Periodic oscillations and backward bifurcation in a model for the dynamics of malaria transmission

Ngonghala, Calistus N.; Ngwa, Gideon A.; Teboh-Ewungkem, Miranda I.

doi:10.1016/j.mbs.2012.06.003

Cited by 43 publications

(26 citation statements)

References 31 publications

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“…We extend the model of Ngonghala et al [65], to a non-autonomous (temperaturedependent) model which includes all immature stages of mosquitoes (eggs, four larval instars and pupae), as well as an exposed class (to account for the delay to infectiousness in the Plasmodium sporogonic cycle) for each stage of the gonotrophic cycle of the adult female mosquitoes. In addition, we consider epidemiological features of malaria transmission such as disease transmission to mosquitoes by asymptomatically-infectious humans, reduced malaria susceptibility in humans due to recovery from prior malaria infection, the possibility of progression from a symptomatically infected to asymptomatically infected state, and the complete loss of partial immunity in humans.…”

Section: Description and Formulation Of Modelmentioning

confidence: 99%

“…To explicitly account for the effect of the gonotrophic cycle on malaria transmission, Ngonghala et al [65] considered a mathematical model for the dynamics of malaria transmission that integrates the gonotrophic cycle of the adult female mosquitoes and its interaction with the human population (their model was an extension of the mosquito population ecology model developed by Ngwa [64, to incorporate disease dynamics in both the human and adult vector populations). The model in Ngonghala et al [65], which considered infection of the female Anopheles mosquitoes to result in infectiousness immediately after interaction with an infected human, was later extended to include the exposed class of mosquitoes, thereby explicitly accounting for the effect of the duration of Plasmodium development in the vector [66]. As shown in the classical Macdonald's malaria model [54], the sporogonic cycle plays a profound role in the epidemiological effectiveness of malaria vectors and, consequently, on malaria incidence in human host populations.…”

Section: Introductionmentioning

confidence: 99%

“…We extend the previous autonomous (temperature-independent) models by Ngonghala et al [65,66] to a non-autonomous (temperature-dependent) model with sporogony represented via the division of the adult female mosquito population into three classes (susceptible, exposed and infectious), while gonotrophy is modelled by additionally splitting the adult mosquito population into three classes corresponding to the gonotrophic stages discussed above (yielding a nine-compartment model for the dynamics of the adult female mosquitoes). Further, we model the immature mosquito lifecycle by including compartments for all major developmental stages (eggs, four larval instars, and pupae), and incorporate dependence on temperature at this stage as well.…”

Section: Introductionmentioning

confidence: 99%

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Weather-driven malaria transmission model with gonotrophic and sporogonic cycles

Okuneye

Eikenberry

Gumel

2019

Journal of Biological Dynamics

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Malaria is mainly a tropical disease and its transmission cycle is heavily influenced by environment: The life-cycles of the Anopheles mosquito vector and Plasmodium parasite are both strongly affected by ambient temperature, while suitable aquatic habitat is necessary for immature mosquito development. Therefore, how global warming may affect malaria burden is an active question, and we develop a new ordinary differential equations-based malaria transmission model that explicitly considers the temperature-dependent Anopheles gonotrophic and Plasmodium sporogonic cycles. Mosquito dynamics are coupled to infection among a human population with symptomatic and asymptomatic disease carriers, as well as temporary immunity. We also explore the effect of incorporating diurnal temperature variations upon transmission. Rigorous analysis of the model show that the non-trivial disease-free equilibrium is locallyasymptotically stable when the associated reproduction number is less than unity (this equilibrium is globally-asymptotically for a special case with no density-dependent larval and disease-induced host mortality). Numerical simulations of the model, for the case where the ambient temperature is held constant, suggest a nonlinear, hyperbolic relationship between the reproduction number and clinical malaria burden. Moreover, malaria burden peaks at 29.5 o C when daily ambient temperature is held constant, but this peak decreases with increasing daily temperature variation, to about 23-25 o C. Malaria burden also varies nonlinearly with temperature, such that small temperature changes influent disease mainly at marginal temperatures, suggesting that in areas where malaria is highly endemic, any response to global warming may be highly nonlinear and most typically minimal, while in areas of more marginal malaria potential (such as the East African highlands), increasing temperatures may translate nearly linearly into increased disease potential. Finally, we observe that while explicitly modelling the stages of the Plasmodium sporogonic cycle is essential, explicitly including the stages of the Anopheles gonotrophic cycle is of minimal importance. ARTICLE HISTORY

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Section: Description and Formulation Of Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weather-driven malaria transmission model with gonotrophic and sporogonic cycles

Okuneye

Eikenberry

Gumel

2019

Journal of Biological Dynamics

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“…Key parameters in the disease system are the transmission () and recovery () rates, which comprise the basic reproductive ratio, . represents the average number of secondary infections in a totally susceptible population caused by a single infectious individual over the lifetime of the infection [46],[49]. The disease can persist endemically if .…”

Section: Infectious Disease Modelmentioning

confidence: 99%

Poverty, Disease, and the Ecology of Complex Systems

et al. 2014

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“…Therefore, the threshold parameter

scriptR

is essential in determining whether the plant population is sustained or eradicated in the presence of lethal and non‐lethal harvesting. The threshold parameter

scriptR

is the equivalent of the vectorial and basic reproduction numbers in vector and epidemiological models (Van den Driessche & Watmough ; Ngonghala, Ngwa & Teboh‐Ewungkem ; Ngonghala, Teboh‐Ewungkem & Ngwa ; Ngonghala et al . ).…”

Section: Model and Analysismentioning

confidence: 99%

Towards a mechanistic understanding of the synergistic effects of harvesting timber and non‐timber forest products

et al. 2015

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Summary Classic theories of resource harvest assume logistic growth and incorporate harvest through an additional loss term. This methodology has been applied successfully in forest products harvesting such as timber logging. However, modelling harvest through a loss term is not appropriate for non‐timber forest products (NTFP) since harvesting in this case does not always require the complete removal of individual plants. Empirical evidence suggest that NTFP harvest affects plant population growth rates. Additionally, timber and NTFP harvest can have synergistic effects on population dynamics. We develop and analyse a simple model that incorporates non‐lethal harvest implicitly through the population growth rate of plants and lethal harvest explicitly through permanent removal of whole plants, with additional synergistic effects on population growth rate. To capture transient dynamics, we model the growth rate of plants explicitly as a dynamic variable affected by harvesting. Transient dynamics results indicate that populations have delayed response to discrete harvesting. We demonstrate exactly how the sustainability of lethal harvest, non‐lethal harvest or both types of harvests depends on the demographic effect of each type of harvest on the population growth rate. Finally, we identify a threshold parameter scriptR, such that combined lethal and non‐lethal harvest results in plant population sustainability when R>1 and extinction when R≤1.

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Periodic oscillations and backward bifurcation in a model for the dynamics of malaria transmission

Cited by 43 publications

References 31 publications

Weather-driven malaria transmission model with gonotrophic and sporogonic cycles

Weather-driven malaria transmission model with gonotrophic and sporogonic cycles

Poverty, Disease, and the Ecology of Complex Systems

Towards a mechanistic understanding of the synergistic effects of harvesting timber and non‐timber forest products

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