Open Access Library Journal

 Journal

 A Mathematical Model For Covid-19 Disease Transmission Dynamics With Impact Of Saturated Treatment: Modeling, Analysis And Simulation.

 Idisi I. Oke, Yakub T. Oyebo, Olamide F. Fakoya, Vigbe S. Benson, Yusuf T. Tunde*

 2021

The emergence of novel coronavirus (Covid-19) in 2019 sprung a sudden outbreak across the globe, presenting clinical and public health management challenges which led to global cancellation of conferences, travel restrictions, social distancing and closure of institutions. Thus, in considering the grave implications of the continuous spread of coronavirus disease, a SEIHRD epidemic model was formulated to gain insight into disease transmission dynamics with impacts of proposing control measures. The model captures the impact of undetected infectious individuals and detected hospitalized individuals with saturated treatment on the spread, death and recovery of Covid-19 patients in Nigeria. The model epidemic threshold and equilibria are determined, and their stabilities are analyzed. The model is validated by fitting it to data from January 28 to December 5, 2020. Results obtained suggest that decreasing the transmission rate for infective alone is not sufficient to eradicate the disease because of the presence of backward bifurcation, and we recommend that Nigerians must also adhere strictly to Covid-19 protocols in mitigating the spread and demise of coronavirus. 

 European Journal Of Mathematics And Statistics.

 Journal

 A Mathematical Model For Lassa Fever Transmission Dynamics With Impacts Of Control Measures: Analysis And Simulation.

 Oke I. Idisi And Tunde T. Yusuf

 2021

Lassa Fever, caused by Lassa virus, is a vector host transmitted infectious disease whose prevalence has been on the upsurge over the past few decades. Thus, considering the grave implications of the continuous spread of the disease, an epidemic model was developed to describe the disease transmission dynamics with impacts of proposed control measures. This is to help inform effective control strategies that would successfully curtail and contain the disease in its endemic areas. The model is qualitatively analyzed in order to contextualize the long run behavior of the model while the model associated basic reproduction number is derived. The model analysis reveals that the disease-free equilibrium is locally and globally stable whenever the basic reproduction number is less than unity and the disease prevalence would be high as long as the basic reproduction number is greater than unity. Finally, the model is numerically solved and simulated for different scenarios of the disease outbreaks while the findings from simulations are discussed. 

 Science Domain

 Journal

 Mathematical Modeling Of Yellow Fever Transmission Dynamics With Multiple Control Measures

 Tunde T. Yusuf1 And David O. Daniel

 2019

Yellow-fever disease remains endemic in some parts of the world despite the availability of a potent vaccine and effective treatment for the disease. This necessitates continuous research to possibly eradicate the spread of the disease and its attendant burden. Consequently, a deterministic model for Yellow-fever disease transmission dynamics within the human and vector population is considered. The model equilibrium solutions are obtained while the criteria for their existence and stability are investigated. The model is solved numerically using the forth order Runge- Kunta scheme and the results are simulated for different scenarios of interest. Findings from the simulations show that the disease will continue to be prevalent in our society (no matter how small) as long as the immunity conferred by the available vaccine is not lifelong and the Yellowfever infected mosquitoes continue to have unhindered access to humans. Thus, justifying the wisdom behind the practice of continuous vaccination and the use of mosquito net in areas of high Yellow-fever endemicity. However, it was equally found that the magnitude of the Yellowfever outbreak can be remarkably reduced to a negligible level with the adoption of chemical or biological control measures which ensure that only mosquitoes with minimal biting tendency thrive in the environment. 

 International Organisation For Scientific Research (IOSR)

 Journal

 Optimal Control Of Meningococcal Meningitis Transmission Dynamics: A Case Study Of Nigeria.

 Tunde T. Yusuf And Abdulmojeed O. Olayinka

 2019

Meningococcal Meningitis disease outbreak is a common phenomenon in the African Meningitis belt. The monumental death tolls resulting from the recurring outbreaks call for public health concern. Consequently, a deterministic model for the transmission dynamics of the disease which incorporates vaccination of the susceptibles and timely treatment of the infectives as control measures is considered. The problem is formulated as an optimal control problem with the goal of minimizing the annual incidence of the disease as well as the cost of implementing the control measures. Based on Pontryagin’s Maximum Principle (PMP), the optimality system to the optimal control problem is derived and it is solved numerically using Runge-Kunta of order four scheme with the forward-backward sweep approach. The numerical result is then simulated for different scenarios of the disease outbreaks and the findings from our simulations are discussed. 

 International Journal Of Scientific & Engineering Research

 Journal

 OPTIMAL CONTROL STRATEGY FOR IMPROVED CANCER BIOCHEMOTHERAPY OUTCOME

 Blessing Ogunmadeji And Tunde T. Yusuf

 2018

A deterministic mathematical model for cancer cells dynamics in the presence of treatment is considered. The model is a system of coupled ordinary differential equations (ODEs) which describes cancer growth on a cell population level in the presence of a combination of immunotherapy and chemotherapy known as biochemotherapy. The modeled scenario is formulated as an optimal control problem with the goal of obtaining the optimal levels of each of the treatment regimen that must be adopted in order to minimize the number of a cancer cells as well as the therapy toxicity while maximizing the immune system performance. The optimality system for the optimal control problem is derived based on Pontryagin’s Maximum Principle and the resulting system is solved numerically with fourth order Runge-Kunta scheme using forward-backward sweep approach. Simulations of the numerical solution were carried out and findings from the simulations show that biochemotherapy could effectively curtail the growth of the cancer cells remarkably within a reasonable short time. 

 Science Domain

 Journal

 Modelling HIV In-vivo Cellular Dynamics In The Presence Of Antiretroviral Therapy

 A. K. Omoyeni And T. T. Yusuf

 2018

A treatment strategy for the total eradication of human immunodeficiency virus (HIV) in infected individuals is presently not feasible. However, the adoption of highly-active antiretroviral therapy (HAART) has been effective in managing HIV/AIDS infected patients in recent times. In this paper, a deterministic mathematical model is proposed and used to monitor the interactions between uninfected CD4+ T-cells, Infected CD4+ T-cells, CD8+ T-cells, infectious virus and immature non-infectious virus in the course of in-host HIV cellular dynamics. The goal is to find the adequate combination of the treatment regimens that will minimize the treatment systemic costs as well as deliver maximal health benefits to the HIV-positive patients. The model analyses show that the model disease-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than unity. Thereafter, the proposed model is solved numerically and the result simulated for different combinations of the two common antiretroviral drugs effectiveness. Finding from the simulations show that treatment outcome would depend largely on patient’s HIV/AIDS status indicators before initiating treatment and his/her antiretroviral therapy history. 

 Columbia International Publishing

 Journal

 Modelling Marijuana Smoking Epidemics Among Adults: An Optimal Control Panacea

 Tunde T. Yusuf

 2014

Reducing the number of individuals involved in substance abuse in any community is usually a challenging problem. We consider the control of the spread of Marijuana smoking, one substance that is majorly abused, among adults. We propose a deterministic model for controlling the spread of Marijuana smoking incorporating education and awareness campaign as well as rehabilitation as control measures. We formulate a ????ixed time optimal control problem subject to the model dynamics with the goal of ????inding the optimal combination of the control measures that will minimize the cost of the control efforts as well as the prevalence of marijuana smoking in a community. We use Pontryagin's maximum principle to derive the optimality system and solve the system numerically. Results from our simulations are discussed. 

 Taylor & Francis

 Journal

 Optimal Strategy For Controlling The Spread Of HIV/AIDS Disease: A Case Study Of South Africa

 Yusuf, T.T. And Benyah, F.

 2011

HIV/AIDS disease continues to spread alarmingly despite the huge amounts of resources invested in fighting it. There is a need to integrate the series of control measures available to ensure a consistent reduction in the incidence of the disease pending the discovery of its cure.We present a deterministic model for controlling the spread of the disease using change in sexual habits and antiretroviral (ARV) therapy as control measures. We formulate a fixed time optimal control problem subject to the model dynamics with the goal of finding the optimal combination of the two control measures that will minimize the cost of the control efforts as well as the incidence of the disease.We estimate the model state initial conditions and parameter values from the demographic and HIV/AIDS data of South Africa. We use Pontryagin’s maximum principle to derive the optimality system and solve the system numerically. Compared with the practice in most resource-limited settings where ARV treatment is given only to patients with fullblown AIDS, our simulation results suggest that starting the treatment as soon as the patients progress to the pre-AIDS stage of the disease coupled with appreciable change in the susceptible individuals’ sexual habits reduces both the incidence and prevalence of the disease faster. In fact, the results predict that the implementation of the proposed strategy would drive new cases of the disease towards eradication in 10 years. 

 Science Publications

 Journal

 Mathematical Model To Simulate Tuberculosis Disease Population Dynamics

 Koriko, O.K. And Yusuf, T.T.

 2008

A mathematical model to depict Tuberculosis disease population dynamics was presented. The model population was compartmentalised as appropriate and the resulting model equations were solved numerically while different instances of the disease transmission were simulated. The graphical profiles of the various sub-populations with time were presented and discussed based on the results from our simulations. Also, the disease-free and endemic equilibrium of the system were established and analyzed for stability. 

 World Academic Press, World Academic Union

 Journal

 Optimal Control Of Vaccination And Treatment For An SIR Epidemiological Model.

 Yusuf, T.T. And Benyah, F.

 2003

We consider an SIR model with variable size population and formulate an optimal control problem subject to the model with vaccination and treatment as controls. Our aim is to find the optimal combination of vaccination and treatment strategies that will minimize the cost of the two control measures as well as the number of infectives. Our model analyses show that the disease free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity while the endemic equilibrium exists and it is globally asymptotically stable whenever the basic reproduction number is greater than unity. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically. The results show that the optimal combination of vaccination and treatment strategy required to achieve the set objective will depend on the relative cost of each of the control measures. The results from our simulation is discussed.