PID Control for Linear and Nonlinear Industrial Processes
The foremost cause of death resulting from cancer is lung cancer. From the statistics, 2.09 milli... more The foremost cause of death resulting from cancer is lung cancer. From the statistics, 2.09 million new cases and 1.7 million deaths from lung cancer were estimated. In this chapter, the analytical solution of the concerned model was studied with help of the Laplace-Adomian Decomposition Method. To obtain the model’s numerical scheme of fractional differential equations, the Caputo fractional derivative operator of order α∈01 is used. To find an approximate solution to a system of nonlinear fractional differential equations, the Laplace-Adomian Decomposition Method is used. Numerical simulations are presented to show the method’s reliability and simplicity.
The disease that essentially affects the skin, the peripheral nerves, mucosal surfaces of the upp... more The disease that essentially affects the skin, the peripheral nerves, mucosal surfaces of the upper respiratory tract and the eyes. It is frequently surrounded by frightening, undesirable social stigmatization to them and their families and tales of leprosy patients being shunned as outcasts. In this paper, a deterministic mathematical model of the dynamics of disease is developed. The epidemic thresholds and equilibria for the model are determined and stabilities analyzed. Results from the analysis of the reproduction number propose that treatment will somehow contribute to a decrease in disease cases. This result recommends that, the control of the disease should lie more on treatment and public health education. Numerical simulations show the dynamics of the transmission of disease.
Regional migration has become an underlying factor in the spread of HIV transmission. In addition... more Regional migration has become an underlying factor in the spread of HIV transmission. In addition, immigrants with HIV status has contributed with high-risk of sexually transmitted infection to its "destination" communities and promotes dissemination of HIV. Efforts to address HIV/AIDS among conflict-affected populations should be properly addressed to eliminate potential role of the spread of the disease and risk of exposure to HIV. Motivated from this situation, HIV-infected immigrants factor to HIV/SIV transmission link will be investigated in this research and examine its potential effect using optimal control method. Nonlinear deterministic mathematical model is used which is a multiple host model comprising of humans and chimpanzees. Some basic properties of the model such as invariant region and positivity of the solutions will be examined. The local stability of the disease-free equilibrium was examined by computing the basic reproduction number, and it was found to be locally asymptotically stable when ℜ 0 < 1 and unstable otherwise. Sensitivity analysis was conducted to determine the parameters that help most in the spread of the virus. Pontryagin's maximum principle is used to obtain the optimality conditions for controlling the disease spread. Numerical simulation was conducted to obtain the analytical results. The results shows that combination of public health awareness, treatment, and culling help in controlling the HIV disease spread.
The purpose of this study is to investigate the transmission dynamics of SIV=HIV in humans, in th... more The purpose of this study is to investigate the transmission dynamics of SIV=HIV in humans, in the presence of chimpanzees that harbor Simian Immunodeficiency Virus (SIV) and to suggest some control strategies in sub-Saharan Africa. SIV was believed by some scientists to have ignited the emergence of HIV. This could be one of the reasons that make the disease endemic in sub-Saharan Africa where these chimpanzees are predominantly found. A basic model that consists of human and chimpanzee populations were formulated and the equilibrium points were determined. It was obtained that the disease free equilibrium point is locally asymptotically stable when the basic reproduction number is found to be less than unity and unstable otherwise
In this paper, a nonlinear mathematical model is developed and analyzed to study the dynamics of ... more In this paper, a nonlinear mathematical model is developed and analyzed to study the dynamics of Ebola virus (EVD) and the effects of some control strategies. The model validity is investigated and was found to be locally asymptotically stable when the basic reproduction number () 0 1 ℜ < and unstable otherwise. Pontryagin's maximum principle is applied to obtain the optimality conditions. Numerical simulation was carried out and the results obtained indicate that a combination of all three control parameters is highly effective in containing the spread of the virus.
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation, 2019
In this work, a new deterministic mathematical model for a cholera carrier epidemic is developed ... more In this work, a new deterministic mathematical model for a cholera carrier epidemic is developed and validated for the existence and uniqueness; hence the Lipschitz conditions are satisfied. The model threshold quantity 0 R for the cholera dynamics is computed using next generation matrix operator approach. The model sensitivity-index of the key parameters that has influence on the basic reproduction number 0 R is carried out. The results showed that the force of infection in the pathogen population, 3 with the value of 0.4895 followed by the force of infection in the carrier population, 2 with the value of 0.4473 are found to be the most sensitive parameters in the cholera prevalence and transmissions targeted for intervention and control strategies in the community. Plotted illustrations are presented to support our findings. Therefore, to curtail the spreads of cholera in the community, it is recommended that public health campaigns be conducted frequently.
Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015), 2016
In this study a nonlinear deterministic mathematical model was developed on the dynamics of HIV-1... more In this study a nonlinear deterministic mathematical model was developed on the dynamics of HIV-1 in sub-Saharan Africa with the final goal of implementing an optimal control using two control parameters of treatment and culling. This could minimize the number of infected humans and chimpanzees. Validity of the model was investigated through Invariant region and the model was found to be epidemiologically meaningful. Basic reproduction number which determines the stability of the disease is obtained using next generation operator. Disease free equilibrium was found to be locally asymptotically stable whenever basic reproduction number is greater than one and unstable otherwise. Numerical simulation results reveal that, the two control strategies optimally help in curtailing the spread of the virus.
A mathematical model which describes the transmission dynamics of HIV/AIDS is developed. The opti... more A mathematical model which describes the transmission dynamics of HIV/AIDS is developed. The optimal control representing education and treatment for this model is explored. The existence of optimal Control is established analytically by the use of optimal control theory. Numerical simulations suggest that education and treatment for the infected has a positive impact on HIV/AIDS control.
PID Control for Linear and Nonlinear Industrial Processes
The foremost cause of death resulting from cancer is lung cancer. From the statistics, 2.09 milli... more The foremost cause of death resulting from cancer is lung cancer. From the statistics, 2.09 million new cases and 1.7 million deaths from lung cancer were estimated. In this chapter, the analytical solution of the concerned model was studied with help of the Laplace-Adomian Decomposition Method. To obtain the model’s numerical scheme of fractional differential equations, the Caputo fractional derivative operator of order α∈01 is used. To find an approximate solution to a system of nonlinear fractional differential equations, the Laplace-Adomian Decomposition Method is used. Numerical simulations are presented to show the method’s reliability and simplicity.
The disease that essentially affects the skin, the peripheral nerves, mucosal surfaces of the upp... more The disease that essentially affects the skin, the peripheral nerves, mucosal surfaces of the upper respiratory tract and the eyes. It is frequently surrounded by frightening, undesirable social stigmatization to them and their families and tales of leprosy patients being shunned as outcasts. In this paper, a deterministic mathematical model of the dynamics of disease is developed. The epidemic thresholds and equilibria for the model are determined and stabilities analyzed. Results from the analysis of the reproduction number propose that treatment will somehow contribute to a decrease in disease cases. This result recommends that, the control of the disease should lie more on treatment and public health education. Numerical simulations show the dynamics of the transmission of disease.
Regional migration has become an underlying factor in the spread of HIV transmission. In addition... more Regional migration has become an underlying factor in the spread of HIV transmission. In addition, immigrants with HIV status has contributed with high-risk of sexually transmitted infection to its "destination" communities and promotes dissemination of HIV. Efforts to address HIV/AIDS among conflict-affected populations should be properly addressed to eliminate potential role of the spread of the disease and risk of exposure to HIV. Motivated from this situation, HIV-infected immigrants factor to HIV/SIV transmission link will be investigated in this research and examine its potential effect using optimal control method. Nonlinear deterministic mathematical model is used which is a multiple host model comprising of humans and chimpanzees. Some basic properties of the model such as invariant region and positivity of the solutions will be examined. The local stability of the disease-free equilibrium was examined by computing the basic reproduction number, and it was found to be locally asymptotically stable when ℜ 0 < 1 and unstable otherwise. Sensitivity analysis was conducted to determine the parameters that help most in the spread of the virus. Pontryagin's maximum principle is used to obtain the optimality conditions for controlling the disease spread. Numerical simulation was conducted to obtain the analytical results. The results shows that combination of public health awareness, treatment, and culling help in controlling the HIV disease spread.
The purpose of this study is to investigate the transmission dynamics of SIV=HIV in humans, in th... more The purpose of this study is to investigate the transmission dynamics of SIV=HIV in humans, in the presence of chimpanzees that harbor Simian Immunodeficiency Virus (SIV) and to suggest some control strategies in sub-Saharan Africa. SIV was believed by some scientists to have ignited the emergence of HIV. This could be one of the reasons that make the disease endemic in sub-Saharan Africa where these chimpanzees are predominantly found. A basic model that consists of human and chimpanzee populations were formulated and the equilibrium points were determined. It was obtained that the disease free equilibrium point is locally asymptotically stable when the basic reproduction number is found to be less than unity and unstable otherwise
In this paper, a nonlinear mathematical model is developed and analyzed to study the dynamics of ... more In this paper, a nonlinear mathematical model is developed and analyzed to study the dynamics of Ebola virus (EVD) and the effects of some control strategies. The model validity is investigated and was found to be locally asymptotically stable when the basic reproduction number () 0 1 ℜ < and unstable otherwise. Pontryagin's maximum principle is applied to obtain the optimality conditions. Numerical simulation was carried out and the results obtained indicate that a combination of all three control parameters is highly effective in containing the spread of the virus.
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation, 2019
In this work, a new deterministic mathematical model for a cholera carrier epidemic is developed ... more In this work, a new deterministic mathematical model for a cholera carrier epidemic is developed and validated for the existence and uniqueness; hence the Lipschitz conditions are satisfied. The model threshold quantity 0 R for the cholera dynamics is computed using next generation matrix operator approach. The model sensitivity-index of the key parameters that has influence on the basic reproduction number 0 R is carried out. The results showed that the force of infection in the pathogen population, 3 with the value of 0.4895 followed by the force of infection in the carrier population, 2 with the value of 0.4473 are found to be the most sensitive parameters in the cholera prevalence and transmissions targeted for intervention and control strategies in the community. Plotted illustrations are presented to support our findings. Therefore, to curtail the spreads of cholera in the community, it is recommended that public health campaigns be conducted frequently.
Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015), 2016
In this study a nonlinear deterministic mathematical model was developed on the dynamics of HIV-1... more In this study a nonlinear deterministic mathematical model was developed on the dynamics of HIV-1 in sub-Saharan Africa with the final goal of implementing an optimal control using two control parameters of treatment and culling. This could minimize the number of infected humans and chimpanzees. Validity of the model was investigated through Invariant region and the model was found to be epidemiologically meaningful. Basic reproduction number which determines the stability of the disease is obtained using next generation operator. Disease free equilibrium was found to be locally asymptotically stable whenever basic reproduction number is greater than one and unstable otherwise. Numerical simulation results reveal that, the two control strategies optimally help in curtailing the spread of the virus.
A mathematical model which describes the transmission dynamics of HIV/AIDS is developed. The opti... more A mathematical model which describes the transmission dynamics of HIV/AIDS is developed. The optimal control representing education and treatment for this model is explored. The existence of optimal Control is established analytically by the use of optimal control theory. Numerical simulations suggest that education and treatment for the infected has a positive impact on HIV/AIDS control.
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Papers by Amiru Sule