Mathematical analysis of a weather-driven model for the population ecology of mosquitoes

Okuneye, Kamaldeen; Abdelrazec, Ahmed; Gumel, Abba B.

doi:10.3934/mbe.2018003

Cited by 9 publications

(15 citation statements)

References 59 publications

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“…The threshold quantity (R MP ) is similar to the vectorial reproduction number described in [70], for which mosquito population exists whenever R MP > 1 (and no mosquito exists for R MP ≤ 1). Ecologically, R MP measures the average number of new adult female mosquitoes produced by one reproductive mosquito during its entire reproductive period.…”

Section: Analysis Of Autonomous Version Of the Modelmentioning

confidence: 99%

“…Moreover, only NDFS will be analyzed (since the former, associated with the absence of mosquitoes in the population, is ecologically unrealistic). The non-trivial disease-free solution (denoted by E N (t)) exists whenever a vectorial reproduction ratio of the mosquito-only compartments, denoted by R Mt , exceeds unity (the detailed computation of R Mt , based on using the theory of linear operators [8,97], is given in Section 4.1 of [70], and not repeated here to save space). The NDFS is given by:…”

Section: Mathematical Analysis Of Non-autonomous Modelmentioning

confidence: 99%

“…The proof of Item (1) of Theorem 4.1, based on using the theory of linear operators [8,70,97], is given in Appendix 3. The proof of Item (2) of Theorem 4.1, based on using the approach in [30,69], is given in Appendix 4.…”

Section: Mathematical Analysis Of Non-autonomous Modelmentioning

confidence: 99%

“…Proof: Computation of R 0t : The vectorial reproduction ratio, associated with the non-autonomous model {(1), (2), (3)}, will be computed using the approach in [8,70,97]. The linearized version of the model {(1), (2), (3)}, at the disease-free solution, E N (t), can be expressed as…”

Section: Appendices Appendix 1 Proof Of Lemma 21mentioning

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: Analysis Of Autonomous Version Of the Modelmentioning

confidence: 99%

Section: Mathematical Analysis Of Non-autonomous Modelmentioning

confidence: 99%

Section: Mathematical Analysis Of Non-autonomous Modelmentioning

confidence: 99%

Section: Appendices Appendix 1 Proof Of Lemma 21mentioning

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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“…Furthermore, the NDFE

reduces to the TDFE

when

. The threshold

is similar to the vectorial reproduction number described in ( Okuneye, Abdelrazec, & Gumel, 2018 ). It measures the average number of new adult female sandflies produced by one reproductive sandfly during its entire reproductive period.…”

Section: Mathematical Analysismentioning

confidence: 99%

Mathematical analysis of a model for zoonotic visceral leishmaniasis

Hussaini

Okuneye

Gumel

2017

Infectious Disease Modelling

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Zoonotic visceral leishmaniasis (ZVL), caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many parts of the world (notably in Africa, Asia and the Mediterranean). This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations. The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models. In the absence of such phenomenon (which is shown to arise due to the disease-induced mortality in the host populations), the nontrivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated reproduction number of the model is less than unity. Using case and demographic data relevant to ZVL dynamics in Arac̣atuba municipality of Brazil, it is shown, for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts, that the associated reproduction number of the model (normalℛ0) ranges from 0.3 to 1.4, with a mean of normalℛ0=0.85. Furthermore, when the effect of such drug treatment is explicitly incorporated in the model (i.e., accounting for the additional larval and sandfly mortality, following feeding on the treated reservoirs), the range of normalℛ0 decreases to normalℛ0∈[0.1,0.25em0.6], with a mean of normalℛ0=0.35 (this significantly increases the prospect of the effective control or elimination of the disease). Thus, ZVL transmission models (in communities where such treatment strategy is implemented) that do not explicitly incorporate the effect of such treatment may be over-estimating the disease burden (as measured in terms of normalℛ0) in the community. It is shown that normalℛ0 is more sensitive to increases in sandfly lifespan than that of the animal reservoir (so, a strategy that focuses on reducing sandflies, rather than the animal reservoir (e.g., via culling), may be more effective in reducing ZVL burden in the community). Further sensitivity analysis of the model ranks the sandfly removal rate (by natural death or by feeding from insecticide-treated reservoir hosts), the biting rate of sandflies on the reservoir hosts and the progression rate of exposed reservoirs to active ZVL as the three parameters with the most effect on the disease dynamics or burden (as measured in terms of the reproduction number normalℛ0). Hence, this study identifies the key parameters that play a key role on the disease dynamics, and thereby contributing in the design of effective control strategies (that target the identified parameters).

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Mathematical analysis of the impact of transmission-blocking drugs on the population dynamics of malaria

Woldegerima

Ouifki

Banasiak

2021

Applied Mathematics and Computation

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Mathematical analysis of a weather-driven model for the population ecology of mosquitoes

Cited by 9 publications

References 59 publications

Weather-driven malaria transmission model with gonotrophic and sporogonic cycles

Weather-driven malaria transmission model with gonotrophic and sporogonic cycles

Mathematical analysis of a model for zoonotic visceral leishmaniasis

Mathematical analysis of the impact of transmission-blocking drugs on the population dynamics of malaria

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