Malaria Incidence Rates from Time Series of 2-Wave Panel Surveys.

Methodology to estimate malaria incidence rates from a commonly occurring form of interval-censored longitudinal parasitological data-specifically, 2-wave panel data-was first proposed 40 years ago based on the theory of continuous-time homogeneous Markov Chains. Assumptions of the methodology were suitable for settings with high malaria transmission in the absence of control measures, but are violated in areas experiencing fast decline or that have achieved very low transmission. No further developments that can accommodate such violations have been put forth since then. We extend previous work and propose a new methodology to estimate malaria incidence rates from 2-wave panel data, utilizing the class of 2-component mixtures of continuous-time Markov chains, representing two sub-populations with distinct behavior/attitude towards malaria prevention and treatment. Model identification, or even partial identification, requires context-specific a priori constraints on parameters. The method can be applied to scenarios of any transmission intensity. We provide an application utilizing data from Dar es Salaam, an area that experienced steady decline in malaria over almost five years after a larviciding intervention. We conducted sensitivity analysis to account for possible sampling variation in input data and model assumptions/parameters, and we considered differences in estimates due to submicroscopic infections. Results showed that, assuming defensible a priori constraints on model parameters, most of the uncertainty in the estimated incidence rates was due to sampling variation, not to partial identifiability of the mixture model for the case at hand. Differences between microscopy- and PCR-based rates depend on the transmission intensity. Leveraging on a method to estimate incidence rates from 2-wave panel data under any transmission intensity, and from the increasing availability of such data, there is an opportunity to foster further methodological developments, particularly focused on partial identifiability and the diversity of a priori parameter constraints associated with different human-ecosystem interfaces. As a consequence there can be more nuanced planning and evaluation of malaria control programs than heretofore.

Modeling huanglongbing transmission within a citrus tree.

The citrus disease huanglongbing (HLB), associated with an uncultured bacterial pathogen, is threatening the citrus industry worldwide. A mathematical model of the transmission of HLB between its psyllid vector and citrus host has been developed to characterize the dynamics of the vector and disease development, focusing on the spread of the pathogen from flush to flush (a newly developing cluster of very young leaves on the expanding terminal end of a shoot) within a tree. This approach differs from that of prior models for vector-transmitted plant diseases where the entire plant is the unit of analysis. Dynamics of vector and host populations are simulated realistically as the flush population approaches complete infection. Model analysis indicates that vector activity is essential for initial infection but is not necessary for continued infection because infection can occur from flush to flush through internal movement in the tree. Flush production, within-tree spread, and latent period are the most important parameters influencing HLB development. The model shows that the effect of spraying of psyllids depends on time of initial spraying, frequency, and efficacy of the insecticides. Similarly, effects of removal of symptomatic flush depend on the frequency of removal and the time of initiation of this practice since the start of the epidemic. Within-tree resistance to spread, possibly affected by inherent or induced resistance, is a major factor affecting epidemic development, supporting the notion that alternate routes of transmission besides that by the vector can be important for epidemic development.

Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity.

A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas.

We present a mathematical model for malaria treatment and spread of drug resistance in an endemic population. The model considers treated humans that remain infectious for some time and partially immune humans who are also infectious to mosquitoes although their infectiousness is always less than their non immune counterparts. The model is formulated by considering delays in the latent periods in both mosquito and human populations and in the period within which partial immunity is lost. Qualitative analysis of the model including positivity and boundedness of solutions is performed. Analysis of the reproductive numbers shows that if the treated humans become immediately uninfectious to mosquitoes then treatment will always reduce the number of sensitive infections. If however treated humans are infectious then for treatment to effectively reduce the number of sensitive infections, the ratio of the infectious period of the treated humans to the infectious period of the untreated humans multiplied by the ratio of the transmission rate from a treated human to the transmission rate of an untreated human should be less than one. Our results show that the spread of drug resistance with treatment as a control strategy depends on the ratio of the infectious periods of treated and untreated humans and on the transmission rates from infectious humans with resistant and sensitive infections. Numerical analysis is performed to assess the effects of treatment on the spread of resistance and infection. The study provides insight into the possible intervention strategies to be employed in malaria endemic populations with resistant parasites by identifying important parameters.

Cost-Effectiveness Analysis of Hospitalization and Home-Based Care Strategies for People Living with HIV/AIDS: The Case of Zimbabwe.

The model of care of people living with HIV/AIDS (PLWHA) has shifted from hospital care to community home-based care (CHBC) because of shortage of space in hospitals and lack of resources. We evaluate the costs and benefits of home-based care and other HIV/AIDS intervention strategies in Zimbabwe, using an interdisciplinary approach which weaves together the techniques of an epidemic transmission model and economic evaluation concepts. The intervention strategies considered are voluntary counselling and testing (VCT), VCT combined with hospitalization (H), VCT combined with CHBC, and all the interventions implemented concurrently. The results of the study indicate that implementing all the strategies concurrently is the most cost-effective, a result which also agrees with the epidemiological model. Our results also show that the effectiveness of a strategy in the epidemiological model does not necessarily imply cost-effectiveness of the strategy and behaviour change, modelled by the parameters p and m, that accompanied the strategies, influencing both the cost-effectiveness of an intervention strategy and dynamics of the epidemic. This study shows that interdisciplinary collaborations can help in improving the accuracy of predictions of the course and cost of the epidemic and help policy makers in implementing the correct strategies.

Recasting the theory of mosquito-borne pathogen transmission dynamics and control.

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonald's formula for R0 and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross-Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

A sticky situation: the unexpected stability of malaria elimination.

Malaria eradication involves eliminating malaria from every country where transmission occurs. Current theory suggests that the post-elimination challenges of remaining malaria-free by stopping transmission from imported malaria will have onerous operational and financial requirements. Although resurgent malaria has occurred in a majority of countries that tried but failed to eliminate malaria, a review of resurgence in countries that successfully eliminated finds only four such failures out of 50 successful programmes. Data documenting malaria importation and onwards transmission in these countries suggests malaria transmission potential has declined by more than 50-fold (i.e. more than 98%) since before elimination. These outcomes suggest that elimination is a surprisingly stable state. Elimination's 'stickiness' must be explained either by eliminating countries starting off qualitatively different from non-eliminating countries or becoming different once elimination was achieved. Countries that successfully eliminated were wealthier and had lower baseline endemicity than those that were unsuccessful, but our analysis shows that those same variables were at best incomplete predictors of the patterns of resurgence. Stability is reinforced by the loss of immunity to disease and by the health system's increasing capacity to control malaria transmission after elimination through routine treatment of cases with antimalarial drugs supplemented by malaria outbreak control. Human travel patterns reinforce these patterns; as malaria recedes, fewer people carry malaria from remote endemic areas to remote areas where transmission potential remains high. Establishment of an international resource with backup capacity to control large outbreaks can make elimination stickier, increase the incentives for countries to eliminate, and ensure steady progress towards global eradication. Although available evidence supports malaria elimination's stickiness at moderate-to-low transmission in areas with well-developed health systems, it is not yet clear if such patterns will hold in all areas. The sticky endpoint changes the projected costs of maintaining elimination and makes it substantially more attractive for countries acting alone, and it makes spatially progressive elimination a sensible strategy for a malaria eradication endgame.

A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010.

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross-Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross-Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross-Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

A mathematical model for antimalarial drug resistance.

We formulate and analyze a mathematical model for malaria with treatment and the well-known three levels of resistance in humans. The model incorporates both sensitive and resistant strains of the parasites. Analytical results reveal that the model exhibits the phenomenon of backward bifurcation (co-existence of a stable disease-free equilibrium with a stable endemic equilibrium), an epidemiological situation where although necessary, having the basic reproduction number less than unity, it is not sufficient for disease elimination. Through quantitative analysis, we show the effects of varying treatment levels in a high transmission area with different levels of resistance. Increasing treatment has limited benefits in a population with resistant strains, especially in high transmission settings. Thus, in a cost-benefit analysis, the rate of treatment and percentage to be treated become difficult questions to address.

Modelling the effects of condom use and antiretroviral therapy in controlling HIV/AIDS among heterosexuals, homosexuals and bisexuals.

A deterministic compartmental sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals in heterosexual settings in which homosexuality and bisexuality issues have remained taboo is presented. We extend the model to focus on the effects of condom use as a single strategy approach in HIV prevention in the absence of any other intervention strategies. Initially, we model the use of male condoms, followed by incorporating the use of both the female and male condoms. The model includes two primary factors in condom use to control HIV which are condom efficacy and compliance. Reproductive numbers for these models are computed and compared to assess the effectiveness of male and female condom use in a community. We also extend the basic model to consider the effects of antiretroviral therapy as a single strategy. The results from the study show that condoms can reduce the number of secondary infectives and thus can slow the development of the HIV/AIDS epidemic. Further, we note from the study that treatment of AIDS patients may enlarge the epidemic when the treatment drugs are not 100% effective and when treated AIDS patients indulge in risky sexual behaviour. Thus, the treatment with amelioration of AIDS patients should be accompanied with intense public health educational programs, which are capable of changing the attitude of treated AIDS patients towards safe sex. It is also shown from the study that the use of condoms in settings with the treatment may help in reducing the number of secondary infections thus slowing the epidemic.

A quantitative analysis of transmission efficiency versus intensity for malaria.

The relationship between malaria transmission intensity and efficiency is important for malaria epidemiology, for the design of randomized control trials that measure transmission or incidence as end points, and for measuring and modelling malaria transmission and control. Five kinds of studies published over the past century were assembled and reanalysed to quantify malaria transmission efficiency and describe its relation to transmission intensity, to understand the causes of inefficient transmission and to identify functions suitable for modelling mosquito-borne disease transmission. In this study, we show that these studies trace a strongly nonlinear relationship between malaria transmission intensity and efficiency that is parsimoniously described by a model of heterogeneous biting. When many infectious bites are concentrated on a few people, infections and parasite population structure will be highly aggregated affecting the immunoepidemiology of malaria, the evolutionary ecology of parasite life history traits and the measurement and stratification of transmission for control using entomological and epidemiological data.