A co-infection model on TB - COVID-19 with optimal control and sensitivity analysis

Bandekar, Shraddha Ramdas; Ghosh, Mini

doi:10.1016/j.matcom.2022.04.001

Cited by 23 publications

(17 citation statements)

References 38 publications

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“…Although many models have been proposed recently to study the coinfection dynamics of COVID-19 and other diseases [41,42,43,44,45,46], our work is the first that takes into account the distinctive features of bacterial pneumonia, in particular, the inclusion of two infection ways (community and hospital transmission).…”

Section: Resultsmentioning

confidence: 99%

“…They determined conditions for the stability of equilibria, showed that the model may undergo a backward bifurcation and derived conditions for optimal control to mitigate the spread of both diseases. Tuberculosis-COVID-19 coinfection has been modelled by Bandedar and Ghosh [43], who considered a model with waning immunity and performed a bifurcation and stability analysis, as well as simulations using data from India. A different model for tuberculosis coinfection was studied by Rwezaura et al [44], who investigated the effects of COVID-19 vaccination and treatment control and performed parameter fitting with data from Indonesia.…”

Section: Introductionmentioning

confidence: 99%

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A model for COVID-19 and bacterial pneumonia coinfection with community- and hospital-acquired infections

Pérez

Oluyori

2022

mmnsa

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We propose a new epidemic model to study the coinfection dynamics of COVID-19 and bacterial pneumonia, which is the first model in the literature used to describe mathematically the interaction of these two diseases while considering two infection ways for pneumonia: community-acquired and hospital-acquired transmission. We show that the existence and local stability of equilibria depend on three different parameters, which are interpreted as the basic reproduction numbers of COVID-19, bacterial pneumonia, and bacterial population in the hospital. Numerical simulations are performed to complement our theoretical analysis, and we show that both diseases can persist if the basic reproduction number of COVID-19 is greater than one.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A model for COVID-19 and bacterial pneumonia coinfection with community- and hospital-acquired infections

Pérez

Oluyori

2022

mmnsa

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“…In this section, we present optimality conditions for the optimal control problem defined above and detail its properties. According to Pontryagin’s Maximum Principle in 4 , 13 , 37 , if is optimal for dynamical system (10) with initial value (11) and (14) with fixed final time , then there exists a non-trivial absolutely continuous mapping called the adjoint vector, such that. The Hamiltonian function is defined as The control system is The adjoint system And the optimality condition is Moreover, the transversality condition is holds for almost all also holds true.…”

Section: Optimal Control Analysis Of the Deterministic Modelmentioning

confidence: 99%

Mathematical modeling analysis on the dynamics of university students animosity towards mathematics with optimal control theory

Teklu

Terefe

2022

Sci Rep

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Animosity towards mathematics is a very common worldwide problem and it is usually caused by wrong information, low participation, low challenge tolerance, falling further behind, being unemployed, and avoiding the advanced math classes needed for success in many careers. In this study, we have considered and formulated the new SEATS compartmental mathematical model with optimal control theory to analyze the dynamics of university students’ animosity towards mathematics. We applied the next-generation matrix, Ruth-Hurwitz criteria, Lyapunov function, and Volterra-Lyapunov stable matrices to show local and global stability of equilibrium points of the model respectively. The study demonstrated that the animosity-free equilibrium point is both locally and globally asymptotically stable whenever the model basic reproduction number is less than unity, whereas the animosity-dominance equilibrium point is both locally and globally asymptotically stable when the model basic reproduction number is greater than unity. Finally, we applied numerical ode45 solvers using the Runge–Kutta method and we have carried out numerical simulations and shown that applying both prevention and treatment controls is the best strategy to minimize and possibly eradicate the animosity-infection in the community under consideration.

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“…To conduct further analysis on the qualitative behaviour of our model, it is important to determine the related basic reproduction number of our proposed model. In many epidemiological models, basic reproduction number holds an important role in determining that the diseases die out or exist in the population [34][35][36][37][38]. Basic reproduction number is defined as the expected number of secondary cases caused by one primary case during infection period in a completely susceptible population [39,40].…”

Section: Malaria-free Equilibrium and The Basic Reproduction Numbermentioning

confidence: 99%

Dynamical Analysis on a Malaria Model with Relapse Preventive Treatment and Saturated Fumigation

Aldila

2022

Computational and Mathematical Methods in Medicine

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Malaria has produced health issues in many parts of the world. One of the reason is due to the recurrence phenomenon, which can happen years after the main infection has appeared in the human body. Furthermore, the fumigation intervention, which has become a major worry in several regions of the world, has yielded unsatisfactory results, as seen by the high number of cases reported each year in several African countries. We present a novel mathematical model that integrates tafenoquine treatments to prevent relapse in the human population and saturation fumigation to control mosquito populations in this study. The endemic threshold, also known as the basic reproduction number, is calculated analytically, as is the existence and local stability of the equilibrium points. Through careful investigation, we discovered that the malaria-free equilibrium is locally asymptotically stable if the basic reproduction number is less than one and unstable if it is greater than one. According to the sensitivity analysis, the utilization of tafenoquine treatment is inversely proportional to the basic reproduction number. Although our model never exhibits a backward bifurcation at the basic reproduction number equal to one, we have demonstrated that it is possible; when the basic reproduction number is greater than one, two stable malaria-endemic equilibrium can exist. As a result, when the basic reproduction number is more than one, the final state will be determined by the initial condition of the population. As a result, enormous temporal fumigation can shift the stability of our malaria model from a big endemic size to a smaller endemic size, which is more advantageous in terms of the malaria prevention strategy. Despite the fact that this is not a case study, the numerical results presented in this article are intended to support any theoretical analysis of current malaria eradication tactics in the field.

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A co-infection model on TB - COVID-19 with optimal control and sensitivity analysis

Cited by 23 publications

References 38 publications

A model for COVID-19 and bacterial pneumonia coinfection with community- and hospital-acquired infections

A model for COVID-19 and bacterial pneumonia coinfection with community- and hospital-acquired infections

Mathematical modeling analysis on the dynamics of university students animosity towards mathematics with optimal control theory

Dynamical Analysis on a Malaria Model with Relapse Preventive Treatment and Saturated Fumigation

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