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Modelling knowlesi malaria transmission in humans: vector preference and host competence
Laith Yakob, Michael B Bonsall, Guiyun Yan
Malaria Journal , 2010, DOI: 10.1186/1475-2875-9-329
Abstract: Using a mathematical model, the influence of human host competency on disease transmission is assessed. Adapting a standard model for vector-borne disease transmission and using an evolutionary invasion analysis, the paper explores how differential host competency between humans and macaques can facilitate the epidemiological processes of P. knowlesi infection between different hosts.Following current understanding of the evolutionary route of other human malaria vectors and parasites, an increasing human population in knowlesi malaria endemic regions will select for a more anthropophilic vector as well as a parasite that preferentially transmits between humans. Applying these adaptations, evolutionary invasion analysis yields threshold conditions under which this macaque disease may become a significant public health issue.These threshold conditions are discussed in the context of malaria vector-parasite co-evolution as a function of anthropogenic effects.Although principally a disease of long-tailed and pig-tailed macaques, Plasmodium knowlesi has recently been revealed to be a widespread, and potentially life-threatening, malaria infection of humans in Southeast Asia [1]. However, before the public health threat that this disease poses can be assessed, a solid understanding of the fundamental epidemiological processes is needed. Using a simple mathematical model, key components of the disease are explored that are of particular influence in its transmission and yet for which data are lacking, thereby highlighting priority research areas.Through a series of laboratory experiments, Chin et al demonstrated the ability of this parasite to transmit from humans to both simian and human hosts [2]. However, the extent of human host competency under natural conditions remains unclear, giving rise to controversy over whether P. knowlesi can be classed as the fifth aetiological agent of human malaria [3-5]. Implicit to the epidemiological understanding of this disease is a
Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective  [PDF]
Jean Claude Kamgang, Vivient Corneille Kamla, Stéphane Yanick Tchoumi
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.519298
Abstract: We propose and analyze an epidemiological model to evaluate the effectiveness of bed nets as a prophylactic measure in malaria-endemic areas. The main purpose in this work is the modeling of the aggressiveness of anopheles mosquitoes relative to the way humans use to protect themselves against bites of mosquitoes. This model is a system of several differential equations: the number of equations depends on the particular assumptions of the model. We compute the basic reproduction number\"\", and show that if\"\", the disease free equilibrium (DFE) is globally asymptotically stable on the non-negative orthant. If\"\", the system admits a unique endemic equilibrium (EE) that is globally and asymptotically stable. Numerical simulations are presented corresponding to scenarios typical of malaria-endemic areas, based on data collected in the literature. Finally, we discuss the relative effectiveness of different kinds of bed nets.
Cognitive Energy Harvesting and Transmission from a Network Perspective  [PDF]
Seunghyun Lee,Kaibin Huang,Rui Zhang
Mathematics , 2012,
Abstract: Wireless networks can be self-sustaining by harvesting energy from radio-frequency (RF) signals. Building on classic cognitive radio networks, we propose a novel method for network coexisting where mobiles from a secondary network, called secondary transmitters (STs), either harvest energy from transmissions by nearby transmitters from a primary network, called primary transmitters (PTs), or transmit information if PTs are sufficiently far away; STs store harvested energy in rechargeable batteries with finite capacity and use all available energy for subsequent transmission when batteries are fully charged. In this model, each PT is centered at a guard zone and a harvesting zone that are disks with given radiuses; a ST harvests energy if it lies in some harvesting zone, transmits fixed-power signals if it is outside all guard zones or else idles. Based on this model, the spatial throughput of the secondary network is maximized using a stochastic-geometry model where PTs and STs are modeled as independent homogeneous Poisson point processes (HPPPs), under the outage constraints for coexisting networks and obtained in a simple closed-form. It is observed from the result that the maximum secondary throughput decreases linearly with the growing PT density, and the optimal ST density is inversely proportional to the derived transmission probability for STs.
Modelling the Impact of Artemisinin Combination Therapy and Long-Acting Treatments on Malaria Transmission Intensity  [PDF]
Lucy C Okell ,Chris J Drakeley,Teun Bousema,Christopher J. M Whitty,Azra C Ghani
PLOS Medicine , 2008, DOI: 10.1371/journal.pmed.0050226
Abstract: Background Artemisinin derivatives used in recently introduced combination therapies (ACTs) for Plasmodium falciparum malaria significantly lower patient infectiousness and have the potential to reduce population-level transmission of the parasite. With the increased interest in malaria elimination, understanding the impact on transmission of ACT and other antimalarial drugs with different pharmacodynamics becomes a key issue. This study estimates the reduction in transmission that may be achieved by introducing different types of treatment for symptomatic P. falciparum malaria in endemic areas. Methods and Findings We developed a mathematical model to predict the potential impact on transmission outcomes of introducing ACT as first-line treatment for uncomplicated malaria in six areas of varying transmission intensity in Tanzania. We also estimated the impact that could be achieved by antimalarials with different efficacy, prophylactic time, and gametocytocidal effects. Rates of treatment, asymptomatic infection, and symptomatic infection in the six study areas were estimated using the model together with data from a cross-sectional survey of 5,667 individuals conducted prior to policy change from sulfadoxine-pyrimethamine to ACT. The effects of ACT and other drug types on gametocytaemia and infectiousness to mosquitoes were independently estimated from clinical trial data. Predicted percentage reductions in prevalence of infection and incidence of clinical episodes achieved by ACT were highest in the areas with low initial transmission. A 53% reduction in prevalence of infection was seen if 100% of current treatment was switched to ACT in the area where baseline slide-prevalence of parasitaemia was lowest (3.7%), compared to an 11% reduction in the highest-transmission setting (baseline slide prevalence = 57.1%). Estimated percentage reductions in incidence of clinical episodes were similar. The absolute size of the public health impact, however, was greater in the highest-transmission area, with 54 clinical episodes per 100 persons per year averted compared to five per 100 persons per year in the lowest-transmission area. High coverage was important. Reducing presumptive treatment through improved diagnosis substantially reduced the number of treatment courses required per clinical episode averted in the lower-transmission settings although there was some loss of overall impact on transmission. An efficacious antimalarial regimen with no specific gametocytocidal properties but a long prophylactic time was estimated to be more effective at reducing
Estimation of heterogeneity in malaria transmission by stochastic modelling of apparent deviations from mass action kinetics
Thomas A Smith
Malaria Journal , 2008, DOI: 10.1186/1475-2875-7-12
Abstract: The relationship between the entomological inoculation rate (EIR) for falciparum malaria and infection risk was reanalysed using published data for cohorts of children in Saradidi (western Kenya). Infection risk was treated as binomially distributed, and measurement-error (Poisson and negative binomial) models were considered for the EIR. Models were fitted using Bayesian Markov chain Monte Carlo algorithms and model fit compared for models that assume either mass-action kinetics, facilitation, competition or saturation of the infection process with increasing EIR.The proportion of inocula that resulted in infection in Saradidi was inversely related to the measured intensity of challenge. Models of facilitation showed, therefore, a poor fit to the data. When sampling error in the EIR was neglected, either competition or saturation needed to be incorporated in the model in order to give a good fit. Negative binomial models for the error in exposure could achieve a comparable fit while incorporating the more parsimonious and biologically plausible mass action assumption. Models that assume negative binomial micro-heterogeneity predict lower incidence of infection at a given average exposure than do those assuming exposure to be uniform. The negative binomial model moreover provides an estimate of the variance of the within-cohort distribution of the EIR and hence of within cohort heterogeneity in exposure.Apparent deviations from mass action kinetics in parasite transmission can arise from spatial and temporal heterogeneity in the inoculation rate, and from imprecision in its measurement. For parasites like P. falciparum, where there is no plausible biological rationale for deviations from mass action, this provides a strategy for estimating true levels of heterogeneity, since if mass-action is assumed, the within-population variance in exposure becomes identifiable in cohort studies relating infection to transmission intensity. Statistical analyses relating infection
Modelling entomological-climatic interactions of Plasmodium falciparum malaria transmission in two Colombian endemic-regions: contributions to a National Malaria Early Warning System
Daniel Ruiz, Germán Poveda, Iván D Vélez, Martha L Qui?ones, Guillermo L Rúa, Luz E Velásquez, Juan S Zuluaga
Malaria Journal , 2006, DOI: 10.1186/1475-2875-5-66
Abstract: The mathematical tool was applied to represent Plasmodium falciparum malaria transmission in two endemic-areas. Entomological exogenous variables were estimated through field campaigns and laboratory experiments. Availability of breeding places was included towards representing fluctuations in vector densities. Diverse scenarios, sensitivity analyses and instabilities cases were considered during experimentation-validation process.Correlation coefficients and mean square errors between observed and modelled incidences reached 0.897–0.668 (P > 0.95) and 0.0002–0.0005, respectively. Temperature became the most relevant climatic parameter driving the final incidence. Accordingly, malaria outbreaks are possible during the favourable epochs following the onset of El Ni?o warm events. Sporogonic and gonotrophic cycles showed to be the entomological key-variables controlling the transmission potential of mosquitoes' population. Simulation results also showed that seasonality of vector density becomes an important factor towards understanding disease transmission.The model constitutes a promising tool to deepen the understanding of the multiple interactions related to malaria transmission conducive to outbreaks. In the foreseeable future it could be implemented as a tool to diagnose possible dynamical patterns of malaria incidence under several scenarios, as well as a decision-making tool for the early detection and control of outbreaks. The model will be also able to be merged with forecasts of El Ni?o events to provide a National Malaria Early Warning System.The World Health Organization estimates that malaria parasites infect from 200 to 300 million persons and kill more than 1 million people each year, primarily children under the age of five [1]. The efficacy of control measures has decreased over the past decades because mosquitoes and parasites are becoming more resistant to the commonly used insecticides and anti-malarial drugs [2]. As a result, malaria kills more p
Modelling malaria elimination on the internet
Richard J Maude, Sompob Saralamba, Adrian Lewis, Dean Sherwood, Nicholas J White, Nicholas PJ Day, Arjen M Dondorp, Lisa J White
Malaria Journal , 2011, DOI: 10.1186/1475-2875-10-191
Abstract: An internet site is presented with a simple mathematical modelling platform for population level models of malaria elimination. It is freely accessible to all and designed to be flexible so both the platform and models can be developed through interaction with users. The site is an accessible introduction to modelling for a non-mathematical audience, and lessons learned from the project will help inform future development of mathematical models and improve communication of modelling results. Currently it hosts a simple model of strategies for malaria elimination and this will be developed, and more models added, over time. The iterative process of feedback and development will result in an educational and planning tool for non-modellers to assist with malaria elimination efforts worldwide.By collaboration with end users, iterative development of mathematical models of malaria elimination through this internet platform will maximize its potential as an educational and public health policy planning tool. It will also assist with preliminary optimisation of local malaria elimination strategies before commitment of valuable resources.Mathematical modelling has great potential as a tool to help guide efforts towards malaria elimination [1]. Different combinations of interventions are required for different epidemiological settings. However, there are limited data available to policymakers to inform their decisions on which strategies to employ. Mathematical modelling combines mechanistic understanding with available data from multiple sources to make predictions. It could potentially be used for preliminary evaluation of different strategies for malaria elimination in different epidemiological contexts much more rapidly and at lower cost than is possible through trial and error in the field [1]. Modelling is particularly useful where a field study cannot be done as is the case with large-scale elimination programmes for which it is desirable to get the strategy right fir
Effect of Transmission Setting and Mixed Species Infections on Clinical Measures of Malaria in Malawi  [PDF]
Marian C. Bruce, Allan Macheso, Louise A. Kelly-Hope, Standwell Nkhoma, Alex McConnachie, Malcolm E. Molyneux
PLOS ONE , 2008, DOI: 10.1371/journal.pone.0002775
Abstract: Background In malaria endemic regions people are commonly infected with multiple species of malaria parasites but the clinical impact of these Plasmodium co-infections is unclear. Differences in transmission seasonality and transmission intensity between endemic regions have been suggested as important factors in determining the effect of multiple species co-infections. Principal Findings In order to investigate the impact of multiple-species infections on clinical measures of malaria we carried out a cross-sectional community survey in Malawi, in 2002. We collected clinical and parasitological data from 2918 participants aged >6 months, and applied a questionnaire to measure malaria morbidity. We examined the effect of transmission seasonality and intensity on fever, history of fever, haemoglobin concentration ([Hb]) and parasite density, by comparing three regions: perennial transmission (PT), high intensity seasonal transmission (HIST) and low intensity seasonal transmission (LIST). These regions were defined using multi-level modelling of PCR prevalence data and spatial and geo-climatic measures. The three Plasmodium species (P. falciparum, P. malariae and P. ovale) were randomly distributed amongst all children but not adults in the LIST and PT regions. Mean parasite density in children was lower in the HIST compared with the other two regions. Mixed species infections had lower mean parasite density compared with single species infections in the PT region. Fever rates were similar between transmission regions and were unaffected by mixed species infections. A history of fever was associated with single species infections but only in the HIST region. Reduced mean [Hb] and increased anaemia was associated with perennial transmission compared to seasonal transmission. Children with mixed species infections had higher [Hb] in the HIST region. Conclusions Our study suggests that the interaction of Plasmodium co-infecting species can have protective effects against some clinical outcomes of malaria but that this is dependent on the seasonality and intensity of malaria transmission.
Transmission dynamics of malaria in Nigeria.
OO Okwa, FI Akinmolayan, V Carter, H Hurd
Annals of African Medicine , 2009,
Abstract: Background: Two of the problems of malaria parasite vector control in Nigeria are the diversity of Anopheline vectors and large size of the country. Anopheline distribution and transmission dynamics of malaria were therefore compared between four ecotypes in Nigeria during the rainy season. Methods: Polymerase chain reaction (PCR) was used in molecular identification after morphological identification microscopically. Enzyme linked immunorsorbent assay (ELISA) was used for the blood meal analysis and sporozoite detection. Results: Five species were identified out of 16,410 anophelines collected. An. gambiae s.s made up approximately 29.2%-36.6% of the population in each zone. All five species acted as vectors for P. falciparum. An. gambiae s.s had the highest sporozoite rate. The most infected mosquitoes were found in the rain forest. More blood meals were taken from bovids, except the savannah forest, where 73.3% were on humans and Human Blood index (HBI) was 57.3%. The Entomological inoculation rate (EIR) was a mean of 13.6 ib/p but was highest in the rainforest zone. Conclusions and limitations: This study demonstrates the complex distribution of anophelines and the considerable variations in the intensity of malaria transmission in Nigeria. We highlight the need to consider diverse epidemiological situations when planning countrywide control programmes.
Interrupting Malaria Transmission: Quantifying the Impact of Interventions in Regions of Low to Moderate Transmission  [PDF]
Michelle L. Gatton,Qin Cheng
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0015149
Abstract: Malaria has been eliminated from over 40 countries with an additional 39 currently planning for, or committed to, elimination. Information on the likely impact of available interventions, and the required time, is urgently needed to help plan resource allocation. Mathematical modelling has been used to investigate the impact of various interventions; the strength of the conclusions is boosted when several models with differing formulation produce similar data. Here we predict by using an individual-based stochastic simulation model of seasonal Plasmodium falciparum transmission that transmission can be interrupted and parasite reintroductions controlled in villages of 1,000 individuals where the entomological inoculation rate is <7 infectious bites per person per year using chemotherapy and bed net strategies. Above this transmission intensity bed nets and symptomatic treatment alone were not sufficient to interrupt transmission and control the importation of malaria for at least 150 days. Our model results suggest that 1) stochastic events impact the likelihood of successfully interrupting transmission with large variability in the times required, 2) the relative reduction in morbidity caused by the interventions were age-group specific, changing over time, and 3) the post-intervention changes in morbidity were larger than the corresponding impact on transmission. These results generally agree with the conclusions from previously published models. However the model also predicted changes in parasite population structure as a result of improved treatment of symptomatic individuals; the survival probability of introduced parasites reduced leading to an increase in the prevalence of sub-patent infections in semi-immune individuals. This novel finding requires further investigation in the field because, if confirmed, such a change would have a negative impact on attempts to eliminate the disease from areas of moderate transmission.
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