Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

Keno, Temesgen Duressa; Dano, Lemesa Bedjisa; Makinde, Oluwole Daniel

doi:10.1155/2022/9667396

Cited by 7 publications

(6 citation statements)

References 32 publications

(36 reference statements)

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“…Proof: The local stability of the disease-free equilibrium point of HIV mono-infection model ( 7) is evaluated by applying the Routh-Hurwitz stability criteria stated in [52].…”

Section: Plos Onementioning

confidence: 99%

“…In this section, we provide a thorough qualitative analysis of the time-dependent HIV/AIDS and COVID-19 co-infection model (3). The Pontryagin's Maximum Principle stated in literatures [25,43,51,52,55] is used to describe this analysis, with the aim of minimizing the HIV/ AIDS infection aware individuals denoted by H a , the COVID-19 infected individuals denoted by C i and the total HIV/AIDS and COVID-19 co-infected individuals denoted by M u + M a . In the case of time-dependent optimal control, we employ Pontryagin's Maximum Principle to derive the necessary conditions for diseases control mechanisms.…”

Section: Analysis Of the Optimal Control Strategymentioning

confidence: 99%

“…Their result suggested that the combination of treatment of infected humans and insecticide spraying was proved to be the best efficient and least costly strategy to eradicate the disease. Keno et al [52] investigated a mathematical model with optimal control strategies for malaria transmission with role of climate variability. Their result suggested that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

2023

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HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin’s Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV/AIDS and COVID-19 co-infection in the community under consideration of the study.

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“…Proof: The local stability of the disease-free equilibrium point of HIV mono-infection model ( 7) is evaluated by applying the Routh-Hurwitz stability criteria stated in [52].…”

Section: Plos Onementioning

confidence: 99%

Section: Analysis Of the Optimal Control Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

2023

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“…Te total number of people averted is calculated by subtracting the total number of new cases with control from the total number of new cases without control using numerical simulation results from the COVID-19 model (40). Utilizing each strategy's specifc cost functions 1/2B 1 u 2 1 , 1/2B 2 u 2 2 and 1/2B 3 u 2 3 [23,44], it is possible to determine the total cost of each strategy over the course of the intervention.…”

Section: Icer �mentioning

confidence: 99%

Optimal Control Strategies of COVID-19 Dynamics Model

Keno

Etana

2023

Journal of Mathematics

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In this paper, we proposed the optimal control for the dynamics of COVID-19 with cost effectiveness strategies. First, we showed that model solution is positive, and bounded in a fixed domain. Besides, we used next-generation matrix to compute the basic reproduction number. If the basic reproduction number is less than one, then the disease-free equilibrium point is both locally and globally stable, respectively, via the help of Jacobian matrix and Lyapunov function, otherwise the endemic equilibrium occurs. The sensitivity analysis was determined with regard to all basic parameters. Then the model is fitted with COVID-19 infected cases reported from October 1, 2022 to October 30, 2022 in Ethiopia. The values of model parameters are then estimated from the data reported using the least-square method. Furthermore, using Pontryagin maximum principle, the model is extended to optimal control incorporating three control namely: personal protective, vaccination, and treatment of infected humans. Finally, based upon the numerical simulation of optimal controls and cost effectiveness analysis, the most optimal and less costly strategy to minimize the disease is combination of vaccination and treatment of infected.

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“…In [24], Mangongo et al added relapse ignorant infected humans compartment to their model. In [25], the effect of climate variability considered in the model and optimal control.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model for Malaria Disease Transmission

Alhaj

2023

J. Math. Anal. Model.

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Malaria is one of the fatal diseases caused by plasmodium parasites and transmitted to humans through biting of the female of {\it Anopheles} mosquitoes. We proposed a deterministic mathematical model for simulating Malaria disease transmission between humans and mosquitoes. The basic reproduction number $\mathcal{R}_{0}$ is determined by using the next-generation matrix approach. Stability conditions for the model equilibrium points with respect to $\mathcal{R}_{0}$ derived and we show that the forward bifurcation occurred. When $\mathcal{R}_{0} <1$ or $\mathcal{R}_{0} >1$ the Malaria disease dies out or spreads, respectively. The sensitivity analysis for the basic reproduction number $\mathcal{R}_{0}$ fulfilled locally and globally. The model simulation was found by using Runge--Kutta fourth order method in MATLAB. Furthermore, The effects of the important parameters were investigated, and the obtained results were presented in graphical forms. Also, we obtained that the simulation results agree with the stability analysis for $E_{def}$. We discussed the impacts of the Malaria disease control interventions on the important parameter for Malaria disease transmission. Recommendation for control and eradicating Malaria disease transmission provided.

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Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

Cited by 7 publications

References 32 publications

Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

Optimal Control Strategies of COVID-19 Dynamics Model

Mathematical Model for Malaria Disease Transmission

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