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Mathematical Analysis of Control Strategies of HCV in a Community with Inflow of Infected Immigrants  [PDF]
Neterindwa Ainea, Estomih S. Massawe, Oluwole Daniel Makinde, Lucy Namkinga
Advances in Infectious Diseases (AID) , 2015, DOI: 10.4236/aid.2015.51001
Abstract: In this paper, we derive and analyse rigorously a mathematical model of control strategies (screening, education, health care and immunization) of HCV in a community with inflow of infected immigrants. Both qualitative and quantitative analysis of the model is performed with respect to stability of the disease free and endemic equilibria. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Using Lyapunov method, endemic equilibrium is globally stable under certain conditions. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the HCV model in a community with inflow of infected immigrants. However, analysis shows that screening, education, health care and immunization have the effect of reducing the transmission of the disease in the community.
Modelling the Effect of Treatment and Infected Immigrants on the Spread of Hepatitis C Virus Disease with Acute and Chronic Stages
American Journal of Computational and Applied Mathematics , 2012, DOI: 10.5923/j.ajcam.20120201.02
Abstract: This paper examines the effect of Treatment and Infected Immigrants on the spread of Hepatitis C Virus (HCV) disease with Acute and Chronic stages. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However the disease becomes more endemic due to the presence of infected immigrants in the community. It is also shown that in the presence of treatment, the rate of infected immigrants (acute and chronic) decreases and consequently the treated infected individuals decreases continuously. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the treatment and infected immigrants on the spread of the disease with acute and chronic stages.
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
Modelling Co-Infection with Malaria and Lymphatic Filariasis  [PDF]
Hannah C. Slater ?,Manoj Gambhir ?,Paul E. Parham ?,Edwin Michael ?
PLOS Computational Biology , 2013, DOI: 10.1371/journal.pcbi.1003096
Abstract: Malaria and lymphatic filariasis (LF) continue to cause a considerable public health burden globally and are co-endemic in many regions of sub-Saharan Africa. These infections are transmitted by the same mosquito species which raises important questions about optimal vector control strategies in co-endemic regions, as well as the effect of the presence of each infection on endemicity of the other; there is currently little consensus on the latter. The need for comprehensive modelling studies to address such questions is therefore significant, yet very few have been undertaken to date despite the recognised explanatory power of reliable dynamic mathematical models. Here, we develop a malaria-LF co-infection modelling framework that accounts for two key interactions between these infections, namely the increase in vector mortality as LF mosquito prevalence increases and the antagonistic Th1/Th2 immune response that occurs in co-infected hosts. We consider the crucial interplay between these interactions on the resulting endemic prevalence when introducing each infection in regions where the other is already endemic (e.g. due to regional environmental change), and the associated timescale for such changes, as well as effects on the basic reproduction number R0 of each disease. We also highlight potential perverse effects of vector controls on human infection prevalence in co-endemic regions, noting that understanding such effects is critical in designing optimal integrated control programmes. Hence, as well as highlighting where better data are required to more reliably address such questions, we provide an important framework that will form the basis of future scenario analysis tools used to plan and inform policy decisions on intervention measures in different transmission settings.
High Antibody Responses against Plasmodium falciparum in Immigrants after Extended Periods of Interrupted Exposure to Malaria  [PDF]
Gemma Moncunill, Alfredo Mayor, Alfons Jiménez, Augusto Nhabomba, Núria Casas-Vila, Laura Puyol, Joseph J. Campo, Maria Nelia Manaca, Ruth Aguilar, María-Jesús Pinazo, Mercè Almirall, Cristina Soler, José Mu?oz, Azucena Bardají, Evelina Angov, Sheetij Dutta, Chetan E. Chitnis, Pedro L. Alonso, Joaquim Gascón, Carlota Doba?o
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0073624
Abstract: Background Malaria immunity is commonly believed to wane in the absence of Plasmodium falciparum exposure, based on limited epidemiological data and short-lived antibody responses in some longitudinal studies in endemic areas. Methods A cross-sectional study was conducted among sub-Saharan African adults residing in Spain for 1 up to 38 years (immigrants) with clinical malaria (n=55) or without malaria (n=37), na?ve adults (travelers) with a first clinical malaria episode (n=20) and life-long malaria exposed adults from Mozambique (semi-immune adults) without malaria (n=27) or with clinical malaria (n=50). Blood samples were collected and IgG levels against the erythrocytic antigens AMA-1 and MSP-142 (3D7 and FVO strains), EBA-175 and DBL-α were determined by Luminex. IgG levels against antigens on the surface of infected erythrocytes (IEs) were measured by flow cytometry. Results Immigrants without malaria had lower IgG levels than healthy semi-immune adults regardless of the antigen tested (P≤0.026), but no correlation was found between IgG levels and time since migration. Upon reinfection, immigrants with malaria had higher levels of IgG against all antigens than immigrants without malaria. However, the magnitude of the response compared to semi-immune adults with malaria depended on the antigen tested. Thus, immigrants had higher IgG levels against AMA-1 and MSP-142 (P≤0.015), similar levels against EBA-175 and DBL-α, and lower levels against IEs (P≤0.016). Immigrants had higher IgG levels against all antigens tested compared to travelers (P≤0.001), both with malaria. Conclusions Upon cessation of malaria exposure, IgG responses to malaria-specific antigens were maintained to a large extent, although the conservation and the magnitude of the recall response depended on the nature of the antigen. Studies on immigrant populations can shed light on the factors that determine the duration of malaria specific antibody responses and its effect on protection, with important implications for future vaccine design and public health control measures.
A Mathematical Framework for Combining Decisions of Multiple Experts toward Accurate and Remote Diagnosis of Malaria Using Tele-Microscopy  [PDF]
Sam Mavandadi, Steve Feng, Frank Yu, Stoyan Dimitrov, Karin Nielsen-Saines, William R. Prescott, Aydogan Ozcan
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0046192
Abstract: We propose a methodology for digitally fusing diagnostic decisions made by multiple medical experts in order to improve accuracy of diagnosis. Toward this goal, we report an experimental study involving nine experts, where each one was given more than 8,000 digital microscopic images of individual human red blood cells and asked to identify malaria infected cells. The results of this experiment reveal that even highly trained medical experts are not always self-consistent in their diagnostic decisions and that there exists a fair level of disagreement among experts, even for binary decisions (i.e., infected vs. uninfected). To tackle this general medical diagnosis problem, we propose a probabilistic algorithm to fuse the decisions made by trained medical experts to robustly achieve higher levels of accuracy when compared to individual experts making such decisions. By modelling the decisions of experts as a three component mixture model and solving for the underlying parameters using the Expectation Maximisation algorithm, we demonstrate the efficacy of our approach which significantly improves the overall diagnostic accuracy of malaria infected cells. Additionally, we present a mathematical framework for performing ‘slide-level’ diagnosis by using individual ‘cell-level’ diagnosis data, shedding more light on the statistical rules that should govern the routine practice in examination of e.g., thin blood smear samples. This framework could be generalized for various other tele-pathology needs, and can be used by trained experts within an efficient tele-medicine platform.
Bayesian modelling of the effect of climate on malaria in Burundi
Hermenegilde Nkurunziza, Albrecht Gebhardt, Jürgen Pilz
Malaria Journal , 2010, DOI: 10.1186/1475-2875-9-114
Abstract: This paper investigates the effects of climate on malaria in Burundi. For the period 1996-2007, real monthly data on both malaria epidemiology and climate in the area of Burundi are described and analysed. From this analysis, a mathematical model is derived and proposed to assess which variables significantly influence malaria incidences in Burundi. The proposed modelling is based on both generalized linear models (GLM) and generalized additive mixed models (GAMM). The modelling is fully Bayesian and inference is carried out by Markov Chain Monte Carlo (MCMC) techniques.The results obtained from the proposed models are discussed and it is found that malaria incidence in a given month in Burundi is strongly positively associated with the minimum temperature of the previous month. In contrast, it is found that rainfall and maximum temperature in a given month have a possible negative effect on malaria incidence of the same month.This study has exploited available real monthly data on malaria and climate over 12 years in Burundi to derive and propose a regression modelling to assess climatic factors that are associated with monthly malaria incidence. The results obtained from the proposed models suggest a strong positive association between malaria incidence in a given month and the minimum temperature (night temperature) of the previous month. An open question is, therefore, how to cope with high temperatures at night.In Burundi, malaria is a major public health issue in terms of both morbidity and mortality with around 2.5 million clinical cases and more than 15,000 deaths each year. During the last decade, for example, malaria cases increased from 550,000 cases in 1991 to 2.8 million in 2001 in a total population estimated at 7 million [1]. In 2001, Burundi was the country most affected by malaria in the world [2]. Malaria is the single main cause of mortality in pregnant women and children below five years of age. Malaria continues to ravage millions of rural Burun
Paludismo importado por inmigrantes Malaria imported by immigrants  [cached]
J. Gascón i Brustenga
Anales del Sistema Sanitario de Navarra , 2006,
Abstract: Los inmigrantes de zonas endémicas que viven en Europa son los que más riesgo tienen de adquirir malaria durante los viajes a sus países, ya que suelen viajar durante más tiempo que el resto de viajeros y a zonas y en condiciones de más riesgo. Las cifras de los a os 2002-2004 en Espa a indican que P. falciparum es la especie más diagnosticada. áfrica es el continente de donde se importan más casos y los inmigrantes contribuyen con el 34-41% de todos ellos. The immigrants from endemic zones who live in Europe are those with the greatest risk of acquiring malaria during trips to their countries, since they usually travel for longer than other travellers and to zones and under conditions of greater risk. The figures for the years 2002-2004 in Spain indicate that P. falciparum is the most diagnosed species. Africa is the continent from which most cases are imported and immigrants contribute 34-41% of all cases.
On the Mathematical Modelling of Microbial Growth
Svetoslav M. Markov
International Journal Bioautomation , 2010,
Abstract: We propose a new approach to mathematical modelling of microbial growth different to the approaches used in Jacob-Monod type models. Such an approach may be useful in the modelling of biotechnological processes, where microorganisms are used for various biodegradation purposes and are often put under extreme unfavourable conditions, such as prolonged depletion or excess of nutrients.
Mathematical Modelling of Sterile Insect Technology for Mosquito Control  [PDF]
Regina Jijoho Patinvoh, Alfred Akpoveta Susu
Advances in Entomology (AE) , 2014, DOI: 10.4236/ae.2014.24027
Abstract: Reduction of mosquito populations will, at least, reduce substantially the transmission of malaria disease. One potential method of achieving this reduction is the environmentally-friendly population control method known as the Sterile Insect Control (SIT) method. The SIT method has so far not been widely used against insect disease vectors, such as mosquitoes, because of various practical difficulties in rearing, sterilization and distribution of the parasite population. For mosquitoes, male-only release is considered essential since sterile females will bite and so may transmit disease, whereas male mosquitoes do not bite. This work concerns the mathematical modelling of the effectiveness of Sterile Insect Technique for Aedes aegypti mosquitoes, when the female sexual preference is incorporated. We found that for a released value of the sterile male mosquito below 40,000, the wild mosquito population decreases over time while the sterile male mosquito population increases. Therefore, the transmission of malaria and dengue infection declines because the sterile male mosquitoes dominated the environment. We also found that for a released value of the sterile male mosquito above 40,000, the wild mosquito population decreases and the sterile male mosquito population decreases as well. Therefore, if the injection of sterile male mosquitoes is large enough, the environment will be rid of mosquitoes over time. The result also shows that if sexual selection is incorporated into a reaction diffusion system, modelling the spread of Aedes aegypti mosquitoes, the Sterile Insect Technique (SIT) will still be a successful control measure.
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