Browsing by Author "Luboobi, Livingstone"

Now showing 1 - 15 of 15

A Deterministic Mathematical Model for the Control of Spread of Prosopis Juliflora Plants
(Journal of Mathematics and Informatics, 2020-09-25) Simon, Joel; Mirau, Silas; Luboobi, Livingstone
Prosopis juliflora plants are the most aggressive invasive species in the world. They spread by animal movement crossing from one place land to another. In this paper a deterministic model to examine the dynamics of Prosopis julifrola plants is formulated and presented by adopting a similar approach of a dynamical system as used in epidemiological modeling. The local and global stability analyses of the equilibrium points of the model performed by using next-generation for the basic reproduction number R0 computation and Lypunov function method. The finding from the study showed that the Prosopis free equilibrium of the model is both locally and globally asymptotically stable if and only if the number of secondary infections, is less than unit, that is R0 < 1. Furthermore, the study showed that there exist Prosopis endemic equilibrium for the spread when 0 R >1. The numerical simulation implemented in MATLAB ODE45 algorithm for solving linear ordinary differential equations. The study findings showed that as the number of ingested animals increase, the plant spread increases on land. Based on the findings, the study recommend the application of the model on endemic areas to improve through: Awareness on animal feeding the plant, provision of insight on plant invasion to policy makers and environmental stakeholders to include in environment framework, seminars and environment clubs by visiting community groups an educating them on plant invasion, through this the plant eradication could be achieved.
The Effect of Seasonal Weather Variation on the Dynamics of the Plague Disease
(Hindawi International Journal of Mathematics and Mathematical Sciences, 2017-08-10) Ngeleja, Rigobert; Luboobi, Livingstone; Nkansah-Gyekye, Yaw
Plague is a historic disease which is also known to be the most devastating disease that ever occurred in human history, caused by gram-negative bacteria known as Yersinia pestis.The disease is mostly affected by variations of weather conditions as it disturbs the normal behavior of main plague disease transmission agents, namely, human beings, rodents, fleas, and pathogens, in the environment. This in turn changes the way they interact with each other and ultimately leads to a periodic transmission of plague disease. In this paper, we formulate a periodic epidemic model system by incorporating seasonal transmission rate in order to study the effect of seasonal weather variation on the dynamics of plague disease.We compute the basic reproduction number of a proposed model.We then use numerical simulation to illustrate the effect of different weather dependent parameters on the basic reproduction number. We are able to deduce that infection rate, progression rates from primary forms of plague disease to more severe forms of plague disease, and the infectious flea abundance affect, to a large extent, the number of bubonic, septicemic, and pneumonic plague infective agents. We recommend that it is more reasonable to consider these factors that have been shown to have a significant effect on 𝑅𝑇 for effective control strategies.
Mathematical model for brucellosis transmission dynamics in livestock and human populations
(Communications in Mathematical Biology and Neuroscience, 2020-01-29) Nyerere, Nkuba; Luboobi, Livingstone; Mpeshe, Saul; Shirima, Gabriel
Brucellosis is a contagious zoonotic infection caused by bacteria of genus brucella which affects humans and animals. The disease is of veterinary importance, public health concern and economic significance in both developed and developing countries. It is transmitted through direct or indirect contact with infected animals or their contaminated products. In this paper we formulate and analyze a deterministic mathematical model for the transmission dynamics of brucellosis. The model formulated incorporates contaminated environment to human, infected livestock to human, and human to human modes of transmission. The impacts of human treatment in controlling the spread of brucellosis in the human population is investigated. Both analytical and numerical solutions reveal that prolonged human treatment has a significant impact in reducing the spread of Brucellosis in human population only while elimination of the disease in domestic ruminants has promising results to both human and ruminants. Thus, brucellosis control strategies should always focus on elimination of the disease in domestic ruminants
A mathematical model for fall armyworm management on maize biomass
(Springer Nature, 2021-02-04) Daudi, Salamida; Luboobi, Livingstone; Kgosimore, Moatlhodi
Fall armyworm (Spodoptera frugiperda), a highly destructive and fast spreading agricultural pest native to North and South America, poses a real threat to global food security. In this paper, to explore the dynamics and implications of fall armyworm outbreak in a field of maize biomass, we propose a new dynamical system for maize biomass and fall armyworm interaction via Caputo fractional-order operator, which is not only a nonlocal operator but also contains all characteristics concerned with memory of the dynamical system. We define the basic reproduction number, which represents the average number of newborns produced by one individual female moth during its life span. We establish that the basic reproduction number is a threshold quantity, which determines persistence and extinction of the pest. Finally, we simulate the Caputo system using the Adam–Bashforth–Moulton method to illustrate the main results.
Mathematical Model for Optimal Control of Soil-Transmitted Helminth Infection
(Hindawi, 2020-08-01) Lambura, Aristide G.; Mwanga, Gasper G.; Luboobi, Livingstone; Kuznetsov, Dmitry
In this paper, we study the dynamics of soil-transmitted helminth infection. We formulate and analyse a deterministic compartmental model using nonlinear differential equations. The basic reproduction number is obtained and both disease-free and endemic equilibrium points are shown to be asymptotically stable under given threshold conditions. The model may exhibit backward bifurcation for some parameter values, and the sensitivity indices of the basic reproduction number with respect to the parameters are determined. We extend the model to include control measures for eradication of the infection from the community. Pontryagian’s maximum principle is used to formulate the optimal control problem using three control strategies, namely, health education through provision of educational materials, educational messages to improve the awareness of the susceptible population, and treatment by mass drug administration that target the entire population(preschool- and school-aged children) and sanitation through provision of clean water and personal hygiene. Numerical simulations were done using MATLAB and graphical results are displayed. The cost effectiveness of the control measures were done using incremental cost-effective ratio, and results reveal that the combination of health education and sanitation is the best strategy to combat the helminth infection. Therefore, in order to completely eradicate soil-transmitted helminths, we advise investment efforts on health education and sanitation controls.
Mathematical model for the effects of treatment and vaccination controls on the dynamics of rotavirus disease with reference to Uganda
(SCIK Publishing Corporation, 2014) Namawejje, Hellen; Luboobi, Livingstone; Kuznetsov, Dmitry; Wobudeya, Eric
In this paper, while Rotavirus has been a recognised disease for a long time in developing countries like Uganda, the control of this endemic disease is still a challenge. We formulated a mathematical model for the dynamics of Rotavirus disease with both treatment and vaccination. The equilibrium points are determined. The disease free equilibrium points are shown to be locally and globally asymptotically stable. We analyzed different reproduction numbers at different doses of vaccination with treatment. Numerical results indicate that rotavirus can be reduced when one or both interventions are implemented. The study recommends that children should always be treated and also complete all their doses of rotavirus vaccines so as to reduce severe infections.
Mathematical model for the infectiology of brucellosis with some control strategies
(BISKA Bilisim Technology, 2019-12-25) Nyerere, Nkuba; Luboobi, Livingstone; Mpeshe, Saul; Shirima, Gabriel
Brucellosis is a neglected zoonotic infection caused by gram-negative bacteria of genus brucella. In this paper, a deterministic mathematical model for the infectiology of brucellosis with vaccination of ruminants, culling of seropositive animals through slaughter, and proper environmental hygiene and sanitation is formulated and analyzed. A positive invariant region of the formulated model is established using the Box Invariance method, the effective reproduction number, Re of the model is computed using the standard next generation approach. We prove that the brucellosis free equilibrium exists, locally and globally asymptotically stable if Re < 1 while the endemic equilibrium point exists, locally and globally asymptotically stable if Re > 1. Sensitivity analysis of the effective reproductive number shows that, natural mortality rate of ruminants, recruitment rate, ruminant to ruminant transmission rate, vaccination rate, and disease induced culling rate are the most sensitive parameters and should be targeted in designing of the control strategies for the disease. Numerical simulation is done to show the variations of each subpopulation with respect to the control parameters.
Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis
(Science Publishing Group, 2015-10-09) Ega, Tesfaye Tadesse; Luboobi, Livingstone; Kuznetsov, Dmitry
In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the parameters of dog population, which shows the responsibility of dog population for human and livestock infection. For a specified set of values of parameters as deduced from the data provided by Ethiopian Public Health Institute of Addis Ababa, the basic reproduction number 0 R and the effective reproduction number e R works out to be 2 and 1.6 respectively, which indicates the disease will be endemic. The numerical simulation of reproduction ratio shows that the combination of vaccination, culling of stray dogs and controlling annual crop of new born puppies are the best method to control rabies transmission within and around Adds Ababa. The disease - free equilibrium 0 e is computed. When the effective reproduction number 1 e R < it is proved to be globally asymptotically stable in the feasible region F . When 1 e R > there exists one endemic equilibrium point which is locally asymptotically stable.
Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies.
(Hindawi, 2020-11-18) Lambura, Aristide; Mwanga, Gasper; Luboobi, Livingstone; Kuznetsov, Dmitry
A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin's Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.
Modeling the Impact of Seasonal Weather Variations on the Infectiology of Brucellosis
(Hindawi, 2020-10-17) Nyerere, Nkuba; Luboobi, Livingstone; Mpeshe, Saul; Shirima, Gabriel
A deterministic mathematical model for brucellosis that incorporates seasonality on direct and indirect transmission parameters for domestic ruminants, wild animals, humans, and the environment was formulated and analyzed in this paper. Both analytical and numerical simulations are presented. From this study, the findings show that variations in seasonal weather have the great impact on the transmission dynamics of brucellosis in humans, livestock, and wild animals. Thus, in order for the disease to be controlled or eliminated, measures should be timely implemented upon the fluctuation in the transmission of the disease.
Modelling the Control of the Impact of Fall Armyworm (Spodoptera frugiperda) Infestations on Maize Production
(Hindawi, 2021-02-18) Daudi, Salamida; Luboobi, Livingstone; Kgosimore, Moatlhodi; Kuznetsov, Dmitry
In this paper, we propose and analyze a stage-structured mathematical model for modelling the control of the impact of Fall Armyworm infestations on maize production. Preliminary analysis of the model in the vegetative and reproductive stages revealed that the two systems had a unique and positively bounded solution for all time . Numerical analysis of the model in both stages under two different cases was also considered: Case 1: different number of the adult moths in the field assumed at and Case 2: the existence of exogenous factors that lead to the immigration of adult moths in the field at time . The results indicate that the destruction of maize biomass which is accompanied by a decrease in maize plants to an average of 160 and 142 in the vegetative and reproductive stages, respectively, was observed to be higher in Case 2 than in Case 1 due to subsequent increase in egg production and density of the caterpillars in first few (10) days after immigration. This severe effect on maize plants caused by the unprecedented number of the pests influenced the extension of the model in both stages to include controls such as pesticides and harvesting. The results further show that the pest was significantly suppressed, resulting in an increase in maize plants to an average of 467 and 443 in vegetative and reproductive stages, respectively.
Optimal Control Strategies for the Infectiology of Brucellosis
(Hindawi, 2020-05-11) Nyerere, Nkuba; Luboobi, Livingstone; Mpeshe, Saul; Shirima, Gabriel
Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. The disease is of public health, veterinary, and economic significance in most of the developed and developing countries. Direct contact between susceptible and infective animals or their contaminated products are the two major routes of the disease transmission. In this paper, we investigate the impacts of controls of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans on the transmission dynamics of Brucellosis. The necessary conditions for an optimal control problem are rigorously analyzed using Pontryagin’s maximum principle. The main ambition is to minimize the spread of brucellosis disease in the community as well as the costs of control strategies. Findings showed that the effective use of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans have a significant impact in minimizing the disease spread in livestock and human populations. Moreover, cost-effectiveness analysis of the controls showed that the combination of livestock vaccination, gradual culling through slaughter, environmental sanitation, and personal protection in humans has high impact and lower cost of prevention.
Optimal Control Strategies for the Infectiology of Brucellosis
(Hindawi, 2020-05-11) Nyerere, Nkuba; Luboobi, Livingstone; Mpeshe, Saul; Shirima, Gabriel
Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. The disease is of public health, veterinary, and economic significance in most of the developed and developing countries. Direct contact between susceptible and infective animals or their contaminated products are the two major routes of the disease transmission. In this paper, we investigate the impacts of controls of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans on the transmission dynamics of Brucellosis. The necessary conditions for an optimal control problem are rigorously analyzed using Pontryagin’s maximum principle. The main ambition is to minimize the spread of brucellosis disease in the community as well as the costs of control strategies. Findings showed that the effective use of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans have a significant impact in minimizing the disease spread in livestock and human populations. Moreover, cost-effectiveness analysis of the controls showed that the combination of livestock vaccination, gradual culling through slaughter, environmental sanitation, and personal protection in humans has high impact and lower cost of prevention.
A Review of the Mathematical Models for Brucellosis Infectiology and Control Strategies
(Journal of Mathematics and Informatics, 2020-07-21) Nyerere, Nkuba; Luboobi, Livingstone; Mpeshe, Saul; Shirima, Gabriel
Brucellosis is a zoonotic bacterial infection that can be acquired by humans from infected animals' meat, urine, body fluids, aborted materials, unpasteurized milk, and milk products or contaminated environment. Mathematical models for infectious diseases have been used as important tools in providing useful information regarding the transmission and effectiveness of the available control strategies. In this paper, a review of the available compartmental mathematical models for Brucellosis was done. The main purpose was to assess their structure, populations involved, the available control strategies and suitability in predicting the disease incidence and prevalence in different settings. Diversities have been observed in the reviewed mathematical models; some models incorporated seasonal variations in a single animal population, some ignored the contributions of the contaminated environment while others considered the cattle or sheep population only. Most of the models reviewed have not considered the contribution of wild animals in the dynamics of Brucellosis. Some models do not match the real situation in most affected areas like sub-Saharan African region and Asian countries where wild animals, cattle and small ruminants share grazing areas and water points. Thus, to avoid unreliable results, this review reveals the need to affirm and incorporate wild animals, livestock, humans and seasonal weather parameters in the spread of Brucellosis and in planning for its controls.
Sensitivity analysis and numerical simulations for the mathematical model of rabies in human and animal within and around Addis ababa
(Asian Journal of Mathematics and Applications, 2015) Ega, Tesfaye Tadesse’; Luboobi, Livingstone; Kuznetsov, Dmitry; Kidane, Abraham Haile
Rabies is one of the neglected tropical diseases that has persisted for centuries in Ethiopia, and it is endemic within and around Addis Ababa. For the purpose of studying the dynamics of the disease we propose a deterministic mathematical model with human, dog and livestock populations and formulated as a system of ordinary differential equations. Basic reproduction number 0 R and effective reproduction number e R are computed using next generation operator. Sensitivity analysis of e R shows the natural death rate of dogs 𝜇𝑑 , the annual birth rate of dogs 𝜗𝑑 , dog-to-dog transmission rate 𝛽𝑑 , and disease induced death rate 𝜎𝑑 are found to be the most sensitive parameters of e R . According to numerical simulations of our system rabies transmission will increase within and around Addis Ababa, and may peak in 2024 and 2026 in human and livestock populations respectively. Our simulation shows that 25% vaccination coverage in livestock populations will reduce the future infection by half. This study suggests that a combination of interventions consisting of 60% of vaccination coverage in dog populations, 15% culling of stray dogs, and reducing annual crop of newborn puppies by 25% will reduce the number of human and livestock infections by 70%, and the disease will be eradicated from the community.