scholarly journals Modeling the dynamics of Wolbachia-infected and uninfected Aedes aegypti populations by delay differential equations

2020 ◽  
Vol 15 ◽  
pp. 76
Author(s):  
A.S. Benedito ◽  
C.P. Ferreira ◽  
M. Adimy

Starting from an age structured partial differential model, constructed taking into account the mosquito life cycle and the main features of the Wolbachia-infection, we derived a delay differential model using the method of characteristics, to study the colonization and persistence of the Wolbachia-transinfected Aedes aegypti mosquito in an environment where the uninfected wild mosquito population is already established. Under some conditions, the model can be reduced to a Nicholson-type delay differential system; here, the delay represents the duration of mosquito immature phase that comprises egg, larva and pupa. In addition to mortality and oviposition rates characteristic of the life cycle of the mosquito, other biological features such as cytoplasmic incompatibility, bacterial inheritance, and deviation on sex ratio are considered in the model. The model presents three equilibriums: the extinction of both populations, the extinction of Wolbachia-infected population and persistence of uninfected one, and the coexistence. The conditions of existence for each equilibrium are obtained analytically and have been interpreted biologically. It is shown that the increase of the delay can promote, through Hopf bifurcation, stability switch towards instability for the nonzero equilibriums. Overall, when the delay increases and crosses predetermined thresholds, the populations go to extinction.

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Angkhana Prommarat ◽  
Farida Chamchod

AbstractDeposition of lipid in the artery wall called atherosclerosis is recognized as a major cause of cardiovascular disease that leads to death worldwide. A better understanding into factors that may influence the delivery of gadolinium nanoparticles (Gd-NPs) that enhances quality of magnetic resonance imaging in diagnosis may provide a vital key for atherosclerotic treatment. In this study, we propose a delay differential model for describing the dynamics of Gd-NPs in bloodstream, peripheral arteries, and vasa vasorum with two phenomena of Gd-NPs during a sojourn in vasa vasorum. We then investigate the dynamical behaviors of Gd-NPs and explore the effects of sojourn time and transfer rates of Gd-NPs on the concentration of Gd-NPs in vasa vasorum at the 12th hour after the administration of gadolinium chelates contrast media and also the maximum concentration of Gd-NPs in peripheral arteries and vasa vasorum. Our results suggest that the sojourn of Gd-NPs in vasa vasorum may lead to complex behaviors of Gd-NPs dynamics, and transfer rates of Gd-NPs may have a significant impact on the concentration of Gd-NPs.


2018 ◽  
Vol 7 (18) ◽  
Author(s):  
Matthew Chung ◽  
Laura Teigen ◽  
Silvia Libro ◽  
Robin E. Bromley ◽  
Nikhil Kumar ◽  
...  

Here, we present a comprehensive transcriptomics data set of Brugia malayi, its Wolbachia endosymbiont wBm, and its vector host. This study samples from 16 stages across the entire B. malayi life cycle, including stage 1 through 4 larvae, adult males and females, embryos, immature microfilariae, and mature microfilariae.


2015 ◽  
Vol 27 (1) ◽  
pp. 131-156
Author(s):  
RONGSONG LIU ◽  
GERGELY RÖST ◽  
STEPHEN A. GOURLEY

Intra-specific competition in insect and amphibian species is often experienced in completely different ways in their distinct life stages. Competition among larvae is important because it can impact on adult traits that affect disease transmission, yet mathematical models often ignore larval competition. We present two models of larval competition in the form of delay differential equations for the adult population derived from age-structured models that include larval competition. We present a simple prototype equation that models larval competition in a simplistic way. Recognising that individual larvae experience competition from other larvae at various stages of development, we then derive a more complex equation containing an integral with a kernel that quantifies the competitive effect of larvae of ageāon larvae of agea. In some parameter regimes, this model and the famous spruce budworm model have similar dynamics, with the possibility of multiple co-existing equilibria. Results on boundedness and persistence are also proved.


2018 ◽  
Vol 229 (5) ◽  
Author(s):  
Mayer L. Calma ◽  
Joannes Luke B. Asis ◽  
Paul Mark B. Medina

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402092211
Author(s):  
Sami Ullah Khan ◽  
Ishtiaq Ali

The numerical techniques are regarded as the backbone of modern research. In literature, the exact solution of time delay differential models are hardly achievable or impossible. Therefore, numerical techniques are the only way to find their solution. In this article, a novel numerical technique known as Legendre spectral collocation method is used for the approximate solution of time delay differential system. Legendre spectral collocation method and their properties are applied to determined the general procedure for solving time delay differential system with detail error and convergence analysis. The method first convert the proposed system to a system of ordinary differential equations and then apply the Legendre polynomials to solve the resultant system efficiently. Finally, some numerical test problems are given to confirm the efficiency of the method and were compared with other available numerical schemes in the literature.


1951 ◽  
Vol 42 (2) ◽  
pp. 355-370 ◽  
Author(s):  
J. Muspratt

Living specimens of Megarhinus brevipalpis were transported from southern Natal to Johannesburg to establish an insectary-bred colony. The natural habitat of these predatory mosquitos consisted of small isolated patches of sub-tropical forest, in which the rainfall is 40–50 ins. (102–127 cm.) with a mean winter temperature of 64°F. (17·7°C.) and an annual range of 27°–33°F. (15°–18°C). The breeding places were leaf axils of Strelitzia nicolai (a plant resembling a wild banana), small rot holes in trees and larger ones in Strelitzia stumps. The larvae were collected from leaf axils with an apparatus consisting of a rubber bulb to which were attached lengths of glass and rubber tubing.The insectary was a room 9 ft.×8 ft. 6 ins. and 9 ft. high which was kept at tropical heat and humidity. Mating of the adults was observed, copulation being effected while at rest or in flight. Oviposition was usually accomplished in flight but also while at rest on the surface of the water. In the summer time two females, which were tested, laid about 85 eggs each during the month following emergence from the pupa, six or seven days elapsing after emergence before the first oviposition. In the middle of the winter, oviposition (with later generations) became very irregular in spite of the temperature and humidity remaining constant. The adults, which were comparable to those of the natural habitat, were fed on sugar solution, honey and fruit juice. One bred out as a gynandromorph.When given an abundant supply of larvae of laboratory bred Aëdes aegypti, the life-cycle of M. brevipalpis was normally : egg (incubation), less than two days ; larva, 11–20 days (average 14·5 days) ; pupa, five days. This does not include a small number of exceptional cases in which the life as a fully grown larva was abnormally prolonged (in one case nearly four months) for reasons which are not absolutely clear. The larvae killed from 100 to 200 or more Aëdes larvae during the normal larval life, but many of these were not eaten when the brevipalpis were in the late fourth instar. By a special technique they were also induced to eat dead tissues including minced pork brawn, minced maggots and minced flies. Except for the latter these were not satisfactory foods although there was slow development.Fourth-instar larvae were kept out of water for three to four weeks (without food), in a damp atmosphere, and afterwards when fed most of them developed normally, but pupation was sometimes suspended for a considerable time. They have been sent by post (out of water) in tubes with damp cotton wool and filter paper.The egg differed from that of other Megarhinus species in having a crown of projections at one end with a cup-like structure in the centre. The exochorion had roughly hexagonal cells but without numerous tubercles as in other species.First-instar larvae remained in the egg-shell after hatching when the eggs-were out of water but on a damp surface and in a saturated atmosphere. They survived like this for up to six days or about the same time as the larvae survived in tap water if there was no food. When liberated in water the head of the first-instar larva was comparatively small with the mouth parts folded in. Within two hours of liberation in water the head enlarged considerably and the mouth parts came into position ; the larva was then ready to catch its Culicine prey. When in water containing dead leaves, these larvae survived from a few days to over four weeks and some grew to the third instar without any Culicine food.Cannibalism was investigated. Fourth-instar larvae did not attack each other readily ; they devoured smaller larvae of their own species and small to medium size larvae resorted to cannibalism, particularly in the absence of Culicine prey. There was evidence that fourth-instar Aëdes aegypti occasionally ate first-instar Megarhinus.The discussion traces attempts which have been made in certain Pacific islands, notably Hawaii and Fiji, to use Megarhines for biological control of disease-carrying mosquitos. M. brevipalpis has a shorter life-cycle than the species introduced into these islands and the conclusion reached is that laboratory breeding, to enable large numbers to be released in certain areas, would be a suitable adjunct to a programme of general control, in this part of the world. Airmail consignments of larvae are being sent to Hawaii with the object of starting a laboratory colony there.


2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Ling Bai ◽  
Kai Zhang ◽  
Wenju Zhao

We consider stochastic suppression and stabilization for nonlinear delay differential system. The system is assumed to satisfy local Lipschitz condition and one-side polynomial growth condition. Since the system may explode in a finite time, we stochastically perturb this system by introducing independent Brownian noises and Lévy noise feedbacks. The contributions of this paper are as follows. (a) We show that Brownian noises or Lévy noise may suppress potential explosion of the solution for some appropriate parameters. (b) Using the exponential martingale inequality with jumps, we discuss the fact that the sample Lyapunov exponent is nonpositive. (c) Considering linear Lévy processes, by the strong law of large number for local martingale, sufficient conditions for a.s. exponentially stability are investigated in Theorem 13.


2019 ◽  
Vol 56 (4) ◽  
pp. 1078-1086 ◽  
Author(s):  
Nancy M Endersby-Harshman ◽  
Jason K Axford ◽  
Ary A Hoffmann

Abstract Wolbachia-infected Aedes aegypti (L.) mosquitoes for control of dengue transmission are being released experimentally in tropical regions of Australia, south-east Asia, and South America. To become established, the Wolbachia Hertig (Rickettsiales: Rickettsiaceae) strains used must induce expression of cytoplasmic incompatibility (CI) in matings between infected males and uninfected females so that infected females have a reproductive advantage, which will drive the infection through field populations. Wolbachia is a Rickettsia-like alphaproteobacterium which can be affected by tetracycline antibiotics. We investigated whether exposure of Wolbachia-infected mosquitoes to chlortetracycline at environmentally relevant levels during their aquatic development resulted in loss or reduction of infection in three strains, wAlbB, wMel, and wMelPop. Wolbachia density was reduced for all three strains at the tested chlortetracycline concentrations of 5 and 50 µg/liter. Two of the strains, wMel and wMelPop, showed a breakdown in CI. The wAlbB strain maintained CI and may be useful at breeding sites where tetracycline contamination has occurred. This may include drier regions where Ae. aegypti can utilize subterranean water sources and septic tanks as breeding sites.


1968 ◽  
Vol 46 (2) ◽  
pp. 135-140 ◽  
Author(s):  
Bro. Joseph Kavelaars ◽  
T. K. R. Bourns

Cercariae of Plagiorchis peterborensis sp. n. were obtained from Lymnaea stagnalis appressa, and the life cycle was completed using Aedes aegypti larvae and laboratory mice as experimental hosts. Description of the adult is based upon whole mounts and serial sections of 14-day-old worms. P. peterborensis resembles most closely P. muris, but differs in stylet shape, adult dimensions, and egg size.


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