Department of Mathematics

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Analysis of the model on the effect of seasonal factors on malaria transmission dynamics
(Hindawi Journal of Applied Mathematics, 202-08) Yiga, Victor; Nampala, Hasifa; Tumwiine, Julius
Malaria is one of the world’s most prevalent epidemics. Current control and eradication efforts are being frustrated by rapid changes in climatic factors such as temperature and rainfall. This study is aimed at assessing the impact of temperature and rainfall abundance on the intensity of malaria transmission. A human host-mosquito vector deterministic model which incorporates temperature and rainfall dependent parameters is formulated. The model is analysed for steady states and their stability. The basic reproduction number is obtained using the next-generation method. It was established that the mosquito population depends on a threshold value θ, defined as the number of mosquitoes produced by a female Anopheles mosquito throughout its lifetime, which is governed by temperature and rainfall. The conditions for the stability of the equilibrium points are investigated, and it is shown that there exists a unique endemic equilibrium which is locally and globally asymptotically stable whenever the basic reproduction number exceeds unity. Numerical simulations show that both temperature and rainfall affect the transmission dynamics of malaria; however, temperature has more influence.
Calculation algorithm for electromagnetic wave processes in multi-wire intersystem ETL
(Discover Electronics, 2024-06-10) Rashad, Huseyn; Arif, Hashimov; Ali, Shokri; Herbert, Mukalazi
The nature of the transient process and the magnitude of the overvoltages are determined by a large number of factors in the HV/EHV AC transmission networks. The paper presents the study of mathematical modelling of electromagnetic wave processes in long-distance electric transmission line (ETL). The mathematical model is based on electromagnetic processes occurring on distributed parameter lines that are characterized by specific derivatives of the system of differential equations. The application of a spline-interpolation technique enables the calculation of currents and voltages at the nodes of the scheme, which obtains the unknown coordinates of the overhead line mode at the beginning of the ETL to solve the transmission line equation. The following results are derived from computer simulations of transients during switching on. With a simulation model, the importance of intelligent control of shunt reactor (SR) and ungrounded reactor (UR) was demonstrated and considered for a 500 kV power networks.
Community perceptions and practices towards waste management and effects on water quality in landing sites along lake Albert: a case of Kitebere landing site, Kagadi district
(Kyambogo University, 2021-02) Opio, Stephen
This study sought to find out Kitebere residents‘ perceptions and practices towards waste management (WM) and investigates the effects of the practices on water quality. To achieve this aim, the study‘s main objective was to assess community perceptions and practices towards waste management and its effects on water quality in Kitebere landing site. The descriptive survey design and cross sectional research design was used with quantitative and qualitative research approaches. These were administered to the households to collect information about perceptions, waste management practices, wastes generated and attitudes, or behaviours. Focus group guides were used to collect data from both women and men. Two gendered FGDs were held among fishermen, fish mongers and boat owners. Information regarding waste collection and disposal practices in the market area and general community were collected. Semi structured questions were administered to key informants including District departments, local councils, health inspectors, traders and area councilors. Key data that were collected included existence of Environment Awareness (EA). Transect walks or guided community walks were conducted with the guide of the area councilor. The purpose of the transect walks was to observe waste management practices and types of wastes generated. Additionally, a handheld camera was used to capture the status of open defecation, waste in the drainage channels, makeshift toilets and urinals draining directly into the lake. The GPS was also used to capture locations of dumpsites, toilets and urinals including their distance from the open water. Secondary data from archival sources, books, articles, reports, internet, newspapers, journals among others were reviewed. The data reviewed was related to environmental health, public health and waste management in communities in regards to their perceptions and practices. A total of 95 participants participated in the study. Systematic and purposive sampling was used to select participants. Interview schedule was used to collect data from 95 residents and the interview guide was used to collect data from the district and sub county representatives. Observation guides and transect walk methods were used to ascertain some responses from participants. Data collected were analysed using Statistical Package for the Social Sciences (SPSS), excel and descriptive statistics were used to analyse the raw data.
Couple-stress nanofluid flow comprised of titanium alloy subject to Hall current and Joule heating effects: Numerical investigation
(AIP Advances, 2024-11-01) Jubair, Sidra; Ali, Bilal; Rafique, Khadija; Ansari, Mushtaq Ahmad; Mahmood, Zafar; Kumar, Abhinav; Mukalazi, Herbert; Alqahtani, Haifa
Nanofluid flowoverarotating disk has several applications in engineering and industrial sectors, such as in cooling systems, heat exchangers, aerospace systems, and renewable energy systems. In the current analysis, the couple stress nanofluid flow over a rotating disk is reported. The nanofluid consists of ethylene glycol and titanium aluminum vanadium (Ti6Al4V) nanoparticles (NPs). The unique properties of Ti6Al4V-NPs, such as biocompatibility, high strength, high boiling point (1604–1660○C), and high corrosion resistance, make them more suitable for automobile industries. For the heat and mass transfer, the Cattaneo–Christov concept is introduced. In addition, the fluid flow is subjected to magnetic field, Hall current, thermal radiation, and Joule heating. The modeled equations are restructured into the dimensionless system of ordinary differential equations (ODEs) by using the similarity approach. The system of ODEs is further numerically solved through a MATLABpackagebased on the finite difference method (BVP4c). The results are presented in figures. It has been observed that the energy and curves of the nanofluid decline with the influence of thermal and solutal time relaxation parameters, respectively.
Didactical Situation of Learning Integer Material based on Local Culture to Support Student Numeracy Literacy
(Jurnal Iqra, 2024-06-25) Yohanis, Ndapa Deda; Hermina, Disnawati; Otaget, Daniel; Suhendra; Darhim
Didactically oriented research that considers the relationship between teachers, students and materials was vital. This research aimed to obtain an overview of the didactical situation in the learning process of whole number concepts as a basis for designing appropriate learning designs based on local culture for junior high school students in North Central Timor. The research method followed the stages of Didactical Design Research (DDR). The research instruments were observation sheets, interview guidelines, and documentation. Data analysis included prospective analysis, observation data, and post-observation data. The results revealed that student preparedness for learning posed a barrier to the otherwise smooth operation of instructor, student, and material interactions. Learning the concept of mixed operations of whole numbers was successful in terms of learning objectives achieved and learning that took place according to plan. The research concluded that the existence of the Topaze Effect and the Aging of Teaching Situations when learning whole number operations in the classroom. Didactical situated research contributes to define the scope and substance of didactics, focusing on the shared values and knowledge that underpin effective numbers instruction. Keywords: Didactical Situation, Integers, Local Culture, Numeracy Literacy
Exact solutions for the Cahn–Hilliard equation in terms of Weierstrass‑elliptic and Jacobi‑elliptic functions
(Scientific Reports, 2024-05) Akhtar, Hussain; Tarek, F. Ibrahim; Osman, Birkea F. M.; Abeer, M. Alotaibi; Bushra, R. Al‑Sinan; Herbert, Mukalazi
Despite the historical position of the F‑expansion method as a method for acquiring exact solutions to nonlinear partial differential equations (PDEs), this study highlights its superiority over alternative auxiliary equation methods. The efficacy of this method is demonstrated through its application to solve the convective–diffusive Cahn–Hilliard (cdCH) equation, describing the dynamic of the separation phase for ternary iron alloys (Fe–Cr–Mo) and (Fe–X–Cu). Significantly, this research introduces an extensive collection of exact solutions by the auxiliary equation, comprising fifty‑ two distinct types. Six of these are associated with Weierstrass‑elliptic function solutions, while the remaining solutions are expressed in Jacobi‑elliptic functions. I think it is important to emphasize that, exercising caution regarding the statement of the term ’new,’ the solutions presented in this context are not entirely unprecedented. The paper examines numerous examples to substantiate this perspective. Furthermore, the study broadens its scope to include soliton‑like and trigonometric‑ function solutions as special cases. This underscores that the antecedently obtained outcomes through the recently specific cases encompassed within the more comprehensive scope of the present findings.
A mathematical model for harvesting in a stage-structured cannibalistic system
(SpringerLink, 2022) Nankinga, Loy; Carlsson, Linus
To increase the production of proteins in East Africa, aquaculture gained increased attention recently. In this paper, we study the interactions of a consumer-resource system with harvesting, in which African Catfish (Glarias gariepinus) consume a food resource. The cannibalistic behavior of African Catfish is captured by using a four stage-structured system. The dynamics of food resource and African Catfish result in a system of ordinary differential equations called a stage-structured fish population model. Existence and stability of steady states are analyzed quantitatively. We have investigated eight different harvesting scenarios which account for yield of the fish stock. Results from the simulations revealed that harvesting large juveniles and small adults under equal harvesting rates gives the highest maximum sustainable yield compared to other harvesting scenarios. In contrast to non-cannibalistic models, we find an increase of the proportion of the adult individuals under harvesting.
Mathematical Modelling of Tuberculosis and Hepatitis C Coinfection Dynamics with No Intervention
(Journal of Mathematics, 2024-05) Kizito, Mohammed; Nampala, Hasifa; Ariho, Pius
In this study, a deterministic tuberculosis (TB)-hepatitis C (HCV) coinfection mathematical model with no intervention is analysed purposely to examine the dynamics of TB-HCV coinfection so as to find conditions for reducing the transmission of both TB and HCV. A unique solution to the model exists; it is positive and is bounded. The analytical and numerical analysis show that for basic reproduction number, R0 = max{RT, RH} < 1, the TB and HCV disease-free equilibrium points are stable. Further analysis shows that when the TB-HCV coinfection basic reproduction number is greater than 1, the endemic equilibrium point is stable. Sensitivity analysis reveals that interventions to reduce TB or HCV infection need to aim and concentrate on minimizing the numbers of the effective contact rate with TB- or HCV-infected humans and the rate of progress from latent TB or acute HCV to infectious TB or chronic HCV stage. Numerical simulations reveal that over time, the number of TB latent humans, acute HCV humans, and the number of dually infected humans have a linear relationship with the effective contact and the progression rates for both TB- and HCV-infected humans. We recommend that health education campaigns to communities aimed at reducing the transmission rates of TB and HCV be conducted. These could include screening and isolation, wearing of face masks for TB cases and screening, sterilization of surgical instruments, and use of condoms for HCV-infected humans.
Parametrized multiplicative integral inequalities
(Advances in Continuous and Discrete Models, 2024-04) Herbert, Mukalazi; Abdelghani, Lakhdari; Ali, Shokri; Meftah, Badreddine; Assia, Frioui
In this paper, we introduce a biparametrized multiplicative integral identity and employ it to establish a collection of inequalities for multiplicatively convex mappings. These inequalities encompass several novel findings and refinements of established results. To enhance readers’ comprehension, we offer illustrative examples that highlight appropriate choices of multiplicatively convex mappings along with graphical representations.
Science teacher shortage and the moonlighting culture: the pathology of the teacher labour market in Uganda
(International Journal of Educational Development., 2014-05) Urwick, James; Kisa, Sarah
The Ugandan Government promotes the rapid expansion of secondary education and requires an emphasis on mathematics and science subjects at that level, but has a “market” approach to the recruitment of teachers. This study uses both national and local evidence to demonstrate that, not only are the teachers of these subjects too few for the policies to be effective, but many of them are employed in more than one school, and some in other work. This “moonlighting” trend, which contributes to problems of poor service, is seen as part of a questionable tendency to commercialise teaching. Policy changes and practical steps are suggested in order to regulate and reduce moonlighting.
Stability analysis of a malaria transmission model for the effect of infected immigrants with temperature and rainfall dependent parameters
(International Journal of Mathematical Modelling & Computations, 2022) Yiga, V.; Nampala, H.; Tumwiine, J.
A human host-mosquito vector model for transmission of malaria with inflow of infected immigrants is formulated. The mosquito population includes aquatic stages (eggs, larvae, and pupae) and mature stages which have highly temperature and rainfall dependent life cycles. Model analysis reveals that the model only attains two (2) endemic equilibria; one in absence of the vector population and the other in presence of the vector population. The endemic equilibrium without the mosquito vector population is unstable. The endemic equilibrium with the vector population is locally stable and globally unstable. Numerical simulations of the model reveal that the proportion of infected humans introduced into the community does not significantly change the pattern of malaria transmission.
Stability analysis of a nonlinear malaria transmission epidemic model using an effective numerical scheme
(Scientific Reports, 2024-07-29) Jian, Jun He; Abeer, Aljohani; Shahbaz, Mustafa; Ali, Shokri; Khalsaraei, Mohammad Mehdizadeh; Mukalazi, Herbert
Malaria is a fever condition that results from Plasmodium parasites, which are transferred to humans by the attacks of infected female Anopheles mosquitos. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. More so, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The reproduction number R (o) was determined to be an asymptotically stable condition for disease free and endemic equilibria. In this paper, we used various schemes such as Runge–Kutta order 4 (RK-4) and non-standard finite difference (NSFD). All of the schemes produce different results, but the most appropriate scheme is NSFD. This is true for all step sizes. Various criteria are used in the NSFD scheme to assess the local and global stability of disease-free and endemic equilibrium points. The Routh–Hurwitz condition is used to validate the local stability and Lyapunov stability theorem is used to prove the global asymptotic stability. Global asymptotic stability is proven for the disease-free equilibrium when R0 ≤ 1. The endemic equilibrium is investigated for stability when R0 ≥ 1. All of the aforementioned schemes and their effects are also numerically demonstrated. The comparative analysis demonstrates that NSFD is superior in every way for the analysis of deterministic epidemic models. The theoretical effects and numerical simulations provided in this text may be used to predict the spread of infectious diseases.
A stage-structured fishery model for African catfish and Nile Tilapia feeding on two food resources with harvesting
(Journal of Applied Mathematics : Hindawi, 2022-01-17) Nankinga, L.; Luboobi, L. S.; Mugisha, J. Y. T.; Nannyonga, B.; Carlsson, L.
In this paper, a fishery model for African catfish and Nile tilapia is formulated. This model is used to compare financial profit and biomass outtakes in a two-species system versus single species systems. We consider a stage-structured fish population model consisting of the aforementioned fish species together with two food resources. The model dynamics include cannibalism, predator-prey, feeding, reproduction, maturation, development, mortality, and harvesting. We prove consistency of the model in the sense that the solutions will stay bounded and nonnegative over time. Conditions for local stability of fish-free equilibrium point are established. The simulation results reveal asymptotically stable solutions with coexistence of African catfish, Nile tilapia, and two food resources. The major conclusion from our findings is that fisheries should culture both species to maximize the biomass outtake and financial profit.

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