Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millio... more Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronic-infected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, R 0 A , R 0 H , and R 0 C , determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identi...
Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millio... more Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronicinfected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, R A 0 , R H 0 , and R C 0 , determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identify the factors that affect the reproduction numbers. The results of the sensitivity analysis paved a way for introducing a controlled system which was solved using Pontryagin's maximum principle (PMP) and the optimality system got. The optimality system was then solved numerically using the forward and backward sweep approach, and graphs were generated, establishing the conditions for local and global stability of the disease-free equilibrium using the Routh-Hurwitz criterion and Castillo-Chavez approach, respectively. We also used Pontryagin's maximum principle to determine the optimality system. The result of the analysis of the stability of the disease-free equilibrium states that hepatitis B virus can be completely wiped out if the rate of infection is kept at a number less than unity. A numerical simulation of the model was carried out and showed that hepatitis B virus transmission can best be controlled when condom use, testing and treatment, and vaccination are implemented.
In this paper, a nonlinear fractional-order PI (NL-FO-PI) controller is proposed for primary freq... more In this paper, a nonlinear fractional-order PI (NL-FO-PI) controller is proposed for primary frequency control (PFC) of a wind farm based on the squirrel cage induction generator. e new structure composites a fractional-order operator and nonlinear function to achieve better control performance for the PFC system. e benchmarking process is demonstrated by investigating the performance of fractional-order PI (FO-PI) and nonlinear PI (NL-PI) controllers. Initially, the controller is applied to a single-area power system for design and stability study and then extended to the two-area interconnected wind farm to validate the applicability in the more realistic power system. e proposed control method ensures the balance of power and keeps the system frequency within a suitable range. e simulation results demonstrate that the proposed NL-FO-PI controller provides less percentage overshoot, settling time, rise time, and peak time than other controllers.
In this paper, a deterministic compartmental model for the control of typhoid fever, which takes ... more In this paper, a deterministic compartmental model for the control of typhoid fever, which takes into account a partially effective vaccine and drug resistance effect was proposed. We incorporated five control strategies which consist of mass public health education, vaccination, treatment, second-line of treatment, and protection or environmental sanitation to curtail the spread of the disease in the population. The model consists of eight (8) compartments that include: Vaccinated population, susceptible population, exposed population, asymptomatic infected human population, symptomatic infected human population, resistant human population, treated human population, and the bacterial population. We developed a non-linear differential equation to study the dynamics of the model. We computed the basic reproduction number for a case of constant control which can be used to control the transmission dynamics of the disease and proved the local and global stability of the disease-free equilibrium, the result of stability analysis revealed that the disease-free equilibrium (DFE) is locally asymptotically stable if the basic reproduction number is less than one (1) using Routh-Hurwitz Criterion (RHC) and globally asymptotically stable if the basic reproduction number is less than one through the method of Castillo-Chavez. The stability analysis of the disease-free equilibrium result indicates that typhoid can be completely wiped out if the average number of secondary infection is kept at a number less than unity. We carry out sensitivity analyses on the reproduction number to ascertain the parameters that affect the reproduction number. Based on the results, an optimal control problem was formulated and analyzed using Pontryagin's Maximum Principle (PMP) to determine the optimality system. We solved the optimality system using the forward and backward sweep method and the results revealed that the combination of vaccination, public health education, treatment, the second line of treatment, and environmental sanitation is the best strategy for controlling the spread of the disease.
This thesis extends the standard SEIR epidemiology model of Ebola virus to include both Human and... more This thesis extends the standard SEIR epidemiology model of Ebola virus to include both Human and Monkey population. Nine (9) compartments were considered, namely: (),
Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millio... more Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronic-infected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, R 0 A , R 0 H , and R 0 C , determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identi...
Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millio... more Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronicinfected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, R A 0 , R H 0 , and R C 0 , determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identify the factors that affect the reproduction numbers. The results of the sensitivity analysis paved a way for introducing a controlled system which was solved using Pontryagin's maximum principle (PMP) and the optimality system got. The optimality system was then solved numerically using the forward and backward sweep approach, and graphs were generated, establishing the conditions for local and global stability of the disease-free equilibrium using the Routh-Hurwitz criterion and Castillo-Chavez approach, respectively. We also used Pontryagin's maximum principle to determine the optimality system. The result of the analysis of the stability of the disease-free equilibrium states that hepatitis B virus can be completely wiped out if the rate of infection is kept at a number less than unity. A numerical simulation of the model was carried out and showed that hepatitis B virus transmission can best be controlled when condom use, testing and treatment, and vaccination are implemented.
In this paper, a nonlinear fractional-order PI (NL-FO-PI) controller is proposed for primary freq... more In this paper, a nonlinear fractional-order PI (NL-FO-PI) controller is proposed for primary frequency control (PFC) of a wind farm based on the squirrel cage induction generator. e new structure composites a fractional-order operator and nonlinear function to achieve better control performance for the PFC system. e benchmarking process is demonstrated by investigating the performance of fractional-order PI (FO-PI) and nonlinear PI (NL-PI) controllers. Initially, the controller is applied to a single-area power system for design and stability study and then extended to the two-area interconnected wind farm to validate the applicability in the more realistic power system. e proposed control method ensures the balance of power and keeps the system frequency within a suitable range. e simulation results demonstrate that the proposed NL-FO-PI controller provides less percentage overshoot, settling time, rise time, and peak time than other controllers.
In this paper, a deterministic compartmental model for the control of typhoid fever, which takes ... more In this paper, a deterministic compartmental model for the control of typhoid fever, which takes into account a partially effective vaccine and drug resistance effect was proposed. We incorporated five control strategies which consist of mass public health education, vaccination, treatment, second-line of treatment, and protection or environmental sanitation to curtail the spread of the disease in the population. The model consists of eight (8) compartments that include: Vaccinated population, susceptible population, exposed population, asymptomatic infected human population, symptomatic infected human population, resistant human population, treated human population, and the bacterial population. We developed a non-linear differential equation to study the dynamics of the model. We computed the basic reproduction number for a case of constant control which can be used to control the transmission dynamics of the disease and proved the local and global stability of the disease-free equilibrium, the result of stability analysis revealed that the disease-free equilibrium (DFE) is locally asymptotically stable if the basic reproduction number is less than one (1) using Routh-Hurwitz Criterion (RHC) and globally asymptotically stable if the basic reproduction number is less than one through the method of Castillo-Chavez. The stability analysis of the disease-free equilibrium result indicates that typhoid can be completely wiped out if the average number of secondary infection is kept at a number less than unity. We carry out sensitivity analyses on the reproduction number to ascertain the parameters that affect the reproduction number. Based on the results, an optimal control problem was formulated and analyzed using Pontryagin's Maximum Principle (PMP) to determine the optimality system. We solved the optimality system using the forward and backward sweep method and the results revealed that the combination of vaccination, public health education, treatment, the second line of treatment, and environmental sanitation is the best strategy for controlling the spread of the disease.
This thesis extends the standard SEIR epidemiology model of Ebola virus to include both Human and... more This thesis extends the standard SEIR epidemiology model of Ebola virus to include both Human and Monkey population. Nine (9) compartments were considered, namely: (),
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Papers by Abubakar Audu