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

Optimal Combinations of Control Strategies and Cost-Effectiveness Analysis of Dynamics of Endemic Malaria Transmission Model

In this study, we propose and analyze a determinastic nonlinear system of ordinary differential equation model for endemic malaria disease transmission and optimal combinations of control strategies with cost effective analysis. Basic properties of the model, existence of disease-free and endemic equilibrium points, and basic reproduction number of the model are derived and analyzed. From this analysis, we conclude that if the basic reproduction number is less than unity, then the disease-free equilibrium point is both locally and globally asymptotically stable. The endemic equilibrium will also exist if the basic reproduction number is greater than unity. Moreover, existence and necessary condition for forward bifurcation is derived and established. Furthermore, optimal combinations of time-dependent control measures are incorporated to the model. By using Pontryagin's maximum principal theory, we derived the necessary conditions of optimal control. Numerical simulations were conducted to confirm our analytical results. Our findings were that malaria disease may be controlled well with strict application of the combination of prevention of drug resistance, insecticide-treated net (ITN), indoor residual spray (IRS), and active treatment. The use of a combination of insecticide-treated net, indoor residual spray, and active treatment is the most optimal cost-effective and efficacious strategy.

Controlling malaria in a population accessing counterfeit antimalarial drugs

A mathematical model is developed for describing malaria transmission in a population consisting of infants and adults and in which there are users of counterfeit antimalarial drugs. Three distinct control mechanisms, namely, effective malarial drugs for treatment and insecticide-treated bednets (ITNs) and indoor residual spraying (IRS) for prevention, are incorporated in the model which is then analyzed to gain an understanding of the disease dynamics in the population and to identify the optimal control strategy. We show that the basic reproduction number, $ R_{0} $, is a decreasing function of all three controls and that a locally asymptotically stable disease-free equilibrium exists when $ R_{0} < 1 $. Moreover, under certain circumstances, the model exhibits backward bifurcation. The results we establish support a multi-control strategy in which either a combination of ITNs, IRS and highly effective drugs or a combination of IRS and highly effective drugs is used as the optimal strategy for controlling and eliminating malaria. In addition, our analysis indicates that the control strategies primarily benefit the infant population and further reveals that a high use of counterfeit drugs and low recrudescence can compromise the optimal strategy.

Modeling malaria transmission in Nepal: impact of imported cases through cross-border mobility

The cross-border mobility of malaria cases poses an obstacle to malaria elimination programmes in many countries, including Nepal. Here, we develop a novel mathematical model to study how the imported malaria cases through the Nepal-India open-border affect the Nepal government's goal of eliminating malaria by 2026. Mathematical analyses and numerical simulations of our model, validated by malaria case data from Nepal, indicate that eliminating malaria from Nepal is possible if strategies promoting the absence of cross-border mobility, complete protection of transmission abroad, or strict border screening and isolation are implemented. For each strategy, we establish the conditions for the elimination of malaria. We further use our model to identify the control strategies that can help maintain a low endemic level. Our results show that the ideal control strategies should be designed according to the average mosquito biting rates that may depend on the location and season.

The influence of biological, epidemiological, and treatment factors on the establishment and spread of drug-resistant Plasmodium falciparum

The effectiveness of artemisinin-based combination therapies (ACTs) to treat Plasmodium falciparum malaria is threatened by resistance. The complex interplay between sources of selective pressure-treatment properties, biological factors, transmission intensity, and access to treatment-obscures understanding how, when, and why resistance establishes and spreads across different locations. We developed a disease modelling approach with emulator-based global sensitivity analysis to systematically quantify which of these factors drive establishment and spread of drug resistance. Drug resistance was more likely to evolve in low transmission settings due to the lower levels of (i) immunity and (ii) within-host competition between genotypes. Spread of parasites resistant to artemisinin partner drugs depended on the period of low drug concentration (known as the selection window). Spread of partial artemisinin resistance was slowed with prolonged parasite exposure to artemisinin derivatives and accelerated when the parasite was also resistant to the partner drug. Thus, to slow the spread of partial artemisinin resistance, molecular surveillance should be supported to detect resistance to partner drugs and to change ACTs accordingly. Furthermore, implementing more sustainable artemisinin-based therapies will require extending parasite exposure to artemisinin derivatives, and mitigating the selection windows of partner drugs, which could be achieved by including an additional long-acting drug.

The role of antimalarial quality in the emergence and transmission of resistance

The emergence and transmission of antimalarial resistance is hampering malaria eradication efforts and is shortening the useful therapeutic life of currently available antimalarials. Drug selection pressure has been identified as a contributing factor to the emergence and transmission of resistance, especially population treatment coverage and sub-therapeutic concentrations of active pharmaceutical ingredient (API) in the bloodstream. Medicine quality can be defined as good quality or poor quality. Poor quality antimalarials can be falsified, substandard or degraded and are estimated to make up between 10 and 50% of the antimalarial market in developing countries, and can be a source of sub-therapeutic doses of antimalarial API(s). The availability and use of poor quality antimalarials and the non-recommended use of quality assured monotherapies have historically been linked to treatment failure and in some cases, have coincided with the emergence and transmission of resistance in regions. We propose and outline the hypotheses that the use of poor quality antimalarial treatments and non-recommended quality assured monotherapies promote the (i) emergence and/or (ii) transmission of antimalarial resistance.

The Impact of Antimalarial Use on the Emergence and Transmission of Plasmodium falciparum Resistance: A Scoping Review of Mathematical Models

The emergence and transmission of resistance to antimalarial treatments continue to hamper malaria elimination efforts. A scoping review was undertaken regarding the impact of antimalarial treatment in the human population on the emergence and transmission of Plasmodium falciparum resistance, to (i) describe the use of mathematical models used to explore this relationship; (ii) discuss model findings; and (iii) identify factors influencing the emergence and transmission of resistance. Search strategies were developed and deployed in six major databases. Thirty-seven articles met the eligibility criteria and were included in the review: nine articles modeled the emergence of resistance, 19 modeled the transmission of resistance, and nine modeled both the emergence and transmission. The proportion of antimalarial use within the population and the presence of residual drug concentrations were identified to be the main predictors of the emergence and transmission of resistance. Influencing factors pertaining to the human, parasite and mosquito populations are discussed. To ensure the prolonged therapeutic usefulness of antimalarial treatments, the effect of antimalarial drug use on the emergence and transmission of resistance must be understood, and mathematical models are a useful tool for exploring these dynamics.

Phytochemical screening and in vivo antimalarial activity of extracts from three medicinal plants used in malaria treatment in Nigeria

The use of plant to meet health-care needs has greatly increased worldwide in the recent times. The search for new plant-derived bioactive agents that can be explored for the treatment of drug-resistant malaria infection is urgently needed. Thus, we evaluated the antimalarial activity of three medicinal plants used in Nigerian folklore for the treatment of malaria infection. A modified Peter's 4-day suppressive test was used to evaluate the antimalarial activity of the plant extracts in a mouse model of chloroquine-resistant Plasmodium berghei ANKA strain. Animals were treated with 250, 500, or 800 mg/kg of aqueous extract. It was observed that of all the three plants studied, Markhamia tomentosa showed the highest chemosuppression of parasites of 73 % followed by Polyalthia longifolia (53 %) at day 4. All the doses tested were well tolerated. Percentage suppression of parasite growth on day 4 post-infection ranged from 1 to 73 % in mice infected with P. berghei and treated with extracts when compared with chloroquine diphosphate, the standard reference drug which had a chemosuppression of 90 %. The percentage survival of mice that received extract ranged from 0 to 60 % (increased as the dose increases to 800 mg/kg). Phytochemical analysis revealed the presence of tannins, saponins, and phenolic compounds in all the three plants tested.

Climate, environmental and socio-economic change: weighing up the balance in vector-borne disease transmission

Arguably one of the most important effects of climate change is the potential impact on human health. While this is likely to take many forms, the implications for future transmission of vector-borne diseases (VBDs), given their ongoing contribution to global disease burden, are both extremely important and highly uncertain. In part, this is owing not only to data limitations and methodological challenges when integrating climate-driven VBD models and climate change projections, but also, perhaps most crucially, to the multitude of epidemiological, ecological and socio-economic factors that drive VBD transmission, and this complexity has generated considerable debate over the past 10-15 years. In this review, we seek to elucidate current knowledge around this topic, identify key themes and uncertainties, evaluate ongoing challenges and open research questions and, crucially, offer some solutions for the field. Although many of these challenges are ubiquitous across multiple VBDs, more specific issues also arise in different vector-pathogen systems.

Development of a functional assay to detect inhibitors of Plasmodium falciparum glutathione reductase utilizing liquid chromatography-mass spectrometry

Plasmodium falciparum (Pf) like most other organisms, has a sophisticated antioxidant system, part of which includes glutathione reductase (GR). GR works by recycling toxic glutathione disulfide to glutathione, thereby reducing reactive oxygen species and making a form of glutathione (GSH) the parasite can use. Inhibition of this enzyme in Pf impedes parasite growth. In addition, it has been confirmed that PfGR is not identical to human GR. Thus, PfGR is an excellent target for antimalarial drug development. A functional assay utilizing liquid chromatography-mass spectrometry was developed to specifically identify and evaluate inhibitors of PfGR. Using recombinant PfGR enzyme and 1,4-naphthoquinone (1) as a reference compound and 4-nitrobenzothiadiazole (2) and methylene blue (3) as additional compounds, we quantified the concentration of GSH produced compared with a control to determine the inhibitory effect of these compounds. Our results coincide with that presented in literature: compounds 1-3 inhibit PfGR with IC50 values of 2.71, 8.38, and 19.23 µm, respectively. Good precision for this assay was exhibited by low values of intraday and interday coefficient of variation (3.1 and 2.4%, respectively). Thus, this assay can be used to screen for other potential inhibitors of PfGR quickly and accurately.

The Implications of HIV Treatment on the HIV-Malaria Coinfection Dynamics: A Modeling Perspective

Most hosts harbor multiple pathogens at the same time in disease epidemiology. Multiple pathogens have the potential for interaction resulting in negative impacts on host fitness or alterations in pathogen transmission dynamics. In this paper we develop a mathematical model describing the dynamics of HIV-malaria coinfection. Additionally, we extended our model to examine the role treatment (of malaria and HIV) plays in altering populations' dynamics. Our model consists of 13 interlinked equations which allow us to explore multiple aspects of HIV-malaria transmission and treatment. We perform qualitative analysis of the model that includes positivity and boundedness of solutions. Furthermore, we evaluate the reproductive numbers corresponding to the submodels and investigate the long term behavior of the submodels. We also consider the qualitative dynamics of the full model. Sensitivity analysis is done to determine the impact of some chosen parameters on the dynamics of malaria. Finally, numerical simulations illustrate the potential impact of the treatment scenarios and confirm our analytical results.

Traditional uses of medicinal plants against malarial disease by the tribal communities of Lesser Himalayas-Pakistan

ETHNOPHARMACOLOGICAL RELEVANCE

Malaria is among the most prevalent infectious diseases in the developing countries of world. Estimated number of annual malaria episodes in Pakistan is 1.5 million, but very little is known about medicinal plant species of Pakistan, which have great potential against malarial disease. Present study was aimed to document medicinal plant species used by the local inhabitants of Lesser Himalayas-Pakistan to treat malaria.

MATERIALS AND METHODS

Data were collected through interviews, questionnaires and contributor observation. A total of 55 informants aged between 25 and 80 years who were familiar with malarial disease participated in the survey.

RESULTS

A total of 84 plant species belonging to 69 genera and 50 families were recorded to treat malaria. Asteraceae was found as most cited botanical family with (11.9%) representation, followed by Lamiaceae (5.9%), Solanaceae and Verbenaceae (4.7%) and Violaceae (3.5%) respectively. About 60% of the inhabitants prefer herbal treatment by local herbalists or self-treatment with locally available medicinal plant species. Of the plants identified during present investigation against malaria, Azadirachta indica, Swertia chirayita and Swertia ciliata exhibited uppermost frequency of encounter (36.3%) and corresponding PR value 5. About 67.2% of the botanical taxa are reported for the first time in the treatment of malaria. It was observed thatover harvesting is the foremost threat to medicinal plant species of the study area.

CONCLUSION

Present survey indicates that traditional knowledge about the use of plant species against various diseases and particularly to treat malaria is in decline. Similarly anthropogenic pressure, over exploitation and grazing of the botanical taxa are the major concerns regarding medicinal plant biodiversity loss. Frequently utilized plant species with significant malarial reduction should be authenticated by in vitro and in vivo standard tests.

Measuring resistant-genotype transmission of malaria parasites: challenges and prospects

Increased gametocytemia in infections with resistant strains of Plasmodium species and their enhanced transmissibility are a matter of concern in planning and evaluating the impact of malaria control strategies. Various studies have determined weekly gametocyte carriage in response to antimalarial drugs in clinical trials. The advent of molecular biology techniques makes it easy to detect and quantify gametocytes, the stages responsible for transmission, and to detect resistant genotypes of the parasite. With the validation of molecular markers of resistance to certain antimalarial drugs, there is a need to devise a simpler formula that could be used with these epidemiological antimalarial resistance tools. Theoretical models for transmission of resistant malaria parasites are difficult to deploy in epidemiological studies. Therefore, devising a simple formula that determines the potential resistant-genotype transmission of malaria parasites should provide further insights into understanding the spread of drug resistance. The present perspective discusses gametocytogenesis in the context of antimalarial treatment and drug resistance. It also highlights the difficulties in applying the available theoretical models of drug resistance transmission and suggests Rashad's devised formula that could perhaps be used in determining potentially transmissible resistant genotypes as well as in mapping areas with high potential risk for the transmission of drug-resistant malaria. The suggested formula makes use of the data on gametocytes and resistant genotypes of malaria parasites, detected by molecular techniques in a certain geographical area within a particular point in time, to calculate the potential risk of resistant genotype transmission.

The impact of heterogeneous transmission on the establishment and spread of antimalarial drug resistance

Despite the important insights gained by extending the classical models of malaria, other factors, such as immunity, heterogeneous biting, and differential patterns of drug use have not been fully explored due to the complexity of modeling multiple simultaneous malaria infections competing within a host. Understanding these factors is important for understanding how to control the spread of drug resistance to artemisinin which is just emerging in Southeast Asia. The emergence of resistance plays out at the population level, but is the result of competition within individuals for transmission events. Most studies of drug resistance evolution have focused on transmission between hosts and ignored the role of within-host competition due to the inherent complexity of modeling at multiple scales. To embed within-host competition in the model, we used an agent-based framework that was developed to understand how deviations from the classical assumptions of the Ross-MacDonald type models, which have been well-described and analyzed, impact the dynamics of disease. While structured to be a stochastic analog to classical Ross-Macdonald type models, the model is nonetheless based on individuals, and thus aspects of within-host competition can be explored. We use this framework to explore the role of heterogeneous biting and transmission on the establishment and spread of resistance in a population. We find that heterogeneous transmission slows the establishment of resistance in a population, but once resistance is established, it speeds the spread of resistance through the population. These results are due to the skewed distribution of biting which makes onward transmission a low probability and suggests that targeting the "core" group of individuals that provide the vast majority of bites could significantly slow the spread of resistance.

Estimating malaria transmission through mathematical models

Evaluating the effectiveness of malaria control interventions on the basis of their impact on transmission is increasingly important as countries move from malaria control to pre-elimination programs. Mathematical modeling can examine relationships between malaria indicators, allowing translation of easily measured data into measures of transmission, and addressing key concerns with traditional methods for quantifying transmission. Simulations show these indicators are statistically correlated, allowing direct comparisons of malaria transmission using data collected using different methods across a range of transmission intensities and seasonal patterns. Results from such models can provide public health officials with accurate estimates of transmission, by seasonal pattern, that are necessary for assessing and tailoring malaria control and elimination programs to specific settings.

Modeling the human infectious reservoir for malaria control: does heterogeneity matter?

The complex biological relationships underlying malaria transmission make it difficult to predict the impact of interventions. Mathematical models simplify these relationships and capture essential components of malaria transmission and epidemiology. Models designed to predict the impact of control programs generally infer a relationship between transmission intensity and human infectiousness to the mosquito, requiring assumptions about how infectiousness varies between individuals. A lack of understanding of human infectiousness precludes a standard approach to this inference, however, and field data reveal no obvious correlation between transmission intensity and human population infectiousness. We argue that model assumptions will have important consequences for predicting the impact of control programs.

Antimalarial drug resistance: a review of the biology and strategies to delay emergence and spread

The emergence of resistance to former first-line antimalarial drugs has been an unmitigated disaster. In recent years, artemisinin class drugs have become standard and they are considered an essential tool for helping to eradicate the disease. However, their ability to reduce morbidity and mortality and to slow transmission requires the maintenance of effectiveness. Recently, an artemisinin delayed-clearance phenotype was described. This is believed to be the precursor to resistance and threatens local elimination and global eradication plans. Understanding how resistance emerges and spreads is important for developing strategies to contain its spread. Resistance is the result of two processes: (i) drug selection of resistant parasites; and (ii) the spread of resistance. In this review, we examine the factors that lead to both drug selection and the spread of resistance. We then examine strategies for controlling the spread of resistance, pointing out the complexities and deficiencies in predicting how resistance will spread.

Optimal control strategies and cost-effectiveness analysis of a malaria model

The aim of this paper is to investigate the effectiveness and cost-effectiveness of three malaria preventive measures (use of treated bednets, spray of insecticides and a possible treatment of infective humans that blocks transmission to mosquitoes). For this, we consider a mathematical model for the transmission dynamics of the disease that includes these measures. We first consider the constant control parameters' case, we calculate the basic reproduction number and investigate the existence and stability of equilibria; the model is found to exhibit backward bifurcation. We then assess the relative impact of each of the constant control parameters measures by calculating the sensitivity index of the basic reproductive number to the model's parameters. In the time-dependent constant control case, we use Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. We also calculate the Infection Averted Ratio (IAR) and the Incremental Cost-Effectiveness Ratio (ICER) to investigate the cost-effectiveness of all possible combinations of the three control measures. One of our findings is that the most cost-effective strategy for malaria control, is the combination of the spray of insecticides and treatment of infective individuals. This strategy requires a 100% effort in both treatment (for 20 days) and spray of insecticides (for 57 days). In practice, this will be extremely difficult, if not impossible to achieve. The second most cost-effective strategy which consists of a 100% use of treated bednets and 87% treatment of infective individuals for 42 and 100 days, respectively, is sustainable and therefore preferable.

Differential impact of sickle cell trait on symptomatic and asymptomatic malaria

Individuals who carry the sickle cell trait (S-gene) have a greatly reduced risk of experiencing symptomatic malaria infections. However, previous studies suggest that the sickle cell trait does not protect against acquiring asymptomatic malaria infections, although the proportion of symptomatic infections is up to 50% in areas where malaria is endemic. To examine the differential impact of the sickle cell trait on symptomatic and asymptomatic malaria, we developed a mathematical model of malaria transmission that incorporates the evolutionary dynamics of S-gene frequency. Our model indicates that the fitness of sickle cell trait is likely to increase with the proportion of symptomatic malaria infections. Our model also shows that control efforts aimed at diminishing the burden of symptomatic malaria are not likely to eradicate malaria in endemic areas, due to the increase in the relative prevalence of asymptomatic infection, the reservoir of malaria. Furthermore, when the prevalence of symptomatic malaria is reduced, both the fitness and frequency of the S-gene may decrease. In turn, a decreased frequency of the S-gene may eventually increase the overall prevalence of both symptomatic and asymptomatic malaria. Therefore, the control of symptomatic malaria might result in evolutionary repercussions, despite short-term epidemiological benefits.

ASSESSMENT OF VECTOR CONTROL AND PHARMACEUTICAL TREATMENT IN REDUCING MALARIA BURDEN: A SENSITIVITY AND OPTIMAL CONTROL ANALYSIS

Vector control and pharmaceutical treatments are currently the main methods of malaria control. To assess their impacts on disease transmission and prevalence, sensitivity and optimal control analysis are performed respectively on a mathematical malaria model. Comparisons are made between the result of sensitivity analysis and that of optimal control analysis. Numerical simulation shows that optimal control strategy is available and cost-efficient. The simulating results also indicates that vector control is always much more beneficial than other anti-malaria measures in an optimal control programme. This further suggests that the results of sensitivity analysis by calculating sensitivity indices cannot help policy-makers to formulate a more effective optimal control programme.

Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity

We derive and analyse a deterministic model for the transmission of malaria disease with mass action form of infection. Firstly, we calculate the basic reproduction number, R(0), and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation. The implication of this occurrence is that the classical epidemiological requirement for effective eradication of malaria, R(0)<1, is no longer sufficient, even though necessary. Secondly, by using optimal control theory we derive the conditions under which it is optimal to eradicate the disease and examine the impact of a possible combined vaccination and treatment strategy on the disease transmission. When eradication is impossible, we derive the necessary conditions for optimal control of the disease using Pontryagin's Maximum Principle. The results obtained from the numerical simulations of the model show that a possible vaccination combined with effective treatment regime would reduce the spread of the disease appreciably.

Mathematical models of malaria--a review

Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease.

Impact of chemo-therapy on optimal control of malaria disease with infected immigrants

We derived and analyzed rigorously a mathematical model that describes the dynamics of malaria infection with the recruitment of infected immigrants, treatment of infectives and spray of insecticides against mosquitoes in the population. Both qualitative and quantitative analysis of the deterministic model are performed with respect to stability of the disease free and endemic equilibria. It is found that in the absence of infected immigrants disease-free equilibrium is achievable and is locally asymptotically stable. Using Pontryagin's Maximum Principle, the optimal strategies for disease control are established. Finally, numerical simulations are performed to illustrate the analytical results.

Population dynamics of a pathogen: the conundrum of vivax malaria

Building a mathematical model of population dynamics of pathogens within their host involves considerations of factors similar to those in ecology, as pathogens can prey on cells in the host. But within the multicellular host, attacked cell types are integrated with other cellular systems, which in turn intervene in the infection. For example, immune responses attempt to sense and then eliminate or contain pathogens, and homeostatic mechanisms try to compensate for cell loss. This review focuses on modeling applied to malarias, diseases caused by single-cell eukaryote parasites that infect red blood cells, with special concern given to vivax malaria, a disease often thought to be benign (if sometimes incapacitating) because the parasite only attacks a small proportion of red blood cells, the very youngest ones. However, I will use mathematical modeling to argue that depletion of this pool of red blood cells can be disastrous to the host if growth of the parasite is not vigorously check by host immune responses. Also, modeling can elucidate aspects of new field observations that indicate that vivax malaria is more dangerous than previously thought.