Journal of Applied Mathematics and Computing, Apr 22, 2022
Tuberculosis is an infectious disease caused by bacteria that most commonly affects the lungs. Du... more Tuberculosis is an infectious disease caused by bacteria that most commonly affects the lungs. Due to its high mortality, it remains a global health issue, and it is one of the leading causes of death in the majority of sub-Saharan African countries. We formulate a six-compartmental deterministic model to investigate the impact of vaccination on the dynamics of tuberculosis in a given population. The qualitative behaviors of the presented model were examined, and the respective threshold quantity was obtained. The tuberculosis-free equilibrium of the system is said to be locally asymptotically stable when the effective reproduction number R 0 < 1 and unstable otherwise. Furthermore, we examined the stability of the endemic equilibrium, and the conditions for the existence of backward bifurcation are discussed. A numerical simulation was performed to demonstrate and support the theoretical findings. The result shows that reducing the effective contact with an infected person and enhancing the rate of vaccinating susceptible individuals with high vaccine efficacy will reduce the burden of tuberculosis in the population.
In this paper, we present a deterministic mathematical model of monkeypox virus by using both cla... more In this paper, we present a deterministic mathematical model of monkeypox virus by using both classical and fractional-order differential equations. The model includes all of the possible interactions that contribute to disease spread in the population. We investigate the model's stability results in the disease-free case when R 0 < 1. When R 0 < 1, we show that the model is stable, otherwise it is unstable. To obtain the best fit that describes the dynamics of this disease in Nigeria, the model is fitted using the nonlinear least square method on cumulative reported cases of monkeypox virus from Nigeria between January to December 2019. Furthermore, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We run numerous simulations of the proposed monkeypox model with varied input parameters to investigate the intricate dynamics of monkeypox infection under the effect of various system input parameters. We investigate the system's dynamical behavior to develop appropriate infection control policies. This allows the public to understand the significance of control parameters in the eradication of monkeypox in the population. Lowering the order of fractional derivatives has resulted in significant modifications. To the community's policymakers, we offered numerous parameters for the control of monkeypox.
Infectious diseases have remained one of humanity’s biggest problems for decades. Multiple diseas... more Infectious diseases have remained one of humanity’s biggest problems for decades. Multiple disease infections, in particular, have been shown to increase the difficulty of diagnosing and treating infected people, resulting in worsening human health. For example, the presence of influenza in the population is exacerbating the ongoing COVID-19 pandemic. We formulate and analyze a deterministic mathematical model that incorporates the biological dynamics of COVID-19 and influenza to effectively investigate the co-dynamics of the two diseases in the public. The existence and stability of the disease-free equilibrium of COVID-19-only and influenza-only sub-models are established by using their respective threshold quantities. The result shows that the COVID-19 free equilibrium is locally asymptotically stable when RC<1, whereas the influenza-only model, is locally asymptotically stable when RF<1. Furthermore, the existence of the endemic equilibria of the sub-models is examined while the conditions for the phenomenon of backward bifurcation are presented. A generalized analytical result of the COVID-19-influenza co-infection model is presented. We run a numerical simulation on the model without optimal control to see how competitive outcomes between-hosts and within-hosts affect disease co-dynamics. The findings established that disease competitive dynamics in the population are determined by transmission probabilities and threshold quantities. To obtain the optimal control problem, we extend the formulated model by including three time-dependent control functions. The maximum principle of Pontryagin was used to prove the existence of the optimal control problem and to derive the necessary conditions for optimum disease control. A numerical simulation was performed to demonstrate the impact of different combinations of control strategies on the infected population. The findings show that, while single and twofold control interventions can be used to reduce disease, the threefold control intervention, which incorporates all three controls, will be the most effective in reducing COVID-19 and influenza in the population.
Journal of Applied Mathematics and Computing, Apr 22, 2022
Tuberculosis is an infectious disease caused by bacteria that most commonly affects the lungs. Du... more Tuberculosis is an infectious disease caused by bacteria that most commonly affects the lungs. Due to its high mortality, it remains a global health issue, and it is one of the leading causes of death in the majority of sub-Saharan African countries. We formulate a six-compartmental deterministic model to investigate the impact of vaccination on the dynamics of tuberculosis in a given population. The qualitative behaviors of the presented model were examined, and the respective threshold quantity was obtained. The tuberculosis-free equilibrium of the system is said to be locally asymptotically stable when the effective reproduction number R 0 &lt; 1 and unstable otherwise. Furthermore, we examined the stability of the endemic equilibrium, and the conditions for the existence of backward bifurcation are discussed. A numerical simulation was performed to demonstrate and support the theoretical findings. The result shows that reducing the effective contact with an infected person and enhancing the rate of vaccinating susceptible individuals with high vaccine efficacy will reduce the burden of tuberculosis in the population.
In this paper, we present a deterministic mathematical model of monkeypox virus by using both cla... more In this paper, we present a deterministic mathematical model of monkeypox virus by using both classical and fractional-order differential equations. The model includes all of the possible interactions that contribute to disease spread in the population. We investigate the model's stability results in the disease-free case when R 0 &lt; 1. When R 0 &lt; 1, we show that the model is stable, otherwise it is unstable. To obtain the best fit that describes the dynamics of this disease in Nigeria, the model is fitted using the nonlinear least square method on cumulative reported cases of monkeypox virus from Nigeria between January to December 2019. Furthermore, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We run numerous simulations of the proposed monkeypox model with varied input parameters to investigate the intricate dynamics of monkeypox infection under the effect of various system input parameters. We investigate the system's dynamical behavior to develop appropriate infection control policies. This allows the public to understand the significance of control parameters in the eradication of monkeypox in the population. Lowering the order of fractional derivatives has resulted in significant modifications. To the community's policymakers, we offered numerous parameters for the control of monkeypox.
Infectious diseases have remained one of humanity’s biggest problems for decades. Multiple diseas... more Infectious diseases have remained one of humanity’s biggest problems for decades. Multiple disease infections, in particular, have been shown to increase the difficulty of diagnosing and treating infected people, resulting in worsening human health. For example, the presence of influenza in the population is exacerbating the ongoing COVID-19 pandemic. We formulate and analyze a deterministic mathematical model that incorporates the biological dynamics of COVID-19 and influenza to effectively investigate the co-dynamics of the two diseases in the public. The existence and stability of the disease-free equilibrium of COVID-19-only and influenza-only sub-models are established by using their respective threshold quantities. The result shows that the COVID-19 free equilibrium is locally asymptotically stable when RC<1, whereas the influenza-only model, is locally asymptotically stable when RF<1. Furthermore, the existence of the endemic equilibria of the sub-models is examined while the conditions for the phenomenon of backward bifurcation are presented. A generalized analytical result of the COVID-19-influenza co-infection model is presented. We run a numerical simulation on the model without optimal control to see how competitive outcomes between-hosts and within-hosts affect disease co-dynamics. The findings established that disease competitive dynamics in the population are determined by transmission probabilities and threshold quantities. To obtain the optimal control problem, we extend the formulated model by including three time-dependent control functions. The maximum principle of Pontryagin was used to prove the existence of the optimal control problem and to derive the necessary conditions for optimum disease control. A numerical simulation was performed to demonstrate the impact of different combinations of control strategies on the infected population. The findings show that, while single and twofold control interventions can be used to reduce disease, the threefold control intervention, which incorporates all three controls, will be the most effective in reducing COVID-19 and influenza in the population.
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Papers by Mayowa M Ojo