The dilution effect of the domestic animal population on the transmission of P. vivax malaria

The diversion of disease carrying insect from humans to animals may reduce transmission of diseases such as malaria. The use of animals to mitigate mosquito bites on human is called ‘zooprophylaxis’. We introduce a mathematical model for Plasmodium vivax malaria transmission with two bloodmeal hosts (humans and domestic animals) to study the effect of zooprophylaxis. After computing the basic reproduction number from the proposed model, we explore how perturbations in the parameters, sensitive to the effects of control measures, affect its value. Zooprophylaxis is shown to determine whether a basic reproduction becomes bigger than an outbreak threshold value or not. Sensitivity analysis shows that increasing the relative animal population size works better in P. vivax malaria control than decreasing the mosquito population when the relative animal population size is larger than a threshold value.     

Malaria's Missing Number: Calculating the Human Component of R0 by a Within-Host Mechanistic Model of Plasmodium falciparum Infection and Transmission

Human infection by malarial parasites of the genus Plasmodium begins with the bite of an infected Anopheles mosquito. Current estimates place malaria mortality at over 650,000 individuals each year, mostly in African children. Efforts to reduce disease burden can benefit from the development of mathematical models of disease transmission. To date, however, comprehensive modeling of the parameters defining human infectivity to mosquitoes has remained elusive. Here, we describe a mechanistic within-host model of Plasmodium falciparum infection in humans and pathogen transmission to the mosquito vector. Our model incorporates the entire parasite lifecycle, including the intra-erythrocytic asexual forms responsible for disease, the onset of symptoms, the development and maturation of intra-erythrocytic gametocytes that are transmissible to Anopheles mosquitoes, and human-to-mosquito infectivity. These model components were parameterized from malaria therapy data and other studies to simulate individual infections, and the ensemble of outputs was found to reproduce the full range of patient responses to infection. Using this model, we assessed human infectivity over the course of untreated infections and examined the effects in relation to transmission intensity, expressed by the basic reproduction number R₀ (defined as the number of secondary cases produced by a single typical infection in a completely susceptible population). Our studies predict that net human-to-mosquito infectivity from a single non-immune individual is on average equal to 32 fully infectious days. This estimate of mean infectivity is equivalent to calculating the human component of malarial R₀. We also predict that mean daily infectivity exceeds five percent for approximately 138 days. The mechanistic framework described herein, made available as stand-alone software, will enable investigators to conduct detailed studies into theories of malaria control, including the effects of drug treatment and drug resistance on transmission.     

A mathematical model for zoonotic transmission of malaria in the Atlantic Forest: Exploring the effects of variations in vector abundance and acrodendrophily

Transmission foci of autochthonous malaria caused by Plasmodium vivax-like parasites have frequently been reported in the Atlantic Forest in Southeastern and Southern Brazil. Evidence suggests that malaria is a zoonosis in these areas as human infections by simian Plasmodium species have been detected, and the main vector of malaria in the Atlantic Forest, Anopheles (Kerteszia) cruzii, can blood feed on human and simian hosts. In view of the lack of models that seek to predict the dynamics of zoonotic transmission in this part of the Atlantic Forest, the present study proposes a new deterministic mathematical model that includes a transmission compartment for non-human primates and parameters that take into account vector displacement between the upper and lower forest strata. The effects of variations in the abundance and acrodendrophily of An. cruzii on the prevalence of infected humans in the study area and the basic reproduction number (R₀) for malaria were analyzed. The model parameters are based on the literature and fitting of the empirical data. Simulations performed with the model indicate that (1) an increase in the abundance of the vector in relation to the total number of blood-seeking mosquitoes leads to an asymptotic increase in both the proportion of infected individuals at steady state and R₀; (2) the proportion of infected humans at steady state is higher when displacement of the vector mosquito between the forest strata increases; and (3) in most scenarios, Plasmodium transmission cannot be sustained only between mosquitoes and humans, which implies that non-human primates play an important role in maintaining the transmission cycle. The proposed model contributes to a better understanding of the dynamics of malaria transmission in the Atlantic Forest.     

Blood Feeding and Plasmodium Infection Alters the miRNome of Anopheles stephensi

Blood feeding is an integral process required for physiological functions and propagation of the malaria vector Anopheles. During blood feeding, presence of the malaria parasite, Plasmodium in the blood induces several host effector molecules including microRNAs which play important roles in the development and maturation of the parasite within the mosquito. The present study was undertaken to elucidate the dynamic expression of miRNAs during gonotrophic cycle and parasite development in Anopheles stephensi. Using next generation sequencing technology, we identified 126 miRNAs of which 17 were novel miRNAs. The miRNAs were further validated by northern hybridization and cloning. Blood feeding and parasitized blood feeding in the mosquitoes revealed regulation of 13 and 16 miRNAs respectively. Expression profiling of these miRNAs revealed that significant miRNAs were down-regulated upon parasitized blood feeding with a repertoire of miRNAs showing stage specific up-regulation. Expression profiles of significantly modulated miRNAs were further validated by real time PCR. Target prediction of regulated miRNAs revealed overlapping targeting by different miRNAs. These targets included several metabolic pathways including metabolic, redox homeostasis and protein processing machinery components. Our analysis revealed tight regulation of specific miRNAs post blood feeding and parasite infection in An. stephensi. Such regulated expression suggests possible role of these miRNAs during gonotrophic cycle in mosquito. Another set of miRNAs were also significantly regulated at 42 h and 5 days post infection indicating parasite stage-specific role of host miRNAs. This study will result in better understanding of the role of miRNAs during gonotrophic cycle and parasite development in mosquito and can probably facilitate in devising novel malaria control strategies at vector level.     

A Malaria Transmission Model with Temperature-Dependent Incubation Period

Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time delay. We derive the basic reproduction ratio \(R_0\) and establish a threshold type result on the global dynamics in terms of \(R_0\), that is, the unique disease-free periodic solution is globally asymptotically stable if \(R_0<1\); and the model system admits a unique positive periodic solution which is globally asymptotically stable if \(R_0>1\). Numerically, we parameterize the model with data from Maputo Province, Mozambique, and simulate the long-term behavior of solutions. The simulation result is consistent with the obtained analytic result. In addition, we find that using the time-averaged EIP may underestimate the basic reproduction ratio.     

Mathematical model for Zika virus dynamics with sexual transmission route

Zika virus is a flavivirus transmitted to humans primarily through the bite of infected Aedes mosquitoes. In addition to vector-borne spread, however, the virus can also be transmitted through sexual contact. In this paper, we formulate and analyze a new system of ordinary differential equations which incorporates both vector and sexual transmission routes. Theoretical analysis of this model when there is no disease induced mortality shows that the disease-free equilibrium is locally and globally asymptotically stable whenever the associated reproduction number is less than unity and unstable otherwise. However, when we extend this same model to include Zika induced mortality, which have been documented in Latin America, we find that the model exhibits a backward bifurcation. Specifically, a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. To further explore model predictions, we use numerical simulations to assess the importance of sexual transmission to disease dynamics. This analysis shows that risky behavior involving multiple sexual partners, particularly among male populations, substantially increases the number of infected individuals in the population, contributing significantly to the disease burden in the community.     

ANOSPEX: A Stochastic,Spatially Explicit Model for Studying Anopheles Metapopulation Dynamics

Anopheles mosquitoes transmit malaria, a major public health problem among many African countries. One of the most effective methods to control malaria is by controlling the Anopheles mosquito vectors that transmit the parasites. Mathematical models have both predictive and explorative utility to investigate the pros and cons of different malaria control strategies. We have developed a C++ based, stochastic spatially explicit model (ANOSPEX; Ano phelesSpatially-Explicit) to simulate Anopheles metapopulation dynamics. The model is biologically rich, parameterized by field data, and driven by field-collected weather data from Macha, Zambia. To preliminarily validate ANOSPEX, simulation results were compared to field mosquito collection data from Macha; simulated and observed dynamics were similar. The ANOSPEX model will be useful in a predictive and exploratory manner to develop, evaluate and implement traditional and novel strategies to control malaria, and for understanding the environmental forces driving Anopheles population dynamics.     

A weather-driven model of malaria transmission

The classic formulae in malaria epidemiology are reviewed that relate entomological parameters to malaria transmission, including mosquito survivorship and age-at-infection, the stability index (S), the human blood index (HBI), proportion of infected mosquitoes, the sporozoite rate, the entomological inoculation rate (EIR), vectorial capacity (C) and the basic reproductive number (R ₀). The synthesis emphasizes the relationships among classic formulae and reformulates a simple dynamic model for the proportion of infected humans. The classic formulae are related to formulae from cyclical feeding models, and some inconsistencies are noted. The classic formulae are used to to illustrate how malaria control reduces malaria transmission and show that increased mosquito mortality has an effect even larger than was proposed by Macdonald in the 1950's.     

Human population, urban settlement patterns and their impact on Plasmodium falciparum malaria endemicity

Background

The length of the gonotrophic cycle varies the vectorial capacity of a mosquito vector and therefore its exact estimation is important in epidemiological modelling. Because the gonotrophic cycle length depends on temperature, its estimation can be satisfactorily computed by means of physiological time analysis.

Methods

A model of physiological time was developed and calibrated for Anopheles pseudopunctipennis, one of the main malaria vectors in South America, using data from laboratory temperature controlled experiments. The model was validated under varying temperatures and could predict the time elapsed from blood engorgement to oviposition according to the temperature.

Results

In laboratory experiments, a batch of An. pseudopunctipennis fed at the same time may lay eggs during several consecutive nights (2–3 at high temperature and > 10 at low temperature). The model took into account such pattern and was used to predict the range of the gonotrophic cycle duration of An. pseudopunctipennis in four characteristic sites of Bolivia. It showed that the predicted cycle duration for An. pseudopunctipennis exhibited a seasonal pattern, with higher variances where climatic conditions were less stable. Predicted mean values of the (minimum) duration ranged from 3.3 days up to > 10 days, depending on the season and the geographical location. The analysis of ovaries development stages of field collected biting mosquitoes indicated that the phase 1 of Beklemishev might be of significant duration for An. pseudopunctipennis. The gonotrophic cycle length of An. pseudopunctipennis correlates with malaria transmission patterns observed in Bolivia which depend on locations and seasons.

Conclusion

A new presentation of cycle length results taking into account the number of ovipositing nights and the proportion of mosquitoes laying eggs is suggested. The present approach using physiological time analysis might serve as an outline to other similar studies and allows the inclusion of temperature effects on the gonotrophic cycle in transmission models. However, to better explore the effects of temperature on malaria transmission, the others parameters of the vectorial capacity should be included in the analysis and modelled accordingly.     

The transmission dynamics of a within-and between-hosts malaria model

In this paper, we developed a novel deterministic coupled model tying together the effects of within-host and population level dynamics on malaria transmission dynamics. We develop within-host and within-vector dynamic models, population level between-hosts models, and a nested coupled model combining these levels. The unique feature of this work is the way the coupling and feedback for the model use the various life stages of the malaria parasite both in the human host and the mosquito vector. Analysis of the coupled and the within-human host models indicate the existence of locally asymptotically stable infection- and parasite-free equilibria when the associated reproduction numbers are less than one. The population-level model, on the other hand, exhibits backward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium. A global sensitivity analysis was carried out to measure the effects of the sensitivity and uncertainty in the various model parameters estimates. The results indicate that the most important parameters driving the pathogen level within an infected human are the production rate of the red blood cells from the bone marrow, the infection rate, the immunogenicity of the infected red blood cells, merozoites and gametocytes, and the immunosensitivity of the merozoites and gametocytes. The key parameters identified at the population level are the human recovery rate, the death rate of the mosquitoes, the recruitment rate of susceptible humans into the population, the mosquito biting rate, the transmission probabilities per contact in mosquitoes and in humans, and the parasite production and clearance rates in the mosquitoes. Defining the feedback functions as a linear function of the mosquito biting rate, numerical exploration of the coupled model reveals oscillations in the parasite populations within a human host in the presence of the host immune response. These oscillations dampen as the mosquito biting rate increases. We also observed that the oscillation and damping effect seen in the within-human host dynamics fed back into the population level dynamics; this in turn amplifies the oscillations in the parasite population within the mosquito-host.     

Malaria Vector Surveillance in Ganghwa-do, a Malaria-Endemic Area in the Republic of Korea

We investigated the seasonality of Anopheles mosquitoes, including its species composition, density, parity, and population densities of mosquitoes infected with the parasite in Ganghwa-do (Island), a vivax malaria endemic area in the Republic of Korea. Mosquitoes were collected periodically with a dry-ice-tent trap and a blacklight trap during the mosquito season (April-October) in 2008. Anopheles sinensis (94.9%) was the most abundant species collected, followed by Anopheles belenrae (3.8%), Anopheles pullus (1.2%), and Anopheles lesteri (0.1%). Hibernating Anopheles mosquitoes were also collected from December 2007 to March 2008. An. pullus (72.1%) was the most frequently collected, followed by An. sinensis (18.4%) and An. belenrae (9.5%). The composition of Anopheles species differed between the mosquito season and hibernation seasons. The parous rate fluctuated from 0% to 92.9%, and the highest rate was recorded on 10 September 2008. Sporozoite infections were detected by PCR in the head and thorax of female Anopheles mosquitoes. The annual sporozoite rate of mosquitoes was 0.11% (2 of 1,845 mosquitoes). The 2 mosquitoes that tested positive for sporozoites were An. sinensis. Malarial infections in anopheline mosquitoes from a population pool were also tried irrespective of the mosquito species. Nine of 2,331 pools of Anopheles mosquitoes were positive. From our study, it can be concluded that An. sinensis, which was the predominant vector species and confirmed as sporozoite-infected, plays an important role in malaria transmission in Ganghwa-do.     

Malaria Drug Resistance: The Impact of Human Movement and Spatial Heterogeneity

Human habitat connectivity, movement rates, and spatial heterogeneity have tremendous impact on malaria transmission. In this paper, a deterministic system of differential equations for malaria transmission incorporating human movements and the development of drug resistance malaria in an \(n\) patch system is presented. The disease-free equilibrium of the model is globally asymptotically stable when the associated reproduction number is less than unity. For a two patch case, the boundary equilibria (drug sensitive-only and drug resistance-only boundary equilibria) when there is no movement between the patches are shown to be locally asymptotically stable when they exist; the co-existence equilibrium is locally asymptotically stable whenever the reproduction number for the drug sensitive malaria is greater than the reproduction number for the resistance malaria. Furthermore, numerical simulations of the connected two patch model (when there is movement between the patches) suggest that co-existence or competitive exclusion of the two strains can occur when the respective reproduction numbers of the two strains exceed unity. With slow movement (or low migration) between the patches, the drug sensitive strain dominates the drug resistance strain. However, with fast movement (or high migration) between the patches, the drug resistance strain dominates the drug sensitive strain.     

Effect of irrigation systems on temporal distribution of malaria vectors in semi-arid regions

Previous research models have used climate data to explain habitat conditions of Anopheles mosquitoes transmitting malaria parasites. Although they can estimate mosquito populations with sufficient accuracy in many areas, observational data show that there is a tendency to underestimate the active growth and reproduction period of mosquitoes in semi-arid agricultural regions. In this study, a new, modified model that includes irrigation as a factor was developed to predict the active growing period of mosquitoes more precisely than the base model for ecophysiological and climatological distribution of mosquito generations (ECD-mg). Five sites with complete sets of observational data were selected in semi-arid regions of India for the comparison. The active growing period of mosquitoes determined from the modified ECD-mg model that incorporated the irrigation factor was in agreement with the observational data, whereas the active growing period was underestimated by the previous ECD-mg model that did not incorporate irrigation. This suggests that anthropogenic changes in the water supply due to extensive irrigation can encourage the growth of Anopheles mosquitoes through the alteration of the natural water balance in their habitat. In addition, it was found that the irrigation systems not only enable the active growth of mosquitoes in dry seasons but also play an important role in stabilizing the growth in rainy seasons. Consequently, the irrigation systems could lengthen the annual growing period of Anopheles mosquitoes and increase the maximum generation number of mosquitoes in semi-arid subtropical regions.     

On the Population Dynamics of the Malaria Vector

A deterministic differential equation model for the population dynamics of the human malaria vector is derived and studied. Conditions for the existence and stability of a non-zero steady state vector population density are derived. These reveal that a threshold parameter, the vectorial basic reproduction number, exist and the vector can established itself in the community if and only if this parameter exceeds unity. When a non-zero steady state population density exists, it can be stable but it can also be driven to instability via a Hopf Bifurcation to periodic solutions, as a parameter is varied in parameter space. By considering a special case, an asymptotic perturbation analysis is used to derive the amplitude of the oscillating solutions for the full non-linear system. The present modelling exercise and results show that it is possible to study the population dynamics of disease vectors, and hence oscillatory behaviour as it is often observed in most indirectly transmitted infectious diseases of humans, without recourse to external seasonal forcing.     

Backward Bifurcation and Optimal Control in Transmission Dynamics of West Nile Virus

The paper considers a deterministic model for the transmission dynamics of West Nile virus (WNV) in the mosquito-bird-human zoonotic cycle. The model, which incorporates density-dependent contact rates between the mosquito population and the hosts (birds and humans), is rigorously analyzed using dynamical systems techniques and theories. These analyses reveal the existence of the phenomenon of backward bifurcation (where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the reproduction number of the disease is less than unity) in WNV transmission dynamics. The epidemiological consequence of backward bifurcation is that the classical requirement of having the reproduction number less than unity, while necessary, is no longer sufficient for WNV elimination from the population. It is further shown that the model with constant contact rates can also exhibit this phenomenon if the WNV-induced mortality in the avian population is high enough. The model is extended to assess the impact of some anti-WNV control measures, by re-formulating the model as an optimal control problem with density-dependent demographic parameters. This entails the use of two control functions, one for mosquito-reduction strategies and the other for personal (human) protection, and redefining the demographic parameters as density-dependent rates. Appropriate optimal control methods are used to characterize the optimal levels of the two controls. Numerical simulations of the optimal control problem, using a set of reasonable parameter values, suggest that mosquito reduction controls should be emphasized ahead of personal protection measures.     

Stable and heritable gene silencing in the malaria vector Anopheles stephensi

Heritable RNA interference (RNAi), triggered from stably expressed transgenes with an inverted repeat (IR) configuration, is an important tool for reverse genetic studies. Here we report on the development of stable RNAi in Anopheles stephensi mosquitoes, the major vector of human malaria in Asia. Trans genic mosquitoes stably expressing a RNAi transgene, designed to produce intron-spliced double-stranded RNA (dsRNA) targeting the green fluorescent protein EGFP gene, were crossed to an EGFP-expressing target line. EGFP expression was dramatically reduced at both the protein and RNA levels. The levels of gene silencing depended upon the RNAi gene copy number and its site of integration. These results demonstrate that specific RNAi-mediated knockdown of gene function can be achieved with high efficiency in Anopheles. This will be invaluable to systematically unravel the function of Anopheles genes determining the vectorial capacity of the malaria parasite.     

Observance of period-doubling bifurcation and chaos in an autonomous ODE model for malaria with vector demography

We illustrate that an autonomous ordinary differential equation model for malaria transmission can exhibit period-doubling bifurcations leading to chaos when ecological aspects of malaria transmission are incorporated into the model. In particular, when demography, feeding, and reproductive patterns of the mosquitoes that transmit the malaria-causing parasite are explicitly accounted for, the resulting model exhibits subcritical bifurcations, period-doubling bifurcations, and chaos. Vectorial and disease reproduction numbers that regulate the size of the vector population at equilibrium and the endemicity of the malaria disease, respectively, are identified and used to simulate the model to show the different bifurcations and chaotic dynamics. A subcritical bifurcation is observed when the disease reproduction number is less than unity. This highlights the fact that malaria control efforts need to be long lasting and sustained to drive the infectious populations to levels below the associated saddle-node bifurcation point at which control is feasible. As the disease reproduction number increases beyond unity, period-doubling cascades that develop into chaos closely followed by period-halving sequences are observed. The appearance of chaos suggests that characterization of the physiological status of disease vectors can provide a pathway toward understanding the complex phenomena that are known to characterize the dynamics of malaria and other indirectly transmitted infections of humans. To the best of our knowledge, there is no known unforced continuous time deterministic host-vector transmission malaria model that has been shown to exhibit chaotic dynamics. Our results suggest that malaria data may need to be critically examined for complex dynamics.     

Transglutaminase-Mediated Semen Coagulation Controls Sperm Storage in the Malaria Mosquito

Insect seminal fluid proteins are powerful modulators of many aspects of female physiology and behaviour including longevity, egg production, sperm storage, and remating. The crucial role of these proteins in reproduction makes them promising targets for developing tools aimed at reducing the population sizes of vectors of disease. In the malaria mosquito Anopheles gambiae, seminal secretions produced by the male accessory glands (MAGs) are transferred to females in the form of a coagulated mass called the mating plug. The potential of seminal fluid proteins as tools for mosquito control demands that we improve our limited understanding of the composition and function of the plug. Here, we show that the plug is a key determinant of An. gambiae reproductive success. We uncover the composition of the plug and demonstrate it is formed through the cross-linking of seminal proteins mediated by a MAG-specific transglutaminase (TGase), a mechanism remarkably similar to mammalian semen coagulation. Interfering with TGase expression in males inhibits plug formation and transfer, and prevents females from storing sperm with obvious consequences for fertility. Moreover, we show that the MAG-specific TGase is restricted to the anopheline lineage, where it functions to promote sperm storage rather than as a mechanical barrier to re-insemination. Taken together, these data represent a major advance in our understanding of the factors shaping Anopheles reproductive biology.     

A targeted amplicon sequencing panel to simultaneously identify mosquito species and Plasmodium presence across the entire Anopheles genus

Anopheles is a diverse genus of mosquitoes comprising over 500 described species, including all known human malaria vectors. While a limited number of key vector species have been studied in detail, the goal of malaria elimination calls for surveillance of all potential vector species. Here, we develop a multilocus amplicon sequencing approach that targets 62 highly variable loci in the Anopheles genome and two conserved loci in the Plasmodium mitochondrion, simultaneously revealing both the mosquito species and whether that mosquito carries malaria parasites. We also develop a cheap, nondestructive, and high-throughput DNA extraction workflow that provides template DNA from single mosquitoes for the multiplex PCR, which means specimens producing unexpected results can be returned to for morphological examination. Over 1000 individual mosquitoes can be sequenced in a single MiSeq run, and we demonstrate the panel’s power to assign species identity using sequencing data for 40 species from Africa, Southeast Asia, and South America. We also show that the approach can be used to resolve geographic population structure within An. gambiae and An. coluzzii populations, as the population structure determined based on these 62 loci from over 1000 mosquitoes closely mirrors that revealed through whole genome sequencing. The end-to-end approach is quick, inexpensive, robust, and accurate, which makes it a promising technique for very large-scale mosquito genetic surveillance and vector control.