On the Population Dynamics of the Malaria Vector

Ngwa, Gideon A.

doi:10.1007/s11538-006-9104-x

Cited by 62 publications

(57 citation statements)

References 20 publications

(19 reference statements)

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“…The forms M B L and M B S are the Verhulst-Pearl logistic (Abdelrazec et al 2014;Ngwa 2005) and Maynard-Smith-Slatkin (Brannstrom and Sumpter 2005) oviposition functions, respectively. It should be mentioned that, in the form B L , the non-negativity condition on B(M) will only hold if M < K (hence, K is assumed to be greater than M).…”

Section: F L (T R)mentioning

confidence: 99%

Mathematical assessment of the role of temperature and rainfall on mosquito population dynamics

Abdelrazec

Gumel

2016

J. Math. Biol.

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A new stage-structured model for the population dynamics of the mosquito (a major vector for numerous vector-borne diseases), which takes the form of a deterministic system of non-autonomous nonlinear differential equations, is designed and used to study the effect of variability in temperature and rainfall on mosquito abundance in a community. Two functional forms of eggs oviposition rate, namely the Verhulst-Pearl logistic and Maynard-Smith-Slatkin functions, are used. Rigorous analysis of the autonomous version of the model shows that, for any of the oviposition functions considered, the trivial equilibrium of the model is locally-and globally-asymptotically stable if a certain vectorial threshold quantity is less than unity. Conditions for the existence and global asymptotic stability of the non-trivial equilibrium solutions of the model are also derived. The model is shown to undergo a Hopf bifurcation under certain conditions (and that increased density-dependent competition in larval mortality reduces the likelihood of such bifurcation). The analyses reveal that the Maynard-Smith-Slatkin oviposition function sustains more oscillations than the Verhulst-Pearl logistic function (hence, it is more suited, from ecological viewpoint, for modeling the egg oviposition process). The non-autonomous model is shown to have a globally-asymptotically stable trivial periodic solution, for each of the oviposition functions, when the associated reproduction threshold is less than unity. Furthermore, this model, in the absence of density-dependent mortality rate for larvae, has a unique and globally-asymptotically stable periodic solution under certain conditions. Numerical simulations of the non-autonomous model, using mosquito surveillance and weather data from the Peel region of Ontario, Canada, show a peak mosquito abundance for temperature and rainfall values in the range [20−25] • C and [15-35] mm, respectively. These ranges are recorded in the Peel region between July and August (hence, this study suggests that anti-mosquito control effects should be intensified during this period).

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Section: F L (T R)mentioning

confidence: 99%

Mathematical assessment of the role of temperature and rainfall on mosquito population dynamics

Abdelrazec

Gumel

2016

J. Math. Biol.

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“…Subsequent contributions have been made to extend the Ross-Macdonald malaria models considering age structure in the human population (Aron and May, 1982;Dietz, 1988;Anderson and May, 1991), acquired immunity (Aron and May, 1982;Aron, 1988), latency (Koella, 1991;Lopez et al, 2002;Koella and Antia, 2003;Koella and Boëte, 2003), spatial heterogeneity (Dye and Hasibeder, 1986;Hasibeder and Dye, 1988;Gupta and Hill, 1995;Gupta et al, 1994;Torres-Sorando and Rodriguez, 1997;Rodriguez and Torres-Sorando, 2001), individual-based models , habitat-based models (Gu and Novak, 2005), integrated models (McKenzie and Bossert, 2005), among other aspects (Bailey, 1982;Chitnis et al, 2006;Gu et al, 2003b;Killeen et al, 2000;McKenzie, 2000;Ngwa, 2006;Smith et al, , 2005.…”

Section: Introductionmentioning

confidence: 99%

On the Delayed Ross–Macdonald Model for Malaria Transmission

2008

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The feedback dynamics from mosquito to human and back to mosquito involve considerable time delays due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a delayed RossMacdonald model. Then we calculate the basic reproduction number R 0 and carry out some sensitivity analysis of R 0 on the incubation periods, that is, to study the effect of time delays on the basic reproduction number. It is shown that the basic reproduction number is a decreasing function of both time delays. Thus, prolonging the incubation periods in either humans or mosquitos (via medicine or control measures) could reduce the prevalence of infection.

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“…As malaria is one of the most serious health problems facing the world today, several studies have been made in an attempt to understand its dynamics and predict what may happen and then suggest strategies to eliminate it [3,8,10,12,15,21,22]. In this paper, a deterministic model (SIS for humans and SI for mosquitoes) has been studied.…”

Section: Discussionmentioning

confidence: 99%

“…An important extension of the model was proposed by Dietz et al [12] who added the inclusion of immunity. Thereafter, other extensive studies for malaria models have been carried out (see [3,19,21,22,29] and the references therein). Other studies concerning the effect of climatic changes and weather on malaria dynamics are shown in [13,23,24].…”

Section: Introductionmentioning

confidence: 99%

Demographic Impact and Controllability of Malaria in an SIS Model with Proportional Fatality

Safan

Ghazi

2015

Bull. Malays. Math. Sci. Soc.

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The aim of this paper is to study the demographic impact of malaria on the host population and investigate the possibility to eliminate it with a strategy based on prevention (e.g., the use of bed nets). In this paper, a deterministic model for the transmission of malaria (with variable human and mosquito population sizes) has been studied. The model equilibria have been found. Their local and global stability have been analyzed. An exact formula for the critical case fatality required to stop the growth of the host has been found. The conditions to eliminate malaria with a strategy based on the use of bed nets have been found.

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On the Population Dynamics of the Malaria Vector

Cited by 62 publications

References 20 publications

Mathematical assessment of the role of temperature and rainfall on mosquito population dynamics

Mathematical assessment of the role of temperature and rainfall on mosquito population dynamics

On the Delayed Ross–Macdonald Model for Malaria Transmission

Demographic Impact and Controllability of Malaria in an SIS Model with Proportional Fatality

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