on effective service delivery. The cost of conducting population census yearly is of great significance to the country’s budget and many countries conduct population census once in a decade. This makes planning and provision of services to be based on mere approximation. Provision of free maternity services, estimation of national hospital insurance fund premium for medical care, and provision of retirement benefits, payment of allowances to the aged require accurate demographic statistics. In this study, population dynamics is described using a stochastic model, where population is put into distinct and disjoint age classes: Juvenile, sub-Adult, Adult, Resting-Adult, Senior Citizens and the Aged. These structures are assigned intra and inter group transmission rates which form the elements of transmission matrix and presented in form of a Leslie model. The model was modified to allow stochastic variation of transition parameters which is affected by demographic and environmental factors, specifically the effect of contraceptives to control population. It was found that intermittent implementation of control strategy at 50% and 70% efficacy yields a steady population growth rate of λ=1.39 and a steady population distribution of P=(23%, 10%, 23%, 18%, 23%, 20%, 6%)T.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116249145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modelling the Effects of Immune Response and Time Delay on HIV-1 in Vivo Dynamics in the Presence of Chemotherapy 化疗存在下免疫反应和时间延迟对HIV-1体内动力学的影响建模

Mathematical Modelling and Applications Pub Date : 2019-07-22 DOI: 10.11648/J.MMA.20190402.11

Cherono Pela, K. Wesley, Adicka Daniel

{"title":"Modelling the Effects of Immune Response and Time Delay on HIV-1 in Vivo Dynamics in the Presence of Chemotherapy","authors":"Cherono Pela, K. Wesley, Adicka Daniel","doi":"10.11648/J.MMA.20190402.11","DOIUrl":"https://doi.org/10.11648/J.MMA.20190402.11","url":null,"abstract":"Numerous models of mathematics have existed to pronounce the immunological response to contagion by human immunodeficiency virus (HIV-1). The models have been used to envisage the regression of HIV-1 in vitro and in vivo dynamics. Ordinarily the studies have been on the interface of HIV virions, CD4+T-cells and Antiretroviral (ARV). In this study, time delay, chemotherapy and role of CD8+T-cells is considered in the HIV-1 in-vivo dynamics. The delay is used to account for the latent time that elapses between exposure of a host cell to HIV-1 and the production of contagious virus from the host cell. This is the period needed to cause HIV-1 to replicate within the host cell in adequate number to become transmittable. Chemotherapy is by use of combination of Reverse transcriptase inhibitor and Protease inhibitor. CD8+T-cells is innate immune response. The model has six variables: Healthy CD4+T-cells, Sick CD4+T-cells, Infectious virus, Non-infectious virus, used CD8+T-cells and unused CD8+T-cells. Positivity and boundedness of the solutions to the model equations is proved. In addition, Reproduction number (R0) is derived from Next Generation Matrix approach. The stability of disease free equilibrium is checked by use of linearization of the model equation. We show that the Disease Free Equilibrium is locally stable if and only if R0 0, Disease Free Equilibrium is stable when τ =0.67. This stability is only achieved if drug efficacy is administered. The results show that when drug efficacy of α1=0.723 and α2=0.723 the DFE is achieved.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127118433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Stability and Bifurcation Analysis of a Fishery Model with Allee Effects 具有狭缝效应的渔业模型的稳定性与分岔分析

Mathematical Modelling and Applications Pub Date : 2019-05-20 DOI: 10.11648/J.MMA.20190401.11

Makwata Harun, L. George, A. Colleta, Adu A. M. Wasike

{"title":"Stability and Bifurcation Analysis of a Fishery Model with Allee Effects","authors":"Makwata Harun, L. George, A. Colleta, Adu A. M. Wasike","doi":"10.11648/J.MMA.20190401.11","DOIUrl":"https://doi.org/10.11648/J.MMA.20190401.11","url":null,"abstract":"We study the equilibrium point (n*, E*) of the fishery model with Allee effect in its population growth dynamics. The Allee effect is considered to be induced by the harvesting of the fish stock. The aggregated model is a set of two differential equations with the fish population and harvesting effort as the dependent variables, with the market price having been taken to evolve faster hence the aggregation from a three dimensional system to a two dimensional system. The analysis of the equilibrium point is performed by looking at three cases in which the threshold population is set at three different values; , and . Three different equilibrium solutions are obtained: A stable equilibrium, coexistence of three equilibria points with two being saddles and the other stable and the co-existence of three equilibria points with two being stable and a saddle between them. The equilibrium solutions depicts three kinds of fishery: A fishery with fish population maintained at high levels far from extinction but with little economic activity, a fishery with co-existence of an over-exploited and an under-exploited state, which is a dilemma since neither of the state supports sustainable fish resource exploitation, and a fishery that is well managed with fish population being harvested in a sustainable manner thus a balance between commercial harvesting and species existence.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129071402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Novel Method for Solving Balance and Unbalance Assignment Problem Using New Approach for Ant Colony Algorithm 利用蚁群算法求解平衡与不平衡分配问题的新方法

Mathematical Modelling and Applications Pub Date : 1900-01-01 DOI: 10.11648/j.mma.20210604.13

Ekanayake E. M. U. S. B.

引用次数: 2

Inequity in Education: Three-factor and Longitudinal Analysis 教育不公平:三因素和纵向分析

Mathematical Modelling and Applications Pub Date : 1900-01-01 DOI: 10.11648/j.mma.20210604.14

Man-Young Jin

引用次数: 0

Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments 基于正交阵列的拉丁超立方体计算机实验设计

Mathematical Modelling and Applications Pub Date : 1900-01-01 DOI: 10.11648/j.mma.20210604.12

Kazeem Adewale Osuolale

引用次数: 0