Optimal control of malaria transmission dynamics combining some usual strategies and an imperfect vaccine

Koutou, Ousmane; Sangaré, Boureima; Traore, Bakary Abou

doi:10.7151/dmdico.1221

Cited by 4 publications

(2 citation statements)

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“…Mathematical modelling helps in comprehending the dynamics of disease transmission and its control strategy. In epidemic models, the theory of optimal control is particularly fascinating and helpful [7,17,25,28]. As far as innovation diffusion modelling is concerned, Chugh et al [2] analyzed a four-compartmental system with the help of optimal control theory to examine the interaction and market dissemination of two product categories.…”

Section: Motivation and Novelty In The Papermentioning

confidence: 99%

An innovation diffusion model with two innovations under two simultaneous effects in a competitive market: co-existence through optimal control

Chugh,

Dhar,

Guha

2024

J. Math. Computer Sci.

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Since mass media plays an important role in influencing the non-adopter population, the adoption rate changes with the media awareness rate. Motivated by this concept, in this paper, a model of three non-intersecting classes of non-adopters, adopters for product-I and adopters for product-II is proposed. Under the influence of media coverage and word-of-mouth, the dynamic behaviour of the system is investigated. The basic influence numbers R 0 1 and R 0 2 associated with the first and second innovations help in performing stability analysis. It is observed from stability analysis that adopter-free equilibrium is conditionally stable. Also, the system has no stable interior equilibrium point. The basic influence numbers determine the sustainability of a particular product in the market. The optimal control theory is used to reduce the frustration rate in both adopter classes. The Hamiltonian function is constructed using the extended optimum control model and is then solved according to Pontryagin's maximum principle to get the cost. Also, coexistence is possible with the implementation of optimal control. Sensitivity analysis has been performed for both the basic influence numbers R 0 1 and R 0 2 . Lastly, numerical experimentations have been executed to assist analytical findings with distinct sets of parameters.

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Section: Motivation and Novelty In The Papermentioning

confidence: 99%

An innovation diffusion model with two innovations under two simultaneous effects in a competitive market: co-existence through optimal control

Chugh,

Dhar,

Guha

2024

J. Math. Computer Sci.

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“…In spite of some control interventions that have been employed, it has kept spreading and has become a serious threat for most developing countries. Therefore, controlling it becomes extremely important [2,23,25]. So, it is now a great necessity to raise the level of comprehension of schistosomiasis' global behaviour in order to propose some good control strategies.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Schistosomiasis Global Dynamics with General Incidence Functions and Two Delays

Koutou

Traoré

Sangaré

2021

Int. J. Appl. Comput. Math

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As most communicable diseases, schistosomiasis transmission mechanism involves some delay due to the incubation period. In this study, we seek to investigate the impact of incubation period on schistosomiasis global transmission dynamics. For that, starting from our previous work and using delay differential equations, we have proposed a more sophisticated model in which the new feature we accounted is the latency period in both human and snail hosts. Then, under some suitable assumptions, the mathematical analysis of the model has been done. Specifically, we calculated the basic reproduction number and showed its dependence on the delays in both humans and snails as follows: when the delays in humans and snails increase, R 0 decreases. We also proved that when R 0 < 1, the no-disease point is globally asymptotically stable and when R 0 > 1, the system is uniformly persistent and admits a unique endemic equilibrium. Besides, by formulating a suitable Lyapunov function, we established that the unique endemic steady state of the model is globally asymptotically stable when the threshold parameter R 0 exceeds 1. Furthermore, sensitivity analysis has been carried out to show how parameters variations affect the model global behaviour. We finished by illustrating some numerical results that are well in keeping with our theoretical findings.

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Optimal control analysis of a COVID-19 and Tuberculosis (TB) co-infection model with an imperfect vaccine for COVID-19

Diabaté

Sangaré

Koutou

2023

SeMA

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This paper presents a co-infection mathematical model of COVID-19 and TB to study their synergistic dynamics. We first investigated the single infection models of each disease and then the co-infection dynamics of the two diseases. Indeed, we calculated the basic reproduction number of each model, and then we studied the existence and the stability of the equilibrium points. We subsequently proved that the TB only infection model and the co-infection model exhibit backward and forward bifurcations. In addition, we performed a sensitivity analysis of the basic reproduction numbers to determine which parameters influence them the most. Furthermore, we applied Pontryagin’s maximum principle to our co-infection model to assess the impact of the use of an imperfect vaccine for COVID-19, taken as an optimal control strategy. Finally, we presented the results of the numerical simulations to support the theoretical findings.

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Optimal control of malaria transmission dynamics combining some usual strategies and an imperfect vaccine

Cited by 4 publications

References 0 publications

An innovation diffusion model with two innovations under two simultaneous effects in a competitive market: co-existence through optimal control

An innovation diffusion model with two innovations under two simultaneous effects in a competitive market: co-existence through optimal control

Analysis of Schistosomiasis Global Dynamics with General Incidence Functions and Two Delays

Optimal control analysis of a COVID-19 and Tuberculosis (TB) co-infection model with an imperfect vaccine for COVID-19

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