The manuscript has been well written but there are many grammatical errors ranging from short sen... more The manuscript has been well written but there are many grammatical errors ranging from short sentences that do not convey meaning, and tenses error. I have identified some of them and encourage the authors do diligently go through the thesis and correct all grammatical errors. Also there are some mathematical issues identified, authors could see them in the attached file and make corrections. So, I advice that major correction been carried out on the manuscript and returned for another round of review.
African Journal of Infectious Diseases, Dec 22, 2022
Background:Ebola Virus causes disease both in human and non-human primates especially in developi... more Background:Ebola Virus causes disease both in human and non-human primates especially in developing countries. In 2014 during its outbreak, it led to majority of deaths especially in some impoverished area of West Africa and its effect is still witnessed up till date.Materials and Methods:We studied the spread of Ebola virus and obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus in a population where control measures were incorporated and a major source of contacting the disease which is the traditional washing of dead bodies was also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease- endemic stability using the center manifold theorem. We also investigated the global stability of the equilibrium points using the LaSalle’s Invariant principle.Results:The result showed that the disease-free and endemic equilibrium where both local and globally stable and that the system exhibits a forward bifurcation.Conclusions:Numerical simulations were carried out and our graphs show that vaccine and condom use is best for susceptible population, quarantine is best for exposed population, isolation is best for infectious population and proper burial of the diseased dead is the best to avoid further disease spread in the population and have quicker and better recovery.
A theoretical study has been conducted to investigate the steady Magnetohydrodynamics (MHD) bound... more A theoretical study has been conducted to investigate the steady Magnetohydrodynamics (MHD) boundary layer flow past a low-heat-resistant sheet moving vertically downwards. The fluid is considered viscous, incompressible and electrically conducting. The non-linear coupled differential equations are solved numerically by applying Runge-Kutta integration scheme coupled with NewtonRaphson shooting technique. The results show that the velocity, temperature, and concentration profiles are appreciably influenced by the presence of the transverse magnetic field. Also, the effects of various parameters on the skin-friction, the Nusselt and the Sherwood numbers are discussed.
Background: HIV is a virus that is directed at destroying the human immune system thereby exposin... more Background: HIV is a virus that is directed at destroying the human immune system thereby exposing the human body to the risk of been affected by other common illnesses and if it is not treated, it generates a more chronic illness called AIDS. Materials and Methods: In this paper, we employed the fixed-point theory in developing the uniqueness and existence of a solution of fractional order HIV/AIDS model having Caputo-Fabrizio operator. This approach adopted in this work is not conventional when solving biological models by fractional derivatives. Results: The results showed that the model has two equilibrium points namely, disease-free, and endemic equilibrium points, respectively. We showed conditions necessitating the existence of the endemic equilibrium point and showed that the disease-free equilibrium point is locally asymptotically stable. We also tested the stability of our solution using the iterative Laplace transform method on our model which was also shown stable agreei...
The Journal of Infection in Developing Countries, 2020
Introduction: Tuberculosis (TB) continues to be a public health problem globally. The burden is f... more Introduction: Tuberculosis (TB) continues to be a public health problem globally. The burden is further exacerbated in developing countries like Nigeria, by poor diagnosis, management and treatment, as well as rapid emergence of drug-resistant TB. This study was conducted to evaluate the prevalence of drug-resistant TB, determine the rpoB gene mutation patterns of Mycobacterium tuberculosis (MTB) and model the dynamics of multidrug resistant TB (MDR-TB) in Enugu, Nigeria. Methodology: A total of 868 samples, from patients accessing DOTS services in designated centres within the zone, were screened by sputum-smear microscopy, while 207 samples were screened by Nucleic Acid Amplification (Xpert® MTB/Rif) Test (NAAT). A deterministic model was formulated to study the transmission dynamics of TB and MDR-TB, using live data generated through epidemiological study. Results: The results showed TB prevalence values of 22.1% and 21.3% by sputum-smear and NAAT assays, respectively. Analysis o...
International Journal of Mathematics and Mathematical Sciences, 2020
Lassa fever is an animal-borne acute viral illness caused by the Lassa virus. This disease is end... more Lassa fever is an animal-borne acute viral illness caused by the Lassa virus. This disease is endemic in parts of West Africa including Benin, Ghana, Guinea, Liberia, Mali, Sierra Leone, and Nigeria. We formulate a mathematical model for Lassa fever disease transmission under the assumption of a homogeneously mixed population. We highlighted the basic factors influencing the transmission of Lassa fever and also determined and analyzed the important mathematical features of the model. We extended the model by introducing various control intervention measures, like external protection, isolation, treatment, and rodent control. The extended model was analyzed and compared with the basic model by appropriate qualitative analysis and numerical simulation approach. We invoked the optimal control theory so as to determine how to reduce the spread of the disease with minimum cost.
In this work, we formulate a multiple-patch Lassa fever model, where each patch denotes a socioec... more In this work, we formulate a multiple-patch Lassa fever model, where each patch denotes a socioeconomic class (SEC). Some of the important epidemiological features such as basic reproduction number of the model were determined and analysed accordingly. We further investigated how varying SECs affect the transmission dynamics of Lassa fever. We analysed the required state at which each SEC is responsible in driving the Lassa fever disease outbreak. Sensitivity analyses were carried out to determine the importance of model parameters to the disease transmission and prevalence. We carried out numerical simulation to support our analytical results. Finally, we extend some of the results of the 2-patch model to the general n-patch model.
International Journal of Mathematics and Mathematical Sciences
Sterile insect technology (SIT) is an environmental-friendly method which depends on the release ... more Sterile insect technology (SIT) is an environmental-friendly method which depends on the release of sterile male mosquitoes that compete with the wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring and as such reduces the population of Zika virus vector population over time, thereby eliminating the spread of Zika virus in a population. The fractional order sterile insect technology (SIT) model to reduce the spread of Zika virus disease is considered in this present work. We employed the use Laplace–Adomian decomposition method (LADM) to determine an analytical (approximate) solution of the model. The Laplace–Adomian decomposition method (LADM) produced a solution in form of an infinite series that further converges to the exact value. We compared solutions of the fractional model with the classical case using our plots and discovered that the fractional order has more degree of freedom and as such the system can be varied to get m...
Malaria is one of the most prevalent illness globally especially in the tropic and sub-tropic reg... more Malaria is one of the most prevalent illness globally especially in the tropic and sub-tropic regions of the world. This work investigates the transmission dynamics of malaria disease and the different ways the disease can be controlled by formulating appropriate mathematical epidemiological model. To evaluate the impacts of control measures, we determine the important mathematical features of the model such as the basic reproduction number and analyze then accordingly. The disease free equilibrium and endemic equilibrium point of the model were derived and its stability investigated. For instance, our analysis showed that the disease free equilibrium point is stable when R0 < 1. Stability analyses of the endemic equilibrium is investigated using the centre manifold theorem. Numerical simulations were carried out using realistic parameter values to support our analytical predictions.
The manuscript has been well written but there are many grammatical errors ranging from short sen... more The manuscript has been well written but there are many grammatical errors ranging from short sentences that do not convey meaning, and tenses error. I have identified some of them and encourage the authors do diligently go through the thesis and correct all grammatical errors. Also there are some mathematical issues identified, authors could see them in the attached file and make corrections. So, I advice that major correction been carried out on the manuscript and returned for another round of review.
African Journal of Infectious Diseases, Dec 22, 2022
Background:Ebola Virus causes disease both in human and non-human primates especially in developi... more Background:Ebola Virus causes disease both in human and non-human primates especially in developing countries. In 2014 during its outbreak, it led to majority of deaths especially in some impoverished area of West Africa and its effect is still witnessed up till date.Materials and Methods:We studied the spread of Ebola virus and obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus in a population where control measures were incorporated and a major source of contacting the disease which is the traditional washing of dead bodies was also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease- endemic stability using the center manifold theorem. We also investigated the global stability of the equilibrium points using the LaSalle’s Invariant principle.Results:The result showed that the disease-free and endemic equilibrium where both local and globally stable and that the system exhibits a forward bifurcation.Conclusions:Numerical simulations were carried out and our graphs show that vaccine and condom use is best for susceptible population, quarantine is best for exposed population, isolation is best for infectious population and proper burial of the diseased dead is the best to avoid further disease spread in the population and have quicker and better recovery.
A theoretical study has been conducted to investigate the steady Magnetohydrodynamics (MHD) bound... more A theoretical study has been conducted to investigate the steady Magnetohydrodynamics (MHD) boundary layer flow past a low-heat-resistant sheet moving vertically downwards. The fluid is considered viscous, incompressible and electrically conducting. The non-linear coupled differential equations are solved numerically by applying Runge-Kutta integration scheme coupled with NewtonRaphson shooting technique. The results show that the velocity, temperature, and concentration profiles are appreciably influenced by the presence of the transverse magnetic field. Also, the effects of various parameters on the skin-friction, the Nusselt and the Sherwood numbers are discussed.
Background: HIV is a virus that is directed at destroying the human immune system thereby exposin... more Background: HIV is a virus that is directed at destroying the human immune system thereby exposing the human body to the risk of been affected by other common illnesses and if it is not treated, it generates a more chronic illness called AIDS. Materials and Methods: In this paper, we employed the fixed-point theory in developing the uniqueness and existence of a solution of fractional order HIV/AIDS model having Caputo-Fabrizio operator. This approach adopted in this work is not conventional when solving biological models by fractional derivatives. Results: The results showed that the model has two equilibrium points namely, disease-free, and endemic equilibrium points, respectively. We showed conditions necessitating the existence of the endemic equilibrium point and showed that the disease-free equilibrium point is locally asymptotically stable. We also tested the stability of our solution using the iterative Laplace transform method on our model which was also shown stable agreei...
The Journal of Infection in Developing Countries, 2020
Introduction: Tuberculosis (TB) continues to be a public health problem globally. The burden is f... more Introduction: Tuberculosis (TB) continues to be a public health problem globally. The burden is further exacerbated in developing countries like Nigeria, by poor diagnosis, management and treatment, as well as rapid emergence of drug-resistant TB. This study was conducted to evaluate the prevalence of drug-resistant TB, determine the rpoB gene mutation patterns of Mycobacterium tuberculosis (MTB) and model the dynamics of multidrug resistant TB (MDR-TB) in Enugu, Nigeria. Methodology: A total of 868 samples, from patients accessing DOTS services in designated centres within the zone, were screened by sputum-smear microscopy, while 207 samples were screened by Nucleic Acid Amplification (Xpert® MTB/Rif) Test (NAAT). A deterministic model was formulated to study the transmission dynamics of TB and MDR-TB, using live data generated through epidemiological study. Results: The results showed TB prevalence values of 22.1% and 21.3% by sputum-smear and NAAT assays, respectively. Analysis o...
International Journal of Mathematics and Mathematical Sciences, 2020
Lassa fever is an animal-borne acute viral illness caused by the Lassa virus. This disease is end... more Lassa fever is an animal-borne acute viral illness caused by the Lassa virus. This disease is endemic in parts of West Africa including Benin, Ghana, Guinea, Liberia, Mali, Sierra Leone, and Nigeria. We formulate a mathematical model for Lassa fever disease transmission under the assumption of a homogeneously mixed population. We highlighted the basic factors influencing the transmission of Lassa fever and also determined and analyzed the important mathematical features of the model. We extended the model by introducing various control intervention measures, like external protection, isolation, treatment, and rodent control. The extended model was analyzed and compared with the basic model by appropriate qualitative analysis and numerical simulation approach. We invoked the optimal control theory so as to determine how to reduce the spread of the disease with minimum cost.
In this work, we formulate a multiple-patch Lassa fever model, where each patch denotes a socioec... more In this work, we formulate a multiple-patch Lassa fever model, where each patch denotes a socioeconomic class (SEC). Some of the important epidemiological features such as basic reproduction number of the model were determined and analysed accordingly. We further investigated how varying SECs affect the transmission dynamics of Lassa fever. We analysed the required state at which each SEC is responsible in driving the Lassa fever disease outbreak. Sensitivity analyses were carried out to determine the importance of model parameters to the disease transmission and prevalence. We carried out numerical simulation to support our analytical results. Finally, we extend some of the results of the 2-patch model to the general n-patch model.
International Journal of Mathematics and Mathematical Sciences
Sterile insect technology (SIT) is an environmental-friendly method which depends on the release ... more Sterile insect technology (SIT) is an environmental-friendly method which depends on the release of sterile male mosquitoes that compete with the wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring and as such reduces the population of Zika virus vector population over time, thereby eliminating the spread of Zika virus in a population. The fractional order sterile insect technology (SIT) model to reduce the spread of Zika virus disease is considered in this present work. We employed the use Laplace–Adomian decomposition method (LADM) to determine an analytical (approximate) solution of the model. The Laplace–Adomian decomposition method (LADM) produced a solution in form of an infinite series that further converges to the exact value. We compared solutions of the fractional model with the classical case using our plots and discovered that the fractional order has more degree of freedom and as such the system can be varied to get m...
Malaria is one of the most prevalent illness globally especially in the tropic and sub-tropic reg... more Malaria is one of the most prevalent illness globally especially in the tropic and sub-tropic regions of the world. This work investigates the transmission dynamics of malaria disease and the different ways the disease can be controlled by formulating appropriate mathematical epidemiological model. To evaluate the impacts of control measures, we determine the important mathematical features of the model such as the basic reproduction number and analyze then accordingly. The disease free equilibrium and endemic equilibrium point of the model were derived and its stability investigated. For instance, our analysis showed that the disease free equilibrium point is stable when R0 < 1. Stability analyses of the endemic equilibrium is investigated using the centre manifold theorem. Numerical simulations were carried out using realistic parameter values to support our analytical predictions.
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