NSUK Repository :: Browsing by Author "Umar, Mallam Abdulkarim"

Browsing by Author "Umar, Mallam Abdulkarim"

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Open Access
Age-Structured Transmission Dynamics Model for Vertical and Horizontal Transmission of HIV/AIDS
(Department of Mathematics, Nasarawa State University Keffi, 2008-01-06) Umar, Mallam Abdulkarim; Olowofeso, E.O.; Ademiluyi, R.A.
Transmission dynamics model for -HlV/AlDS, along the line of Mckendrick-Forester age-structured model is proposed with the natural mortality rate and the fertility functions assumed to bE age depended, similar, to Doma, Gurlin-MacCnmy definitions. The solution^ to the governing equations are obtained and the steady stales are examined for their local stability. The model is further extended to study the case of constant mortality . rate and an exponential type of interaction function. It is observed that the endemic steady'.exist, and. .. asymptotically stable.
Open Access
Age-Structures Epidemic Model for Transmission Dynamics of Tuberculosis
(Department of Mathematics, Nasarawa State University Keffi, 2007-02-02) Umar, Mallam Abdulkarim
Open Access
A Comparative Study of Box-Jenkins, Arima, Holt-Winter and Exponential Smoothing Models as Applied to Exchange Rate on Naira to Dollar
(Department of Mathematics, Nasarawa State University Keffi, 2005-01-06) Umar, Mallam Abdulkarim
Open Access
The Dynamics of Natural Mortality, Life Expectancy and TB in an Structured Population.
(Department of Mathematics, Nasarawa State University Keffi, 2008-01-09) Umar, Mallam Abdulkarim
We have extended live classical Mckcndriok-Focrstcr age structured population model to study the olicet ol population area size on the transmission dynamics of tuberculosis in an ngo*otniciurccl population, in wliicli infective recovers, nfior irontmontond bocomo suscoptiblo again when in contact with Die disease. The natural mortality rate J3 assumed density mid nren size depended, wiUi the population assumed lo be in propoi tionm.0 mixing. Wo defined n niodol in which tlie area sizes and the total population influences the rale at. which death by nature in 1110 population. This model is extended to study Iho influence the area size of the population has on the natural mortality rate, life expectancy of the population and the transmission dynamics oT the infection. The analytical solutions of the governing equations arc obtained. The existence of the non trivial a toady .states in oxnminod with their local and global .stability.
Open Access
Effect of Vaccination, Treatment and Population Area Size on the Transmission Dynamics of Bird-Flu Epidemics in a Proportiona,
(Department of Mathematics, Nasarawa State University Keffi, 2007-01-06) Umar, Mallam Abdulkarim
We have examined the effect of vaccination, nnrl population nren size on the transmission dynamics oT bird flu epidemics in a poultry farm, using two class of models, an age -structured epidemic model and n homogeneous epidemics model in which the transmission rate in the ease of homogeneous model, is assumed not age-depended, while it is assumed age-dependent in the agc-struclurcd model. The per capital contact rate and the vital rates arc assumed not age depended. It is observed in both eases, that llic area size occupied by the population influences the rate of transmission of the virus. Wild birds, which arc normally on free range, arc observed to be responsible for the spread of the virus to poultry farms; however the transmission rate may be less than in poultry birds, due to their free range nature. This is not investigated this work. This is assumed to has helped to control the concentration of the wild birds population density in n particular location, where they arc found, and less per cnpilnl contact rale. Thus, the disease spread is minimal. Threshold parameters for both models arc examined to determine the stability of the non -trivial steady stales.
Open Access
Effect of Vaccination, Treatment and Population Area Size on the Transmission Dynamics of Tuberculosis in a Proportionate Mixing Population
(Department of Mathematics, Nasarawa State University Keffi, 2007-01-06) Umar, Mallam Abdulkarim
Open Access
Effects of minimum epidemic and population sizes on a global epidemic in simulations of final size data
(Department of Mathematics, Nasarawa State University Keffi, 2020-08-08) Umar, Mallam Abdulkarim; Ndakwo, Husseini S.
The stochastic SIR household epidemic model is well discussed in [2], [3] and [4]. The work of [1] • also proposed maximum likelihood based algori hm for its inference by assuming independence of epidemic in each household, contrary to the dependency assn uption in [4]. 8 ° * Using simulations, we examined the ne id for an appropriate choice of cut-off between small and large epidemics often referred to as minimum epidemic size, using rejection sampling, for a global infection to occur and then compared the estimates of the model parameters over a range of theoretical parameters, XL and Xc with corresponding z 6 [0,1]. We found that with large population size, appropriate choice of the minimum epidemic size and Xc =£ 0 facilitate the occurrence of a global epidemic. Thus, given these scenarios, the adequacy of the model fitness to the final size epidemic data is then realised.
Open Access
A Global Stability Analysis of a Susceptible-Infected-Removed-Prevented-Controlled Epidemic Model
(Department of Mathematics, Nasarawa State University Keffi, 2014-03-06) Muhammad, Yau A.; Ndakwo, Husseini S.; Umar, Mallam Abdulkarim
A mathematical model off HIV transmission dynamics Is proposed and analysed. The population is partitioned into five compartments of susceptible 5(C),Infected I{£), Removed rtp), .Prevented* t/(C) and the Controlled W(t). Each of the compartments comprises of cohort of individuals. Five sys tems of nonlinear equations are derived to represent each of the compartments. The general bility of the disease free equilibrium (DFE) and the endemic equilibrium states of the linearized model are established using the linear stability analysis (Routh-Hurwitz) method which is found to be locally asymptotically stable when the Infected individuals receive ART and use the condom. The reproduction number is also derived using the idea of Diekmann and is found to be strictly less than one. This means that the epidemic will die out.
Open Access
Influence of Environmental Pollution on the Transmission Dynamics of Infections
(Department of Mathematics, Nasarawa State University Keffi, 2014-01-06) Umar, Mallam Abdulkarim
Open Access
Mathematical Model for Vertical Transmission of HIV/AIDS, in a Homogeneous Mixing Population
(Department of Mathematics, Nasarawa State University Keffi, 2007-03-03) Umar, Mallam Abdulkarim; Ndakwo, Husseini S.
Open Access
Mathematical prototype for the control of malaria by interrupting the life cycle of the Anopheles mosquito through the use of biological enemies in the larva, pupa and adult stages
(Department of Mathematics, Nasarawa State University Keffi, 2023-01-19) Emmanuel, Atanyi Yusuf; Oduwole, H.K.; Umar, Mallam Abdulkarim
Mathematical prototype to fight malaria by interrupting the life cycle of the Anopheles mosquito through the use of biological enemies in the larval, pupal and adult stages has been derived to eradicate larvae, pupae and adult Anopheles mosquitoes using natural predators. The new model is a control flowchart of the predator-prey interaction model in the mosquito life cycle, considering an open population of mosquitoes and predators. These models provide a osolid understanding of malaria control in our environment, especially when models are based on vector population ecology; and a solid understanding of transmission-relevant parameters and variables Model equations were derived using parameters and variables from the model Stability analysis of free equilibrium states was analyzed simultaneously using equilibrium point, Maple software, elimination and substitution methods. The number of larvae that pupate is almost zero, and the number ofp upae that turn into adults is minimal, and the number of adults that'escape to the vector stage is negligible, which means that thd life cycle could be disrupted at larval, pupal and adult stages with the introduction of natural enemies, with the natural implication 'there will be no adult Anopheles mosquito for transmission of the malaria. The contribution of this research to knowledge is to produce the model or the mathematical formula and the biologically sound methods that will contribute to the eradication of the adult Anopheles mosquito, which will also lead to° the eradication of malaria in our society.
Open Access
MODELING THE DYNAMICS OFT4-CELLS COUNTS IN AN HIV-INFECTED INDIVIDUAL
(Department of Mathematics, Nasarawa State University Keffi, 2011-11-11) Umar, Mallam Abdulkarim; Ndakwo, Husseini S.
In this work, w e examined, the stages of HIV progression to AI DS and proposed .a stochastic model of • the number of T 4 - cells counts in an HIV infected person. Tlie mean number of 14 - cells in each disease, phase is obtained and the conditions for a stable level of CD +4 — lymphoc^'te cells in an infected host are suggested. TIic need for antiretroviral therapies to sustain this level is emphasized.
Open Access
Modeling Vaccination and Treatment of HTV/AIDS Epidemics in an Age-Structured Population A
(Department of Mathematics, Nasarawa State University Keffi, 2011-10-10) Umar, Mallam Abdulkarim
We proposed a deterministic age- structured vaccination and treatment model of HIV and AIDS, along the line oflvlcCamy - Foester age-structured population model, with structured population. compartments and-class dependent Activity level (interaction functions), per-capital force of infection, natural mortality rate and disease • induced death rate . The models equations Are reduced to ordinary differential equations. Their, steady state solutions are obtained and examined for local stability. The, disease-free state is found to be stable if vaccination and removal rates are simultaneously maximized. This will lend to a corresponding decrease in the size of HIV infected individuals and the number of infected cases progressing to AIDS.
Open Access
Modelling the Effects of Three Natural Predators on the Aquactic and Adult Stages of Anopheles Mosquitoes in the Control of Malaria Transmission
(Department of Mathematics, Nasarawa State University Keffi, 2023-01-16) Emmanuel, Atanyi Yusuf; Oduwole, H.K.; Umar, Mallam Abdulkarim
Modelling the effects of three natural predators on the aquatic and adult anopheles’ mosquitoes in the control of malaria transmission was derived aimed’at "eradicating anopheles’ larva, pupa and adult anopheles' mosquito by introduction of natural predators ucopepods, tadpoles and purple martins” so that there should not be anopheles ’ adult mosquito for malaria transmission in our society. The new model is a control flow diagram of predator-prey interaction model in mosquito life-cycle. The population is sub-divided based on mosquito life- cycle and natural predators. Under a mosquito life-cycle, the population is divided into four compartments', * Egg compartment E(t), Larva compartment L(t), Pupa compartment P(t), and Adult compartment A(t), and natural predators, it is divided into three compartments’, namely; Copepods CP(t), Tadpoles TP(t) and Purple martins PM (t). From the stability analysis of steady state we observed that the model free equilibrium state is stable, implies that the equilibrium point or steady state is stable and the stability of the model (1) - (10) means, there will not be anopheles adult mosquito ip our society for malaria transmission and from the idea of Beltrami’s conditions and Diekmann condition, we observed that the Determinant of the Jacobian matrix is greater than zero {Det(J) > 0}, Trace of the Jacobian matrix is less than zero {Tr(j) < 0} and R0 < 1 which implies that the model disease free equilibrium state is stable. Hence the number of larva that transform to pupa ♦ is almost zero and the number of pupa that develop to adult is minimal and number of adult that escape to vector stage are inconsequential and microscopic and that means the life-cycle could be broken at the larva, pupa, and adult stages with the introduction of natural predators, with the natural implication there will not be anopheles adult mosquito for malaria transmission and we also use maple for symbolical and numerical solution and presented the results graphically.
Open Access
On Cardinality in Finite Semigroup of Full Order-Preserving ContractionsOn Cardinality in Finite Semigroup of Full Order-Preserving Contractions
(Department of Mathematics, Nasarawa State University Keffi, 2022-04-04) Habibu, Shamsuddeen; Umar, Mallam Abdulkarim; Oduwole, H.K.; Ibrahim, Yusuf Kakangi; Braimoh, Jaiyeola Olorunshola
In this work, we considered the semigroup OCTn consisting of all mappings of a finite set Xn = {1, 2, 3,---- , n} which are both order - preserving and contraction, that is mapping a •• Xn -» Xn such that, for all x ,y E Xnfx- x a
Open Access
On Number of Idempotent Elements in Finite Semigroup of Full Order -Preserving Contractions
(Department of Mathematics, Nasarawa State University Keffi, 2021-10-28) Amadu, Kabiru; Umar, Mallam Abdulkarim; Habibu, Shamsuddeen; Bello, Asma'u
In this paper, we considered the semigroupOCTn consisting of all mappings of a-finite set Xn - (1, 2, 3, - - - , n} which are both order — preserving and contraction, that is mappinga : Xn -» Xn ^ ich that, for all ,y e Xn, x => x a £ y a,anc | x a — *y a <1 x—y| . In particular, we proposed a closed form formula for the number of idempotent elements in OCTn, (that is elements oc satisfying oc2=oc).
Open Access
An Optimal Control Analysis of Malaria by Coinfection Model
(Department of Mathematics, Nasarawa State University Keffi, 2022-07-03) Ashafa, S.U.; Oduwole, H.K.; Umar, Mallam Abdulkarim
Malaria and Hepatitis B Virus (HB V) are diseases that poses serious challenges health wise in the world especially in countries that are developing:-Both diseases belong to t the most widespread diseases, and therefore, a major public health concerns in tropical developing countries. In this research, a mathematical model showing dynamics of Co infection of Malaria and HBV diseases was developed using ordinary differential equations which consists of 9 compartments. The study covers the model*s futdre solution positivity, model invariant region and disease-free points. The next generation matrix method was used to compute the basic reproduction number, R0, for the coinfection model using and the disease free equilibrium point and was shown to be Locally Asymptotically Stable ifJl0 < 1 and unstable if > 1. Then, the coinfection model was extended to optimal control by incorporating four control interventions. The optimality System was obtained using the Pontryagin’s maximum principle. Simulation of the optimality system was done and five strategies was proposed to qheck the effect of the controls. First, prevention only for both diseases was considered, and the result shows that, applying prevention control has a great impact in bringing down the expansion of malaria, HBV infection, and their coinfection in the specified period of time. Other approaches are prevention effort for malaria and treatment effort for HBV infection, prevention effort for HBV infection and treatment effort for malaria, treatment effort for both diseases, and using all interventions. We obtained that the listed strategies were effective in ,,minimizing the expansion of Malaria HBV coinfeciious population in the specified period of time.
Open Access
The Pictorial Integral of Malaria Control with Maple
(Department of Mathematics, Nasarawa State University Keffi, 2023-01-03) Emmanuel, Atanyi Yusuf; Oduwole, H.K.; Umar, Mallam Abdulkarim
The pictorial integral of malaria control with maple has bepn derived to eradicate larvae, pupae and adult Anopheles mosquitoes using natural predators to eradicate "copepods, tadpoles and purple swallows" ( an organism that eats mosquitoes). The new model is a control flowchart of the predator-prey interaction model in the mosquito life cycle, considering an open population of mosquitoes and predators. These models provide a solid understanding of malaria control in our environment, especially when models are based on vector population ecology and a solid understanding of transmission-relevant parameters and variables Model equations were derived using parameters and variables from the model Stability analysis of free equilibrium states was analyzed simultaneously using equilibrium point, Maple software', elimination and substitution methods. Therefore, the number of larvae that pupate is almost zero, and the number of pupae that turn into adults is minimal, and the number of adults that escape to the vector stage is negligible, this means that the life cycle could be disrupted at the end of the larval, pupal and adult stages with the introduction of natural enemies, with the natural implication that there will be no adult Anopheles mosquito for transmission of the malaria, and we also use maple for the symbolic and numerical solution and graphically presented the results. . The contribution of this research to knowledge is to produce the mathematical formula and the biologically sound methods that will contribute to the eradication of the adult Anopheles mosquito, which will also lead to the eradication of malaria in our society. ,
Open Access
Stochastic SIR Household Epidemic Model with Misclassification .
(Department of Mathematics, Nasarawa State University Keffi, 2021-01-03) Umar, Mallam Abdulkarim
n this work, we developed a theoretical framework leading to misclassifi cation of the final size epidemic data for the stochastic SIR (Suscepti- ble-Infective-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algo rithm is then employed for its Inference. We then.analyzed and- compared
Open Access
Stochastic SIR Household Epidemic Model with Misspecification
(Department of Mathematics, Nasarawa State University Keffi, 2021-08-09) Umar, Mallam Abdulkarim
The stochastic SIR household epidemic model is well discussed in [3]>, (4], [5] and also in [I] by assuming that the infection period distribution is known. Sometimes this may wrongly be assumed in the model estimation and hence the adequacy of the model fitness to the final size data is affected, we examined this problem using simulations with large population size and theoretical parameters in which the final size data is first simulated with exp(4.1) infectious period distribution and estimated with P(2,4.1/2) infectious period distribution and vice The estimates of the two dimensional mjodels are further explored for a range of local and global infection rates with corresponding prpportion infected and found to be biased and imprecise.