Analysis of a malaria model with mosquito host choice and bed-net control

Buonomo, Bruno

doi:10.1142/s1793524515500771

Cited by 23 publications

(12 citation statements)

References 39 publications

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“…Furthermore, by using the modelling approach employed first in [9] and later in [4][5][6]29], we divide humans into two compartments: susceptible, S h (t), who are not infected with malaria, and infectious, I h (t), who carry gametocytes. We denote the increased relative attractiveness of infectious humans as compared to susceptible humans (vector-bias parameter) by p. For simplicity, we assume that humans infected with malaria are always infectious; thus ignoring the incubation period and any variations in gametocyte density over time.…”

Section: The Modelmentioning

confidence: 99%

Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans

2016

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We develop and analyse a deterministic population-based ordinary differential equation of malaria transmission to consider the impact of three common assumptions of malaria models: (1) malaria infection does not change the attractiveness of humans to mosquitoes; (2) exposed mosquitoes (infected with malaria but not yet infectious to humans) have the same biting rate as susceptible mosquitoes; and (3) mosquitoes infectious to humans have the same biting rate as susceptible mosquitoes. We calculate the basic reproductive number, R 0 , for this model and show the existence of a transcritical bifurcation at R 0 = 1, in common with most epidemiological models. We further show that for some sets of parameter values, this bifurcation can be backward (subcritical). We show with numerical simulations that increasing the relative attractiveness of infectious humans, increases R 0 but reduces the equilibrium prevalence of infectious humans; decreasing the biting rate of exposed mosquitoes increases R 0 and the equilibrium prevalence of infectious humans and mosquitoes; and increasing the biting rate of infectious mosquitoes has no impact on R 0 or the equilibrium prevalence of infectious humans, but decreases the infectious prevalence of infectious mosquitoes. These analyses of a simple malaria model show that common assumptions around the relative attractiveness of infectious humans and the relative biting rates of exposed and infectious mosquitoes can have substantial and counter-intuitive effects on malaria transmission dynamics.

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Section: The Modelmentioning

confidence: 99%

Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans

2016

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“…h is the annual rate of infections of individuals [12], 0 < k ≤ 0.4466 and 0.4466 = 76.6 × 58.3 is the probability to be likely protected from the common perfect possession and use of the bed nets in Cameroon [2], [5] over three years of use of the Long-lasting insecticide-treated bed nets (LLINs). We have the average value γ = 1 180 180 0 γ(t)dt (180 days is estimated by Raoult [22]) of γ that leads to…”

Section: A Model Equationmentioning

confidence: 99%

“…C. Simulation of model (1) with initial condition P 2 and g(t, θ) = 1 − 1 10 γ(t, θ) In this case, the immigration rate in humans is e = 1000 59 * 365 (see Table 1, page 4, [5]). For other parameter values, see Table I with α = 0.85 (assumed).…”

Section: Numerical Simulationsmentioning

confidence: 99%

Mathematical model for acquiring immunity to malaria: a PDE approach

Tchoumi¹,

Kouakep

Fotsa³

et al. 2021

BIOMATH

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We develop a new model of integro-differential equations coupled with a partial differential equation that focuses on the study of the? naturally acquiring immunity to malaria induced by exposure to infection. We analyze a continuous acquisition of immunity after infected individuals are treated. It exhibits complex and realistic mechanisms precised mathematically in both disease free or endemic context and in several numerical simulations showing the interplay between infection through the bite of mosquitoes. The model confirms the (partial) premunition of the human population in the regions where malaria is endemic. As common in literature, we indicate an equivalence of the basic reproduction rate as the spectral radius of a next generation operator.

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“…To improve malaria control, there is need to study and identify the mechanisms by which other sensory cues are detected by mosquito and the potential strategies to block them (Agusto et al, 2013;Buonomo, 2013;Chitnis, 2010;Hawlay, 2003;WHO, 2013WHO, , 2014. Insect repellents and other protective odorants can be used to prevent bites.…”

Section: Related Literaturesmentioning

confidence: 99%

Simulation of a Mathematical Model of Malaria Transmission Dynamics in the Presence of Mosquito Net, Fumigation And Treatment

Chinebu¹,

Ezennorom²,

Okwor³

2018

IJTSRD

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We proposed and solved a combined control malaria system of fifteen ordinary differential equations modeling the transmission dynamics of malaria between humans and mosquitoes. Since our aim is to minimize the number of exposed and infectious human, we discussed the disease free equilibrium and estimated the basic reproduction number using the next generation matrix method. The disease free equilibrium was asymptotically stable when the reproduction number is less than one and unstable when it is greater than one. Numerical results are provided using matlab software to confirm the analyzed results. Our findings were that malaria may be controlled using the combined control method, the insecticide treated bed nets, fumigation of the surroundings and active malaria drug as this will reduce the contact rate between human and mosquito through reduction in mosquito population and malaria transmission.

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Analysis of a malaria model with mosquito host choice and bed-net control

Cited by 23 publications

References 39 publications

Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans

Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans

Mathematical model for acquiring immunity to malaria: a PDE approach

Simulation of a Mathematical Model of Malaria Transmission Dynamics in the Presence of Mosquito Net, Fumigation And Treatment

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