Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model

Kamgang, Jean Claude; Thron, Christopher

doi:10.1007/s11538-019-00637-6

Cited by 3 publications

(6 citation statements)

References 55 publications

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“…In the population of female mosquitoes, we consider two states of anopheles, namely the active state (looking for the blood meal) and the resting state [13,15,28]. The new anopheles enter the compartment of susceptible in activity at rate Λ v .…”

Section: Mosquito Population Structure and Dynamicsmentioning

confidence: 99%

“…In this subsection, we determine a stability threshold condition using a technique well described and used in [13,28]. In our case, this threshold can be biologically interpreted as the basic reproduction number R 0 [15].…”

Section: Computation Of Threshold Conditionmentioning

confidence: 99%

“…The very first model is that of Ross-MacDonald who thus laid the foundations for modeling malaria [19,26]. Models that include therapeutic (treatment and vaccination) and non-therapeutic (insecticide-treated bed net) measures have flourished in literature [8,13,15,24]. Because insecticide-treated nets (ITNs) reduces human/mosquito contacts, distribution campaigns have been organized in affected countries, including Cameroon.…”

Section: Introductionmentioning

confidence: 99%

“…Mosquitoes insecticide-treated bednets could influence the force of infection, the rate of recruitment of new females mosquitoes or the death rate of mosquitoes [2,6,7,13,15]. In addition to that we consider also that the use of bednet can influence the rate of loss of immunity.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, we focus on a bednet control strategy since the other controls measures are expensive. By other vector controls, we mean outdoor application of larvicides (chemical or biological), breeding habitat reduction (e.g., draining standing water), outdoor vector control (mosquito fogging, attractive toxic sugar bait (ATSB)), indoor residual spraying (IRS), repellents, including topical repellents, mosquito coils, etc, rapid diagnosis and treatment (RDT), preventative drugs like seasonal malaria chemo-prevention (SMC), intermittent preventative treatment (IPT) [15]. Generally, the bednet control in literature concerns bednets, including insecticide-treated bed nets (ITNs), long-lasting insecticide-treated nets (LLINs), and untreated bednets (UBNs) [15].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Optimal Control of a Malaria Model with Long-Lasting Insecticide-Treated Nets

Tchoumi¹,

Kouakep²,

Fotsa³

et al. 2020

Preprint

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A deterministic multi-stage malaria model with a non-therapeutic control measure, the use of mosquito bednet is formulated and analyzed. The model basic reproduction number is derived, and analytical results show that the models equilibria are locally and globally asymptotically stable when certain threshold conditions are satisfied. Pontryagin's Maximum Principle with respect to a time dependent constant is used to derive the necessary conditions for the optimal usage of the Long-Lasting Insecticide-treated bed Nets(LLINs) to mitigate the malaria transmission dynamics. This is accomplished by introducing biologically admissible controls and %-approximate sub-optimal controls. The results from this study could help public health planners and policy decision-makers to design reachable and more practical malaria prevention programs "close" to the optimal strategy.

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Section: Mosquito Population Structure and Dynamicsmentioning

confidence: 99%

Section: Computation Of Threshold Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal Control of a Malaria Model with Long-Lasting Insecticide-Treated Nets

Tchoumi¹,

Kouakep²,

Fotsa³

et al. 2020

Preprint

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Exploring the effects of awareness and time delay in controlling malaria disease propagation

Basir

Banerjee

Ray

2020

International Journal of Nonlinear Sciences and Numerical Simulation

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In this article, a mathematical model has been derived for studying the dynamics of malaria disease and the influence of awareness-based interventions, for control of the same, that depend on ‘level of awareness’. We have assumed the disease transmission rates from vector to human and from human to vector, as decreasing functions of ‘level of awareness’. The effect of insecticides for controlling the mosquito population is influenced by the level of awareness, modelled using a saturated term. Organizing any awareness campaign takes time. Therefore a time delay has been incorporated in the model. Some basic mathematical properties such as nonnegativity and boundedness of solutions, feasibility and stability of equilibria have been analysed. The basic reproduction number is derived which depends on media coverage. We found two equilibria of the model namely the disease-free and endemic equilibrium. Disease-free equilibrium is stable if basic reproduction number (ℛ0) is less than unity (ℛ0 < 1). Stability switches occur through Hopf bifurcation when time delay crosses a critical value. Numerical simulations confirm the main results. It has been established that awareness campaign in the form of using different control measures can lead to eradication of malaria.

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Optimal control of a malaria model with long-lasting insecticide-treated nets

Tchoumi¹,

Kouakep²,

Fotsa³

et al. 2021

MMC

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<abstract><p>A deterministic multi-stage malaria model with a non-therapeutic control measure and the effect of loss of immunity due to the use of the Long-Lasting bednets with a control perspective is formulated and analyzed both theoretically and numerically. The model basic reproduction number is derived, and analytical results show that the model's equilibria are locally and globally asymptotically stable when certain threshold conditions are satisfied. Pontryagin's Maximum Principle with respect to a time dependent constant is used to derive the necessary conditions for the optimal usage of the Long-Lasting Insecticide-treated bednets (LLINs) to mitigate the malaria transmission dynamics. This is accomplished by introducing biologically admissible controls and $ \epsilon\% $-approximate sub-optimal controls. Forward-backward fourth-order Runge-Kutta method is used to numerically solve the optimal control problem. We observe that the disadvantage (loss of immunity, even at its maximum) in the use of bednets is compensated by the benefit of the number of susceptible/infected individuals excluded from the malaria disease dynamics, the only danger being the poor use of the long-lasting bednets. Moreover, it is possible to get closer to the optimal results with a realistic strategy. The results from this study could help public health planners and policy decision-makers to design reachable and more practical malaria prevention programs "close" to the optimal strategy.</p></abstract>

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Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model

Cited by 3 publications

References 55 publications

Optimal Control of a Malaria Model with Long-Lasting Insecticide-Treated Nets

Optimal Control of a Malaria Model with Long-Lasting Insecticide-Treated Nets

Exploring the effects of awareness and time delay in controlling malaria disease propagation

Optimal control of a malaria model with long-lasting insecticide-treated nets

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