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Research paper thumbnail of Stability of Covid-19 Dynamics: A Case Study of Nigeria

Britain International of Exact Sciences (BIoEx) Journal

In this paper, a SEIR epidemic model is considered; where individuals in the population are assig... more In this paper, a SEIR epidemic model is considered; where individuals in the population are assigned to different compartments of SEIR defined with respect to epidemic status of Covid-19 in Nigeria. The article has demonstrated a simple mathematical model for the transmission of Covid-19 disease taking into account loss of human immunity with the aim that this model proves useful in controlling the possibility of a person contracting Covid-19 twice. When the basic reproduction number means that the Covid-19 free equilibrium solution is locally asymptotically stable. This suggests that the number of new cases of the disease will decrease over time and eventually will vanish as that whcih causes are established. The basic reproduction number and the model analysis (local stability of disease-free equilibrium and disease-endemic equilibrium) of the system were calculated and the stability of the SEIR model was checked.

Research paper thumbnail of Stability of Covid-19 Dynamics: A Case Study of Nigeria

In this paper, a SEIR epidemic model is considered; where individuals in the population are assig... more In this paper, a SEIR epidemic model is considered; where individuals in the population are assigned to different compartments of SEIR defined with respect to epidemic status of Covid-19 in Nigeria. The article has demonstrated a simple mathematical model for the transmission of Covid-19 disease taking into account loss of human immunity with the aim that this model proves useful in controlling the possibility of a person contracting Covid-19 twice. When the basic reproduction number means that the Covid-19 free equilibrium solution is locally asymptotically stable. This suggests that the number of new cases of the disease will decrease over time and eventually will vanish as that whcih causes are established. The basic reproduction number and the model analysis (local stability of disease-free equilibrium and disease-endemic equilibrium) of the system were calculated and the stability of the SEIR model was checked.

Research paper thumbnail of Analyzing Corruption Dynamics and Control Measures in Nigeria: A Mathematical Model

Asian Journal of Pure and Applied Mathematics , 2023

This article aims to examine the dynamics of corruption and three control measures proposed to co... more This article aims to examine the dynamics of corruption and three control measures proposed to combat corruptions in Nigeria system. The dynamics of the corruption model were described by the Susceptible-Exposed-Corrupt-Jailed-Honest (SECJH) model using linear ODEs. The corruption elimination threshold is derived from the reproduction number. The optimal control approach employed the application of Pontryagin's maximum principle, which was used to test the effectiveness of proposed control measures. The numerical simulation of the state and adjoint equations was obtained through the application a numerical approach known as Forward-Backward Sweep method and a MATLAB script written for the implementation of the method through Runge-Kutta fourth order method with the controls repeatedly updated for the varying values of 4 . This paper positioned the proposed control measures on three strategies for numerical simulation of the corruption model, the graphical results show the effect of changing 4  on the number of corrupted population by keeping the other parameters constant and It was equally shown that there is a significant increase from strategy A to strategy C. This study shows that compliance with control measures requirements is an effective anti-corruption strategy and a corruptionfree society is possible when the proposed control measures are implemented. It therefore advisable that the proportion of individuals adhering to the honest class and control levels in this work should be interpreted and used with caution.

Research paper thumbnail of Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

Open Journal of Optimization, 2023

In this paper, we characterize lower semi-continuous pseudo-convex functions { } : f X → +∞   o... more In this paper, we characterize lower semi-continuous pseudo-convex functions { } : f X → +∞   on convex subset of real Banach spaces K X ⊂ with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions { } : f X → +∞   on convex subset of real Banach spaces K X ⊂ with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

Research paper thumbnail of Parameters Estimation of COVID-19 SEIR Model

This research study aims to estimate and analysis the transmission rate, progression rate, recove... more This research study aims to estimate and analysis the transmission rate, progression rate, recovery rate, death rate and the basic reproduction number for the Nigeria COVID-19 cases using the non-linear leastsquares method. The disease-dynamics is described by susceptibleexposedinfectedrecovered (SEIR) epidemic model using the non-linear ODEs. The disease eradication threshold is derived from the reproduction number 0 R , where 201866. 2 0  R. The estimated parameters are used to model the disease outbreak's possible trajectories. The computed R-squared for the curve-fit is 0.97 and the error of our model estimate, for the first 62 days, is between 0 and 0.000001. These results point to the reliability and accuracy of the model estimates. Our result further shows that the peak day of the spread of the virus will be 155 th day from the start of the outbreak of the infection with about 13,981,546 infected. The observed death case is very minimal, though the number of infected persons is high. The computed immunity rate show that very small (negligible) numbers of recovered persons become susceptible again. Our numerical results shows that administration of covid-19 vaccine with 50% or above effectiveness will reduce the product rates of transmission and progression compared to the social distancing order.

Research paper thumbnail of Optimal Control of COVID-19: Examining the Incidence of Contamination and Its Recurrence in Nigeria

American Journal of Applied Mathematics, Jun 2023

COVID-19 is an epidemic virus infection that is ravaging the world today. There are no pre-existi... more COVID-19 is an epidemic virus infection that is ravaging the world today. There are no pre-existing immunity and People were easily infected by this virus known as severe acute respiratory syndrome coronavirus (SARS-CoV-2) which caused Covid-19 (CDC, 2020). According to available data, the COVID-19 virus transmits most easily amongst people who are in proximity, typically within some feet (6) or meters. In this paper, we present the Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model for the dynamics of COVID-19 outbreak and its optimal control in Nigeria. SEIR is characterized by a system of four non-linear differential equations. We established the existence and uniqueness of solutions of these equations. Using Nigeria's COVID-19 data, we computed the basic reproduction number of the system. Further, an optimal control approach is performed to study the effect of control measure against the spread of the virus, the control level which minimizes the spread and optimal value of the control which maximizes the objective function. Through the application of Pontryagin's Maximum Principle, we determined how the spread of the virus could be suppressed. The investigation shows that an effective strategy in combating the Covid-19 epidemic is adhering to the dictates of the control measures.

Research paper thumbnail of Stability of Covid-19 Dynamics: A Case Study of Nigeria

Britain International of Exact Sciences (BIoEx) Journal

In this paper, a SEIR epidemic model is considered; where individuals in the population are assig... more In this paper, a SEIR epidemic model is considered; where individuals in the population are assigned to different compartments of SEIR defined with respect to epidemic status of Covid-19 in Nigeria. The article has demonstrated a simple mathematical model for the transmission of Covid-19 disease taking into account loss of human immunity with the aim that this model proves useful in controlling the possibility of a person contracting Covid-19 twice. When the basic reproduction number means that the Covid-19 free equilibrium solution is locally asymptotically stable. This suggests that the number of new cases of the disease will decrease over time and eventually will vanish as that whcih causes are established. The basic reproduction number and the model analysis (local stability of disease-free equilibrium and disease-endemic equilibrium) of the system were calculated and the stability of the SEIR model was checked.

Research paper thumbnail of Stability of Covid-19 Dynamics: A Case Study of Nigeria

In this paper, a SEIR epidemic model is considered; where individuals in the population are assig... more In this paper, a SEIR epidemic model is considered; where individuals in the population are assigned to different compartments of SEIR defined with respect to epidemic status of Covid-19 in Nigeria. The article has demonstrated a simple mathematical model for the transmission of Covid-19 disease taking into account loss of human immunity with the aim that this model proves useful in controlling the possibility of a person contracting Covid-19 twice. When the basic reproduction number means that the Covid-19 free equilibrium solution is locally asymptotically stable. This suggests that the number of new cases of the disease will decrease over time and eventually will vanish as that whcih causes are established. The basic reproduction number and the model analysis (local stability of disease-free equilibrium and disease-endemic equilibrium) of the system were calculated and the stability of the SEIR model was checked.

Research paper thumbnail of Analyzing Corruption Dynamics and Control Measures in Nigeria: A Mathematical Model

Asian Journal of Pure and Applied Mathematics , 2023

This article aims to examine the dynamics of corruption and three control measures proposed to co... more This article aims to examine the dynamics of corruption and three control measures proposed to combat corruptions in Nigeria system. The dynamics of the corruption model were described by the Susceptible-Exposed-Corrupt-Jailed-Honest (SECJH) model using linear ODEs. The corruption elimination threshold is derived from the reproduction number. The optimal control approach employed the application of Pontryagin's maximum principle, which was used to test the effectiveness of proposed control measures. The numerical simulation of the state and adjoint equations was obtained through the application a numerical approach known as Forward-Backward Sweep method and a MATLAB script written for the implementation of the method through Runge-Kutta fourth order method with the controls repeatedly updated for the varying values of 4 . This paper positioned the proposed control measures on three strategies for numerical simulation of the corruption model, the graphical results show the effect of changing 4  on the number of corrupted population by keeping the other parameters constant and It was equally shown that there is a significant increase from strategy A to strategy C. This study shows that compliance with control measures requirements is an effective anti-corruption strategy and a corruptionfree society is possible when the proposed control measures are implemented. It therefore advisable that the proportion of individuals adhering to the honest class and control levels in this work should be interpreted and used with caution.

Research paper thumbnail of Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

Open Journal of Optimization, 2023

In this paper, we characterize lower semi-continuous pseudo-convex functions { } : f X → +∞   o... more In this paper, we characterize lower semi-continuous pseudo-convex functions { } : f X → +∞   on convex subset of real Banach spaces K X ⊂ with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions { } : f X → +∞   on convex subset of real Banach spaces K X ⊂ with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

Research paper thumbnail of Parameters Estimation of COVID-19 SEIR Model

This research study aims to estimate and analysis the transmission rate, progression rate, recove... more This research study aims to estimate and analysis the transmission rate, progression rate, recovery rate, death rate and the basic reproduction number for the Nigeria COVID-19 cases using the non-linear leastsquares method. The disease-dynamics is described by susceptibleexposedinfectedrecovered (SEIR) epidemic model using the non-linear ODEs. The disease eradication threshold is derived from the reproduction number 0 R , where 201866. 2 0  R. The estimated parameters are used to model the disease outbreak's possible trajectories. The computed R-squared for the curve-fit is 0.97 and the error of our model estimate, for the first 62 days, is between 0 and 0.000001. These results point to the reliability and accuracy of the model estimates. Our result further shows that the peak day of the spread of the virus will be 155 th day from the start of the outbreak of the infection with about 13,981,546 infected. The observed death case is very minimal, though the number of infected persons is high. The computed immunity rate show that very small (negligible) numbers of recovered persons become susceptible again. Our numerical results shows that administration of covid-19 vaccine with 50% or above effectiveness will reduce the product rates of transmission and progression compared to the social distancing order.

Research paper thumbnail of Optimal Control of COVID-19: Examining the Incidence of Contamination and Its Recurrence in Nigeria

American Journal of Applied Mathematics, Jun 2023

COVID-19 is an epidemic virus infection that is ravaging the world today. There are no pre-existi... more COVID-19 is an epidemic virus infection that is ravaging the world today. There are no pre-existing immunity and People were easily infected by this virus known as severe acute respiratory syndrome coronavirus (SARS-CoV-2) which caused Covid-19 (CDC, 2020). According to available data, the COVID-19 virus transmits most easily amongst people who are in proximity, typically within some feet (6) or meters. In this paper, we present the Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model for the dynamics of COVID-19 outbreak and its optimal control in Nigeria. SEIR is characterized by a system of four non-linear differential equations. We established the existence and uniqueness of solutions of these equations. Using Nigeria's COVID-19 data, we computed the basic reproduction number of the system. Further, an optimal control approach is performed to study the effect of control measure against the spread of the virus, the control level which minimizes the spread and optimal value of the control which maximizes the objective function. Through the application of Pontryagin's Maximum Principle, we determined how the spread of the virus could be suppressed. The investigation shows that an effective strategy in combating the Covid-19 epidemic is adhering to the dictates of the control measures.