A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population

We describe and develop a difference equation model for the dynamics of malaria in a mosquito population feeding on, infecting and getting infected from a heterogeneous population of hosts. Using the force of infection from different classes of humans to mosquitoes as parameters, we evaluate a number of entomological parameters, indicating malaria transmission levels, which can be compared to field data. By assigning different types of vector control interventions to different classes of humans and by evaluating the corresponding levels of malaria transmission, we can compare the effectiveness of these interventions. We show a numerical example of the effects of increasing coverage of insecticide-treated bed nets in a human population where the predominant malaria vector is Anopheles gambiae.     

Dynamics of malaria transmission model with sterile mosquitoes

In this paper, a malaria transmission model with sterile mosquitoes is considered. We first formulate a simple SEIR malaria transmission model as our baseline model. Then sterile mosquitoes are introduced into the baseline model. We consider the case that the release rate of sterile mosquitoes is proportional to the wild mosquito population size. To investigate the impact of releasing sterile mosquitoes on the malaria transmission, the dynamics of the baseline model and the models with the sterile mosquitoes are discussed. We derive formulas of the reproductive numbers and explore the existence of endemic equilibrium as the reproductive number is more than unity for these models. It is shown that both the baseline model and the models with the sterile mosquitoes undergo backward bifurcations. Based on theoretical analysis and numerical simulation, we investigate the impact of releasing sterile mosquitoes on malaria transmission.     

Genetic engineering of malaria parasite resistance in vector mosquitoes

Malaria is the most significant vector‐borne disease and mostly affects people living in the lesser developed countries of tropical and sub‐tropical regions. Climate changes, rapid global transportation, immigration and invasion of exotic mosquito vectors bring the threat of introduction of the disease to developed nations. Sustainability of malaria control requires the discovery of therapeutic and prophylactic drugs, development of effective vaccines and control of vector mosquitoes. Drug development and vaccine research have been pursued aggressively over the past 20 years, and progress in novel approaches to vector control is now evident. Our long‐term objective is the production and utilization of strains of vector mosquitoes that are genetically refractory to the transmission of malaria parasites. These insects will be used to test the hypothesis that an increase in the frequency of a gene or allele that confers decreased vector competence to a population of mosquitoes will result in a reduction in the incidence and prevalence of malaria. Completed studies make it possible to develop strains of Anopheles mosquitoes expressing specific effector molecules that interfere completely with the transmission of the most lethal human malaria parasite, Plasmodium falciparum. Data are reviewed here that support the use of single‐chain monoclonal antibodies (scFv) that disable parasites in the midgut and hemolymph of transgenic mosquitoes.     

A mathematical model for malaria involving differential susceptibility,exposedness and infectivity of human host

The main purpose of this article is to formulate a deterministic mathematical model for the transmission of malaria that considers two host types in the human population. The first type is called “non-immune” comprising all humans who have never acquired immunity against malaria and the second type is called “semi-immune”. Non-immune are divided into susceptible, exposed and infectious and semi-immune are divided into susceptible, exposed, infectious and immune. We obtain an explicit formula for the reproductive number, R ₀ which is a function of the weight of the transmission semi-immune-mosquito-semi-immune, R _0a , and the weight of the transmission non-immune-mosquito-non-immune, R _0e . Then, we study the existence of endemic equilibria by using bifurcation analysis. We give a simple criterion when R ₀ crosses one for forward and backward bifurcation. We explore the possibility of a control for malaria through a specific sub-group such as non-immune or semi-immune or mosquitoes.     

A mathematical model of population dynamics for Batesian mimicry system

We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.     

A mathematical model of a crocodilian population using delay-differential equations

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.     

The impact of host species and vector control measures on the fitness of African malaria vectors

Many malaria vector mosquitoes in Africa have an extreme preference for feeding on humans. This specialization allows them to sustain much higher levels of transmission than elsewhere, but there is little understanding of the evolutionary forces that drive this behaviour. In Tanzania, we used a semi-field system to test whether the well-documented preferences of the vectors, Anopheles arabiensis and Anopheles gambiae sensu stricto (s.s.) for cattle and humans, respectively, are predicted by the fitness they obtain from host-seeking on these species relative to other available hosts. Mosquito fitness was contrasted, when humans were fully exposed and when they were protected by a typical bednet. The fitness of both vectors varied between host species. The predicted relationship between host preference and fitness was confirmed in An. arabiensis, but not in An. gambiae s.s., whose fitness was similar on humans and other mammals. Use of typical, imperfect bednets generated only minor reductions in An. gambiae s.s. feeding success and fitness on humans, but was predicted to generate a significant reduction in the lifetime reproductive success of An. arabiensis on humans relative to cows. This supports the hypothesis that such human-protective measures could additionally benefit malaria control by increasing selection for zoophily in vectors.     

Seasonal changes in the feeding pattern of Culex pipiens pallens govern the transmission dynamics of multiple lineages of avian malaria parasites in Japanese wild bird community

Heterogeneity in the transmission of mosquito-borne pathogens is determined largely by distribution patterns of mosquito bites among wild animal populations. Although mosquitoes are crucial for transmission of avian malaria parasites, little is known about the ecology of natural vectors. We examined bloodmeal and parasite incidence in Culex pipiens pallens by a polymerase chain reaction (PCR)-based procedure to determine how the feeding pattern of mosquitoes govern transmission dynamics of avian malaria parasites in Japanese wild birds. We collected 881 unfed and 486 blood-fed Cx. pipiens pallens resting on vegetation in a park in Tokyo. The mosquitoes were separated into abdomen and thorax prior to PCR screening. Abdomens of unfed mosquitoes were combined into 95 pools. From these, we amplified Plasmodium DNA in 32 (33.7%) pools. Among blood-fed mosquitoes, 371 individuals were screened for blood-sources and Plasmodium parasites. Plasmodium DNA was amplified from mosquitoes fed on 6 of 13 avian species identified as blood-sources. Ten Plasmodium lineages were identified on the basis of 478 bp of the cytochrome b gene, with 0.2-10% sequence divergence. The three commonest Plasmodium lineages (CXPIP09, SGS1 and PADOM02) were detected in both the abdomens and thoraxes of mosquitoes, strongly suggesting transmission of these lineages. Jungle crow (Corvus macrorhynchos) served as a natural host for the three commonest Plasmodium lineages and made up 63.8% of blood-sources. As a significant increase in feeding of vector mosquitoes on jungle crows coincided with their breeding season, jungle crows were considered to be the primary reservoir of Plasmodium transmission in this study.     

Within-host population dynamics and the evolution of microparasites in a heterogeneous host population

Abstract Why do parasites harm their hosts? The general understanding is that if the transmission rate and virulence of a parasite are linked, then the parasite must harm its host to maximize its transmission. The exact nature of such trade‐offs remains largely unclear, but for vertebrate hosts it probably involves interactions between a microparasite and the host immune system. Previous results have suggested that in a homogeneous host population in the absence of super‐ or coinfection, within‐host dynamics lead to selection of the parasite with an intermediate growth rate that is just being controlled by the immune system before it kills the host (Antia et al. 1994). In this paper, we examine how this result changes when heterogeneity is introduced to the host population. We incorporate the simplest form of heterogeneity–random heterogeneity in the parameters describing the size of the initial parasite inoculum, the immune response of the host, and the lethal density at which the parasite kills the host. We find that the general conclusion of the previous model holds: parasites evolve some intermediate growth rate. However, in contrast with the generally accepted view, we find that virulence (measured by the case mortality or the rate of parasite‐induced host mortality) increases with heterogeneity. Finally, we link the within‐host and between‐host dynamics of parasites. We show how the parameters for epidemiological spread of the disease can be estimated from the within‐host dynamics, and in doing so examine the way in which trade‐offs between these epidemiological parameters arise as a consequence of the interaction of the parasite and the immune response of the host.     

The remarkable journey of adaptation of the Plasmodium falciparum malaria parasite to New World anopheline mosquitoes

Plasmodium falciparum originated in Africa, dispersed around the world as a result of human migration and had to adapt to several different indigenous anopheline mosquitoes. Anophelines from the New World are evolutionary distant form African ones and this probably resulted in a more stringent selection of Plasmodium as it adapted to these vectors. It is thought that Plasmodium has been genetically selected by some anopheline species through unknown mechanisms. The mosquito immune system can greatly limit infection and P. falciparum evolved a strategy to evade these responses, at least in part mediated by Pfs47, a highly polymorphic gene. We propose that adaptation of P. falciparum to new vectors may require evasion of their immune system. Parasites with a Pfs47 haplotype compatible with the indigenous mosquito vector would be able to survive and be transmitted. The mosquito antiplasmodial response could be an important determinant of P. falciparum population structure and could affect malaria transmission in the Americas.     

A mathematical model for the population dynamics of army ants

A stochastic cellular automata model for the population dynamics of the army antEciton burchelli on Barro Colorado Island in Panama is set up. It is simulated on the computer and shown to give good agreement with biological data. It is analysed using two approximations akin to the mean field approximation in statistical mechanics, and good agreement with the simulations is obtained. Finally, the role of distance between successive statary phase bivouacs is discussed with regard to the rate of colony growth. There are two aspects of the biological system studied here that make it of general importance. First, the population is structured, since the size of each colony of army ants is crucial. Second, the spatial behaviour of the population, as in many others, is not diffusion-like, although it is random. This has implications for the kind of model that is chosen.     

A standard photomap of ovarian nurse cell chromosomes in the European malaria vector Anopheles atroparvus

Anopheles atroparvus (Diptera: Culicidae) is one of the main malaria vectors of the Maculipennis group in Europe. Cytogenetic analysis based on salivary gland chromosomes has been used in taxonomic and population genetic studies of mosquitoes from this group. However, a high‐resolution cytogenetic map that could be used in physical genome mapping in An. atroparvus is still lacking. In the present study, a high‐quality photomap of the polytene chromosomes from ovarian nurse cells of An. atroparvus was developed. Using fluorescent in situ hybridization, 10 genes from the five largest genomic supercontigs on the polytene chromosome were localized and 28% of the genome was anchored to the cytogenetic map. The study established chromosome arm homology between An. atroparvus and the major African malaria vector Anopheles gambiae, suggesting a whole‐arm translocation between autosomes of these two species. The standard photomap constructed for ovarian nurse cell chromosomes of An. atroparvus will be useful for routine physical mapping. This map will assist in the development of a fine‐scale chromosome‐based genome assembly for this species and will also facilitate comparative and evolutionary genomics studies in the genus Anopheles.     

The dynamics of acute malaria infections. I. Effect of the parasite's red blood cell preference

What determines the dynamics of parasite and anaemia during acute primary malaria infections? Why do some strains of malaria reach higher densities and cause greater anaemia than others? The conventional view is that the fastest replicating parasites reach the highest densities and cause the greatest loss of red blood cells (RBCs). Other current hypotheses suggest that the maximum parasite density is achieved by strains that either elicit the weakest immune responses or infect the youngest RBCs (reticulocytes). Yet another hypothesis is a simple resource limitation model where the peak parasite density and the maximum anaemia (percentage loss of RBCs) during the acute phase of infection equal the fraction of RBCs that the malaria parasite can infect. We discriminate between these hypotheses by developing a mathematical model of acute malaria infections and confronting it with experimental data from the rodent malaria parasite Plasmodium chabaudi. We show that the resource limitation model can explain the initial dynamics of infection of mice with different strains of this parasite. We further test the model by showing that without modification it closely reproduces the dynamics of competing strains in mixed infections of mice with these strains of P. chabaudi. Our results suggest that a simple resource limitation is capable of capturing the basic features of the dynamics of both parasite and RBC loss during acute malaria infections of mice with P. chabaudi, suggesting that it might be worth exploring if similar results might hold for other acute malaria infections, including those of humans.     

A mathematical model for the leukocyte filtration process

Leukocyte filters are applied clinically to remove leukocytes from blood. In order to optimize leukocyte filters, a mathematical model to describe the leukocyte filtration process was developed by modification of a general theoretical model for depth filtration. The model presented here can be used to predict the time-dependent leukocyte filtration as a function of cell-cell interaction in the filter, filter efficiency, filter capacity, filter dimensions, and leukocyte concentration in the suspension applied to the filter. The results of different leukocyte filtration experiments previously reported in the literature could be well described by the present model. (c) 1995 John Wiley & Sons, Inc.     

A mathematical model for Crimean-Congo haemorrhagic fever: tick-borne dynamics with conferred host immunity

Crimean-Congo haemorrhagic fever (CCHF) is a highly contagious tick-borne disease that impacts many countries in parts of Africa, Europe, Asia, and the Middle East. Outbreaks are episodic, but deadly. Due to the highly contagious nature of this disease, suspected cases are taken extremely serious, with very strong control measures implemented almost immediately. It is primarily those living on farms, livestock workers, and medical workers who are at risk. The virus responsible for CCHF is transmitted asymptomatically and transiently to livestock, and symptomatically to humans. The fatality rate in human cases can be very high. The number of methods and directions of viral transmission is large, including tick-to-tick, tick-to-livestock, tick-to-human, livestock-to-tick, livestock-to-human, and human-to-human. We model CCHF using a deterministic system of nonlinear differential equations. This compartment model allows us to analyse threshold parameters and equilibria describing the magnitude and progression of cases of the disease in a hypothetical outbreak.     

A mathematical model of population dynamics for Batesian mimicry system

We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.     

Evolution of rotifer population dynamics in a heterogeneous habitat: mathematical modeling

We present the results of mathematical modeling of a rotifer species inhabiting two coupled habitats with different environmental conditions. We use the modified Consensus model and show that the exchange between the habitats can lead to chaotization of originally regular plankton dynamics and synchronization of plankton biomass oscillations. As a result, the invasion of a chaotic regime takes place.     

Stability results for delayed-recruitment models in population dynamics

This paper relates the stability properties of a class of delay-difference equations to those of an associated scalar difference equation. Simple but powerful conditions for testing global stability are presented which are independent of the length of the time delay involved. For models which do not have globally stable equilibria, estimates of stability regions are obtained. Some well known baleen whale models are used to illustrate the results.