Mathematical models of malaria--a review

Modeling and investigating malaria P. Falciparum and P. Vivax infections: Application to Djibouti data

Malaria is an infectious and communicable disease, caused by one or more species of Plasmodium parasites. There are five species of parasites responsible for malaria in humans, of which two, Plasmodium Falciparum and Plasmodium Vivax, are the most dangerous. In Djibouti, the two species of Plasmodium are present in different proportions in the infected population: 77% of P. Falciparum and 33% of P. Vivax. In this study we present a new mathematical model describing the temporal dynamics of Plasmodium Falciparum and Plasmodium Vivax co-infection. We focus briefly on the well posedness of this model and on the calculation of the basic reproductive numbers for the infections with each Plasmodium species that help us understand the long-term dynamics of this model (i.e., existence and stability of various eqiuilibria). Then we use computational approaches to: (a) identify model parameters using real data on malaria infections in Djibouti; (b) illustrate the influence of different estimated parameters on the basic reproduction numbers; (c) perform global sensitivity and uncertainty analysis for the impact of various model parameters on the transient dynamics of infectious mosquitoes and infected humans, for infections with each of the Plasmodium species. The originality of this research stems from employing the FAST method and the LHS method to identify the key factors influencing the progression of the disease within the population of Djibouti. In addition, sensitivity analysis identified the most influential parameter for Falciparium and Vivax reproduction rates. Finally, the uncertainty analysis enabled us to understand the variability of certain parameters on the infected compartments.

A global mathematical model of climatic suitability for Plasmodium falciparum malaria

Climatic conditions are a key determinant of malaria transmission intensity, through their impacts on both the parasite and its mosquito vectors. Mathematical models relating climatic conditions to malaria transmission can be used to develop spatial maps of climatic suitability for malaria. These maps underpin efforts to quantify the distribution and burden of malaria in humans, enabling improved monitoring and control. Previous work has developed mathematical models and global maps for the suitability of temperature for malaria transmission. In this paper, existing temperature-based models are extended to include two other important bioclimatic factors: humidity and rainfall. This model is combined with fine spatial resolution climatic data to produce a more biologically-realistic global map of climatic suitability for Plasmodium falciparum malaria. The climatic suitability index developed corresponds more closely than previous temperature suitability indices with the global distribution of P. falciparum malaria. There is weak agreement between the Malaria Atlas Project estimates of P. falciparum prevalence in Africa and the estimates of suitability solely based on temperature (Spearman Correlation coefficient of ρ = 0.24 ). The addition of humidity and then rainfall improves the comparison ( ρ = 0.62 when humidity added; ρ = 0.70 when both humidity and rainfall added). By incorporating the impacts of humidity and rainfall, this model identifies arid regions that are not climatically suitable for transmission of P. falciparum malaria. Incorporation of this improved index of climatic suitability into geospatial models can improve global estimates of malaria prevalence and transmission intensity.

Ronald Ross: Pioneer of Malaria Research and Nobel Laureate

Sir Ronald Ross, a British medical doctor and researcher, is renowned for his pioneering work in malaria research. His discovery of the malaria parasite's lifecycle within mosquitoes revolutionized the understanding and control of malaria, transitioning the field from the miasma theory to vector-based strategies. This literature review aims to explore the comprehensive contributions of Ronald Ross to malaria research and their enduring impact on public health.

The Legacy of Sir Ronald Ross: From Malaria Research to Multifaceted Achievements

Sir Ronald Ross (13th May 1857 - 16th September 1932), a British doctor, was awarded the Nobel Prize in Physiology/Medicine in 1902 for research on the spread of malaria. This article highlights the multifaceted and significant scientific work by Ross. In 1897, he demonstrated that malaria is transmitted via mosquito bites and that malaria parasites exist in the gastrointestinal tract of the mosquito. Ross elucidated the transmission cycle in mosquitoes and birds infected with Plasmodium. His 25-year career in the Indian Medical Service laid the foundation for his ground-breaking work in malaria. Besides medicine, Ross excelled in poetry, music, and mathematics. The London School of Hygiene & Tropical Medicine has a frieze dedicated to 23 people chosen for their accomplishments in the field of public health, one of whom is Sir Ronald Ross. His legacy lives on through various honors and institutions, like the Ross Institute.

Geospatial joint modeling of vector and parasite serology to microstratify malaria transmission

The World Health Organization identifies a strong surveillance system for malaria and its mosquito vector as an essential pillar of the malaria elimination agenda. Anopheles salivary antibodies are emerging biomarkers of exposure to mosquito bites that potentially overcome sensitivity and logistical constraints of traditional entomological surveys. Using samples collected by a village health volunteer network in 104 villages in Southeast Myanmar during routine surveillance, the present study employs a Bayesian geostatistical modeling framework, incorporating climatic and environmental variables together with Anopheles salivary antigen serology, to generate spatially continuous predictive maps of Anopheles biting exposure. Our maps quantify fine-scale spatial and temporal heterogeneity in Anopheles salivary antibody seroprevalence (ranging from 9 to 99%) that serves as a proxy of exposure to Anopheles bites and advances current static maps of only Anopheles occurrence. We also developed an innovative framework to perform surveillance of malaria transmission. By incorporating antibodies against the vector and the transmissible form of malaria (sporozoite) in a joint Bayesian geostatistical model, we predict several foci of ongoing transmission. In our study, we demonstrate that antibodies specific for Anopheles salivary and sporozoite antigens are a logistically feasible metric with which to quantify and characterize heterogeneity in exposure to vector bites and malaria transmission. These approaches could readily be scaled up into existing village health volunteer surveillance networks to identify foci of residual malaria transmission, which could be targeted with supplementary interventions to accelerate progress toward elimination.

Mathematical models of Plasmodium vivax transmission: A scoping review

Plasmodium vivax is one of the most geographically widespread malaria parasites in the world, primarily found across South-East Asia, Latin America, and parts of Africa. One of the significant characteristics of the P. vivax parasite is its ability to remain dormant in the human liver as hypnozoites and subsequently reactivate after the initial infection (i.e. relapse infections). Mathematical modelling approaches have been widely applied to understand P. vivax dynamics and predict the impact of intervention outcomes. Models that capture P. vivax dynamics differ from those that capture P. falciparum dynamics, as they must account for relapses caused by the activation of hypnozoites. In this article, we provide a scoping review of mathematical models that capture P. vivax transmission dynamics published between January 1988 and May 2023. The primary objective of this work is to provide a comprehensive summary of the mathematical models and techniques used to model P. vivax dynamics. In doing so, we aim to assist researchers working on mathematical epidemiology, disease transmission, and other aspects of P. vivax malaria by highlighting best practices in currently published models and highlighting where further model development is required. We categorise P. vivax models according to whether a deterministic or agent-based approach was used. We provide an overview of the different strategies used to incorporate the parasite's biology, use of multiple scales (within-host and population-level), superinfection, immunity, and treatment interventions. In most of the published literature, the rationale for different modelling approaches was driven by the research question at hand. Some models focus on the parasites' complicated biology, while others incorporate simplified assumptions to avoid model complexity. Overall, the existing literature on mathematical models for P. vivax encompasses various aspects of the parasite's dynamics. We recommend that future research should focus on refining how key aspects of P. vivax dynamics are modelled, including spatial heterogeneity in exposure risk and heterogeneity in susceptibility to infection, the accumulation of hypnozoite variation, the interaction between P. falciparum and P. vivax, acquisition of immunity, and recovery under superinfection.

Time lag effect on malaria transmission dynamics in an Amazonian Colombian municipality and importance for early warning systems

Malaria remains a significant public health problem worldwide, particularly in low-income regions with limited access to healthcare. Despite the use of antimalarial drugs, transmission remains an issue in Colombia, especially among indigenous populations in remote areas. In this study, we used an SIR Ross MacDonald model that considered land use change, temperature, and precipitation to analyze eco epidemiological parameters and the impact of time lags on malaria transmission in La Pedrera-Amazonas municipality. We found changes in land use between 2007 and 2020, with increases in forested areas, urban infrastructure and water edges resulting in a constant increase in mosquito carrying capacity. Temperature and precipitation variables exhibited a fluctuating pattern that corresponded to rainy and dry seasons, respectively and a marked influence of the El Niño climatic phenomenon. Our findings suggest that elevated precipitation and temperature increase malaria infection risk in the following 2 months. The risk is influenced by the secondary vegetation and urban infrastructure near primary forest formation or water body edges. These results may help public health officials and policymakers develop effective malaria control strategies by monitoring precipitation, temperature, and land use variables to flag high-risk areas and critical periods, considering the time lag effect.

A model for malaria treatment evaluation in the presence of multiple species

Plasmodium falciparum and P. vivax are the two most common causes of malaria. While the majority of deaths and severe morbidity are due to P. falciparum, P. vivax poses a greater challenge to eliminating malaria outside of Africa due to its ability to form latent liver stage parasites (hypnozoites), which can cause relapsing episodes within an individual patient. In areas where P. falciparum and P. vivax are co-endemic, individuals can carry parasites of both species simultaneously. These mixed infections complicate dynamics in several ways: treatment of mixed infections will simultaneously affect both species, P. falciparum can mask the detection of P. vivax, and it has been hypothesised that clearing P. falciparum may trigger a relapse of dormant P. vivax. When mixed infections are treated for only blood-stage parasites, patients are at risk of relapse infections due to P. vivax hypnozoites. We present a stochastic mathematical model that captures interactions between P. falciparum and P. vivax, and incorporates both standard schizonticidal treatment (which targets blood-stage parasites) and radical cure treatment (which additionally targets liver-stage parasites). We apply this model via a hypothetical simulation study to assess the implications of different treatment coverages of radical cure for mixed and P. vivax infections and a "unified radical cure" treatment strategy where P. falciparum, P. vivax, and mixed infections all receive radical cure after screening glucose-6-phosphate dehydrogenase (G6PD) normal. In addition, we investigated the impact of mass drug administration (MDA) of blood-stage treatment. We find that a unified radical cure strategy leads to a substantially lower incidence of malaria cases and deaths overall. MDA with schizonticidal treatment was found to decrease P. falciparum with little effect on P. vivax. We perform a univariate sensitivity analysis to highlight important model parameters.

An Agent-Based Model of Biting Midge Dynamics to Understand Bluetongue Outbreaks

Bluetongue (BT) is a well-known vector-borne disease that infects ruminants such as sheep, cattle, and deer with high mortality rates. Recent outbreaks in Europe highlight the importance of understanding vector-host dynamics and potential courses of action to mitigate the damage that can be done by BT. We present an agent-based model, entitled 'MidgePy', that focuses on the movement of individual Culicoides spp. biting midges and their interactions with ruminants to understand their role as vectors in BT outbreaks, especially in regions that do not regularly experience outbreaks. The results of our sensitivity analysis suggest that midge survival rate has a significant impact on the probability of a BTV outbreak as well as its severity. Using midge flight activity as a proxy for temperature, we found that an increase in environmental temperature corresponded with an increased probability of outbreak after identifying parameter regions where outbreaks are more likely to occur. This suggests that future methods to control BT spread could combine large-scale vaccination programs with biting midge population control measures such as the use of pesticides. Spatial heterogeneity in the environment is also explored to give insight on optimal farm layouts to reduce the potential for BT outbreaks.

[Predictions of a SEIR model for COVID-19 cases in Cali-Colombia]

OBJECTIVE

To predict the number of cases of COVID-19 in the city of Cali-Colombia through the development of a SEIR model.

METHODS

A SEIR compartmental deterministic model was used considering the states: susceptible (S), exposed (E), infected (I) and recovered (R). The model parameters were selected according to the literature review, in the case of the case fatality rate data from the Municipal Secretary of Health were used. Several scenarios were considered taking into account variations in the basic number of reproduction (R0), and the prediction until april 9 was compared with the observed data.

RESULTS

Through the SEIR model it was found that with the highest basic number of reproduction [2,6] and using the case fatality rate for the city of 2,0%, the maximum number of cases would be reached on June 1 with 195 666 (prevalence). However, when comparing the observed with the expected cases, at the beginning the observed occurrence was above the projected, but then the trend changes decreasing the slope.

CONCLUSIONS

SEIR epidemiological models are widely used methods for projecting cases in infectious diseases, however it must be taken into account that they are deterministic models that can use assumed parameters and could generate imprecise results.

Assessing the spatiotemporal malaria transmission intensity with heterogeneous risk factors: A modeling study in Cambodia

Malaria control can significantly benefit from a holistic and precise way of quantitatively measuring the transmission intensity, which needs to incorporate spatiotemporally varying risk factors. In this study, we conduct a systematic investigation to characterize malaria transmission intensity by taking a spatiotemporal network perspective, where nodes capture the local transmission intensities resulting from dominant vector species, the population density, and land cover, and edges describe the cross-region human mobility patterns. The inferred network enables us to accurately assess the transmission intensity over time and space from available empirical observations. Our study focuses on malaria-severe districts in Cambodia. The malaria transmission intensities determined using our transmission network reveal both qualitatively and quantitatively their seasonal and geographical characteristics: the risks increase in the rainy season and decrease in the dry season; remote and sparsely populated areas generally show higher transmission intensities than other areas. Our findings suggest that: the human mobility (e.g., in planting/harvest seasons), environment (e.g., temperature), and contact risk (coexistences of human and vector occurrence) contribute to malaria transmission in spatiotemporally varying degrees; quantitative relationships between these influential factors and the resulting malaria transmission risk can inform evidence-based tailor-made responses at the right locations and times.

An Overview of Malaria Transmission Mechanisms, Control, and Modeling

In sub-Saharan Africa, malaria is a leading cause of mortality and morbidity. As a result of the interplay between many factors, the control of this disease can be challenging. However, few studies have demonstrated malaria's complexity, control, and modeling although this perspective could lead to effective policy recommendations. This paper aims to be a didactic material providing the reader with an overview of malaria. More importantly, using a system approach lens, we intend to highlight the debated topics and the multifaceted thematic aspects of malaria transmission mechanisms, while showing the control approaches used as well as the model supporting the dynamics of malaria. As there is a large amount of information on each subject, we have attempted to provide a basic understanding of malaria that needs to be further developed. Nevertheless, this study illustrates the importance of using a multidisciplinary approach to designing next-generation malaria control policies.

Collateral Effects of Insecticide-Treated Nets on Human and Environmental Safety in an Epidemiological Model for Malaria with Human Risk Perception

Malaria remains a major health problem in many parts of the world, including Sub-Saharan Africa. Insecticide-treated nets, in combination with other control measures, have been effective in reducing malaria incidence over the past two decades. Nevertheless, there are concerns about improper handling and misuse of nets, producing possible health effects from intoxication and collateral environmental damage. The latter is caused, for instance, from artisanal fishing. We formulate a model of impulsive differential equations to describe the interplay between malaria dynamics, human intoxication, and ecosystem damage; affected by human awareness to these risks and levels of net usage. Our results show that an increase in mosquito net coverage reduces malaria prevalence and increases human intoxications. In addition, a high net coverage significantly reduces the risk perception to disease, naturally increases the awareness for intoxications from net handling, and scarcely increases the risk perception to collateral damage from net fishing. According to our model, campaigns aiming at reducing disease prevalence or intoxications are much more successful than those creating awareness to ecosystem damage. Furthermore, we can observe from our results that introducing closed fishing periods reduces environmental damage more significantly than strategies directed towards increasing the risk perception for net fishing.

The impact of reactive case detection on malaria transmission in Zanzibar in the presence of human mobility

Malaria persists at low levels on Zanzibar despite the use of vector control and case management. We use a metapopulation model to investigate the role of human mobility in malaria persistence on Zanzibar, and the impact of reactive case detection. The model was parameterized using survey data on malaria prevalence, reactive case detection, and travel history. We find that in the absence of imported cases from mainland Tanzania, malaria would likely cease to persist on Zanzibar. We also investigate potential intervention scenarios that may lead to elimination, especially through changes to reactive case detection. While we find that some additional cases are removed by reactive case detection, a large proportion of cases are missed due to many infections having a low parasite density that go undetected by rapid diagnostic tests, a low rate of those infected with malaria seeking treatment, and a low rate of follow up at the household level of malaria cases detected at health facilities. While improvements in reactive case detection would lead to a reduction in malaria prevalence, none of the intervention scenarios tested here were sufficient to reach elimination. Imported cases need to be treated to have a substantial impact on prevalence.

: A code for fitting multi-wave epidemic models

The COVID-19 pandemic has given rise to a great demand for computational models capable of describing and inferring the evolution of an epidemic outbreak in the short term. In this sense, we introduce epidWaves, a package that provides a framework for fitting multi-wave epidemic models to data from actual outbreaks of COVID-19 and other infectious diseases.

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 potential of genomics for infectious disease forecasting

Genomic technologies have led to tremendous gains in understanding how pathogens function, evolve and interact. Pathogen diversity is now measurable at high precision and resolution, in part because over the past decade, sequencing technologies have increased in speed and capacity, at decreased cost. Alongside this, the use of models that can forecast emergence and size of infectious disease outbreaks has risen, highlighted by the coronavirus disease 2019 pandemic but also due to modelling advances that allow for rapid estimates in emerging outbreaks to inform monitoring, coordination and resource deployment. However, genomics studies have remained largely retrospective. While they contain high-resolution views of pathogen diversification and evolution in the context of selection, they are often not aligned with designing interventions. This is a missed opportunity because pathogen diversification is at the core of the most pressing infectious public health challenges, and interventions need to take the mechanisms of virulence and understanding of pathogen diversification into account. In this Perspective, we assess these converging fields, discuss current challenges facing both surveillance specialists and modellers who want to harness genomic data, and propose next steps for integrating longitudinally sampled genomic data with statistical learning and interpretable modelling to make reliable predictions into the future.

The impact of COVID-19 on a Malaria dominated region: A mathematical analysis and simulations

One of society’s major concerns that have continued for a long time is infectious diseases. It has been demonstrated that certain disease infections, in particular multiple disease infections, make it more challenging to identify and treat infected individuals, thus deteriorating human health. As a result, a COVID-19-malaria co-infection model is developed and analyzed to study the effects of threshold quantities and co-infection transmission rate on the two diseases’ synergistic relationship. This allowed us to better understand the co-dynamics of the two diseases in the population. The existence and stability of the disease-free equilibrium of each single infection were first investigated by using their respective reproduction number. The COVID-19 and malaria-free equilibrium are locally asymptotically stable when the individual threshold quantities RC and RM are below unity. Additionally, the occurrence of the malaria prevalent equilibrium is examined, and the requirements for the backward bifurcation’s existence are provided. Sensitivity analysis reveals that the two main parameters that influence the spread of COVID-19 infection are the disease transmission rate (βc) and the fraction of the exposed individuals becoming symptomatic (ψ), while malaria transmission is influenced by the abundance of vector population, which is driven by recruitment rate (πv) with an increase in the effective biting rate (b), probability of malaria transmission per mosquito bite (βm), and probability of malaria transmission from infected humans to vectors (βv). The findings from the numerical simulation of the model show that COVID-19 will predominate in the populace and drives malaria to extinction when RM<1<RC, whereas malaria will dominate in the population and drives COVID-19 into extinction when RC<1<RM. At the disease’s endemic equilibrium, the two diseases will coexist with the one with the highest reproduction number predominating but not eradicating the other. It was demonstrated in particular that COVID-19 will invade a population where malaria is endemic if the invasion reproduction number exceeds unity. The findings also demonstrate that when the two diseases are at endemic equilibrium, the prevalence of co-infection increases COVID-19’s burden on the population while decreasing malaria incidence.

Application of Mathematical Modeling and Computational Tools in the Modern Drug Design and Development Process

The conventional drug discovery approach is an expensive and time-consuming process, but its limitations have been overcome with the help of mathematical modeling and computational drug design approaches. Previously, finding a small molecular candidate as a drug against a disease was very costly and required a long time to screen a compound against a specific target. The development of novel targets and small molecular candidates against different diseases including emerging and reemerging diseases remains a major concern and necessitates the development of novel therapeutic targets as well as drug candidates as early as possible. In this regard, computational and mathematical modeling approaches for drug development are advantageous due to their fastest predictive ability and cost-effectiveness features. Computer-aided drug design (CADD) techniques utilize different computer programs as well as mathematics formulas to comprehend the interaction of a target and drugs. Traditional methods to determine small-molecule candidates as a drug have several limitations, but CADD utilizes novel methods that require little time and accurately predict a compound against a specific disease with minimal cost. Therefore, this review aims to provide a brief insight into the mathematical modeling and computational approaches for identifying a novel target and small molecular candidates for curing a specific disease. The comprehensive review mainly focuses on biological target prediction, structure-based and ligand-based drug design methods, molecular docking, virtual screening, pharmacophore modeling, quantitative structure-activity relationship (QSAR) models, molecular dynamics simulation, and MM-GBSA/MM-PBSA approaches along with valuable database resources and tools for identifying novel targets and therapeutics against a disease. This review will help researchers in a way that may open the road for the development of effective drugs and preventative measures against a disease in the future as early as possible.

Systems biology of malaria explored with nonhuman primates

"The Primate Malarias" book has been a uniquely important resource for multiple generations of scientists, since its debut in 1971, and remains pertinent to the present day. Indeed, nonhuman primates (NHPs) have been instrumental for major breakthroughs in basic and pre-clinical research on malaria for over 50 years. Research involving NHPs have provided critical insights and data that have been essential for malaria research on many parasite species, drugs, vaccines, pathogenesis, and transmission, leading to improved clinical care and advancing research goals for malaria control, elimination, and eradication. Whilst most malaria scientists over the decades have been studying Plasmodium falciparum, with NHP infections, in clinical studies with humans, or using in vitro culture or rodent model systems, others have been dedicated to advancing research on Plasmodium vivax, as well as on phylogenetically related simian species, including Plasmodium cynomolgi, Plasmodium coatneyi, and Plasmodium knowlesi. In-depth study of these four phylogenetically related species over the years has spawned the design of NHP longitudinal infection strategies for gathering information about ongoing infections, which can be related to human infections. These Plasmodium-NHP infection model systems are reviewed here, with emphasis on modern systems biological approaches to studying longitudinal infections, pathogenesis, immunity, and vaccines. Recent discoveries capitalizing on NHP longitudinal infections include an advanced understanding of chronic infections, relapses, anaemia, and immune memory. With quickly emerging new technological advances, more in-depth research and mechanistic discoveries can be anticipated on these and additional critical topics, including hypnozoite biology, antigenic variation, gametocyte transmission, bone marrow dysfunction, and loss of uninfected RBCs. New strategies and insights published by the Malaria Host-Pathogen Interaction Center (MaHPIC) are recapped here along with a vision that stresses the importance of educating future experts well trained in utilizing NHP infection model systems for the pursuit of innovative, effective interventions against malaria.

Exploring predictive frameworks for malaria in Burundi

In Burundi, malaria infection has been increasing in the last decade despite efforts to increase access to health services, and several intervention programs. The use of heterogeneous data can help to build predictive models of malaria cases. We built predictive frameworks: the generalized linear model (GLM), and artificial neural network (ANN), to predict malaria cases in four sub-groups and the overall general population. Descriptive results showed that more than half of malaria infections are observed in pregnant women and children under 5 years, with high burden to children between 12 and 59 months. Modelling results showed that, ANN model performed better in predicting total cases compared to GLM. Both model frameworks showed that education rates and Insecticide Treated Bed Nets (ITNs) had decreasing effects on malaria cases, some other variables had an increasing effect. Thus, malaria control and prevention interventions program are encouraged to understand those variables, and take appropriate measures such as providing ITNs, sensitization in schools and the communities, starting within high dense communities, among others. Early prediction of cases can provide timely information needed to be proactive for intervention strategies, and it can help to mitigate the epidemics and reduce its impact on populations and the economy.

Receptivity to malaria: meaning and measurement

"Receptivity" to malaria is a construct developed during the Global Malaria Eradication Programme (GMEP) era. It has been defined in varied ways and no consistent, quantitative definition has emerged over the intervening decades. Despite the lack of consistency in defining this construct, the idea that some areas are more likely to sustain malaria transmission than others has remained important in decision-making in malaria control, planning for malaria elimination and guiding activities during the prevention of re-establishment (POR) period. This manuscript examines current advances in methods of measurement. In the context of a decades long decline in global malaria transmission and an increasing number of countries seeking to eliminate malaria, understanding and measuring malaria receptivity has acquired new relevance.

The changing risk patterns of Plasmodium vivax malaria in Greece due to climate change

It has great importance to study the potential effects of climate change on Plasmodium vivax malaria in Greece because the country can be the origin of the spread of vivax malaria to the northern areas. The potential lengths of the transmission seasons of Plasmodium vivax malaria were forecasted for 2041-2060 and 2061-2080 and were combined. The potential ranges were predicted by Climate Envelope Modelling Method. The models show moderate areal increase and altitudinal shift in the malaria-endemic areas in Greece in the future. The length of the transmission season is predicted to increase by 1 to 2 months, mainly in the mid-elevation regions and the Aegean Archipelago. The combined factors also predict the decrease of vivax malaria-free area in Greece. It can be concluded that rather the elongation of the transmission season will lead to an increase of the malaria risk in Greece than the increase in the suitability values.

Understanding dynamics of Plasmodium falciparum gametocytes production: Insights from an age-structured model

Many models of within-host malaria infection dynamics have been formulated since the pioneering work of Anderson et al. in 1989. Biologically, the goal of these models is to understand what governs the severity of infections, the patterns of infectiousness, and the variation thereof across individual hosts. Mathematically, these models are based on dynamical systems, with standard approaches ranging from K-compartments ordinary differential equations (ODEs) to delay differential equations (DDEs), to capture the relatively constant duration of replication and bursting once a parasite infects a host red blood cell. Using malariatherapy data, which offers fine-scale resolution on the dynamics of infection across a number of individual hosts, we compare the fit and robustness of one of these standard approaches (K-compartments ODE) with a partial differential equations (PDEs) model, which explicitly tracks the "age" of an infected cell. While both models perform quite similarly in terms of goodness-of-fit for suitably chosen K, the K-compartments ODE model particularly overestimates parasite densities early on in infections when the number of repeated compartments is not large enough. Finally, the K-compartments ODE model (for suitably chosen K) and the PDE model highlight a strong qualitative connection between the density of transmissible parasite stages (i.e., gametocytes) and the density of host-damaging (and asexually-replicating) parasite stages. This finding provides a simple tool for predicting which hosts are most infectious to mosquitoes -vectors of Plasmodium parasites- which is a crucial component of global efforts to control and eliminate malaria.

Dynamic analysis of a malaria reaction-diffusion model with periodic delays and vector bias

One of the most important vector-borne disease in humans is malaria, caused by Plasmodium parasite. Seasonal temperature elements have a major effect on the life development of mosquitoes and the development of parasites. In this paper, we establish and analyze a reaction-diffusion model, which includes seasonality, vector-bias, temperature-dependent extrinsic incubation period (EIP) and maturation delay in mosquitoes. In order to get the model threshold dynamics, a threshold parameter, the basic reproduction number $ R_{0} $ is introduced, which is the spectral radius of the next generation operator. Quantitative analysis indicates that when $ R_{0} < 1 $, there is a globally attractive disease-free $ \omega $-periodic solution; disease is uniformly persistent in humans and mosquitoes if $ R_{0} > 1 $. Numerical simulations verify the results of the theoretical analysis and discuss the effects of diffusion and seasonality. We study the relationship between the parameters in the model and $ R_{0} $. More importantly, how to allocate medical resources to reduce the spread of disease is explored through numerical simulations. Last but not least, we discover that when studying malaria transmission, ignoring vector-bias or assuming that the maturity period is not affected by temperature, the risk of disease transmission will be underestimate.

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R0<1. A similar result is obtained for the endemic equilibrium when R0>1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge–Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note.

Vector-Borne Disease Models with Active and Inactive Vectors: A Simple Way to Consider Biting Behavior

Vector-borne diseases are a serious public health problem, mosquitoes being one of the most important vectors. To analyze the dynamics of this type of disease, Ross-Macdonald models are commonly used. In its simplest formulation and the most common in scientific literature, it is assumed that all mosquitoes are biting at a given rate. To improve this general assumption, we developed a vector-borne disease model with active and inactive vectors as a simple way to incorporate the more general characteristics of mosquito feeding behavior into disease dynamics. Our objective is to obtain an estimate of the Ross-Macdonald biting rate from the feeding parameters that reproduce the same dynamics as the model with active and inactive vectors. Two different cases were analyzed: a SIS-SI model and a SIR-SI model with a single epidemic. Different methods to estimate the biting rate in the Ross-Macdonald model were proposed and analyzed. To compare the results of the models, different epidemiological indicators were considered. When the biting rate is estimated considering that both models have the same basic reproduction number, very similar disease dynamics are obtained. This method is a simple way to incorporate the mosquito feeding behavior into the standard Ross-Macdonald model.

How radical is radical cure? Site-specific biases in clinical trials underestimate the effect of radical cure on Plasmodium vivax hypnozoites

BACKGROUND

Plasmodium vivax blood-stage relapses originating from re-activating hypnozoites are a major barrier for control and elimination of this disease. Radical cure is a form of therapy capable of addressing this problem. Recent clinical trials of radical cure have yielded efficacy estimates ranging from 65 to 94%, with substantial variation across trial sites.

METHODS

An analysis of simulated trial data using a transmission model was performed to demonstrate that variation in efficacy estimates across trial sites can arise from differences in the conditions under which trials are conducted.

RESULTS

The analysis revealed that differences in transmission intensity, heterogeneous exposure and relapse rate can yield efficacy estimates ranging as widely as 12-78%, despite simulating trial data under the uniform assumption that treatment had a 75% chance of clearing hypnozoites. A longer duration of prophylaxis leads to a greater measured efficacy, particularly at higher transmission intensities, making the comparison between the protection of different radical cure treatment regimens against relapse more challenging. Simulations show that vector control and parasite genotyping offer two potential means to yield more standardized efficacy estimates that better reflect prevention of relapse.

CONCLUSIONS

Site-specific biases are likely to contribute to variation in efficacy estimates both within and across clinical trials. Future clinical trials can reduce site-specific biases by conducting trials in low-transmission settings where re-infections from mosquito bite are less common, by preventing re-infections using vector control measures, or by identifying and excluding likely re-infections that occur during follow-up, by using parasite genotyping methods.

COVID-19: Estimation of the transmission dynamics in Spain using a stochastic simulator and black-box optimization techniques

BACKGROUND AND OBJECTIVES

Epidemiological models of epidemic spread are an essential tool for optimizing decision-making. The current literature is very extensive and covers a wide variety of deterministic and stochastic models. However, with the increase in computing resources, new, more general, and flexible procedures based on simulation models can assess the effectiveness of measures and quantify the current state of the epidemic. This paper illustrates the potential of this approach to build a new dynamic probabilistic model to estimate the prevalence of SARS-CoV-2 infections in different compartments.

METHODS

We propose a new probabilistic model in which, for the first time in the epidemic literature, parameter learning is carried out using gradient-free stochastic black-box optimization techniques simulating multiple trajectories of the infection dynamics in a general way, solving an inverse problem that is defined employing the daily information from mortality records.

RESULTS

After the application of the new proposal in Spain in the first and successive waves, the result of the model confirms the accuracy to estimate the seroprevalence and allows us to know the real dynamics of the pandemic a posteriori to assess the impact of epidemiological measures by the Spanish government and to plan more efficiently the subsequent decisions with the prior knowledge obtained.

CONCLUSIONS

The model results allow us to estimate the daily patterns of COVID-19 infections in Spain retrospectively and examine the population's exposure to the virus dynamically in contrast to seroprevalence surveys. Furthermore, given the flexibility of our simulation framework, we can model situations -even using non-parametric distributions between the different compartments in the model- that other models in the existing literature cannot. Our general optimization strategy remains valid in these cases, and we can easily create other non-standard simulation epidemic models that incorporate more complex and dynamic structures.

Modelling infectious diseases with herd immunity in a randomly mixed population

The conventional susceptible-infectious-recovered (SIR) model tends to magnify the transmission dynamics of infectious diseases, and thus the estimated total infections and immunized population may be higher than the threshold required for infection control and eradication. The study developed a new SIR framework that allows the transmission rate of infectious diseases to decline along with the reduced risk of contact infection to overcome the limitations of the conventional SIR model. Two new SIR models were formulated to mimic the declining transmission rate of infectious diseases at different stages of transmission. Model A utilized the declining transmission rate along with the reduced risk of contact infection following infection, while Model B incorporated the declining transmission rate following recovery. Both new models and the conventional SIR model were then used to simulate an infectious disease with a basic reproduction number (r₀) of 3.0 and a herd immunity threshold (HIT) of 0.667 with and without vaccination. Outcomes of simulations were assessed at the time when the total immunized population reached the level predicted by the HIT, and at the end of simulations. Further, all three models were used to simulate the transmission dynamics of seasonal influenza in the United States and disease burdens were projected and compared with estimates from the Centers for Disease Control and Prevention. For the simulated infectious disease, in the initial phase of the outbreak, all three models performed expectedly when the sizes of infectious and recovered populations were relatively small. As the infectious population increased, the conventional SIR model appeared to overestimate the infections even when the HIT was achieved in all scenarios with and without vaccination. For the same scenario, Model A appeared to attain the level predicted by the HIT and in comparison, Model B projected the infectious disease to be controlled at the level predicted by the HIT only at high vaccination rates. For infectious diseases with high r₀, and at low vaccination rates, the level at which the infectious disease was controlled cannot be accurately predicted by the current theorem. Transmission dynamics of infectious diseases with herd immunity can be accurately modelled by allowing the transmission rate of infectious diseases to decline along with the reduction of contact infection risk after recovery or vaccination. Model B provides a credible framework for modelling infectious diseases with herd immunity in a randomly mixed population.

Elucidating relationships between P.falciparum prevalence and measures of genetic diversity with a combined genetic-epidemiological model of malaria

There is an abundance of malaria genetic data being collected from the field, yet using these data to understand the drivers of regional epidemiology remains a challenge. A key issue is the lack of models that relate parasite genetic diversity to epidemiological parameters. Classical models in population genetics characterize changes in genetic diversity in relation to demographic parameters, but fail to account for the unique features of the malaria life cycle. In contrast, epidemiological models, such as the Ross-Macdonald model, capture malaria transmission dynamics but do not consider genetics. Here, we have developed an integrated model encompassing both parasite evolution and regional epidemiology. We achieve this by combining the Ross-Macdonald model with an intra-host continuous-time Moran model, thus explicitly representing the evolution of individual parasite genomes in a traditional epidemiological framework. Implemented as a stochastic simulation, we use the model to explore relationships between measures of parasite genetic diversity and parasite prevalence, a widely-used metric of transmission intensity. First, we explore how varying parasite prevalence influences genetic diversity at equilibrium. We find that multiple genetic diversity statistics are correlated with prevalence, but the strength of the relationships depends on whether variation in prevalence is driven by host- or vector-related factors. Next, we assess the responsiveness of a variety of statistics to malaria control interventions, finding that those related to mixed infections respond quickly (∼months) whereas other statistics, such as nucleotide diversity, may take decades to respond. These findings provide insights into the opportunities and challenges associated with using genetic data to monitor malaria epidemiology.

A modified age-structured SIR model for COVID-19 type viruses

We present a modified age-structured SIR model based on known patterns of social contact and distancing measures within Washington, USA. We find that population age-distribution has a significant effect on disease spread and mortality rate, and contribute to the efficacy of age-specific contact and treatment measures. We consider the effect of relaxing restrictions across less vulnerable age-brackets, comparing results across selected groups of varying population parameters. Moreover, we analyze the mitigating effects of vaccinations and examine the effectiveness of age-targeted distributions. Lastly, we explore how our model can applied to other states to reflect social-distancing policy based on different parameters and metrics.

Mechanistic within-host models of the asexual Plasmodium falciparum infection: a review and analytical assessment

Background

Malaria blood-stage infection length and intensity are important drivers of disease and transmission; however, the underlying mechanisms of parasite growth and the host’s immune response during infection remain largely unknown. Over the last 30 years, several mechanistic mathematical models of malaria parasite within-host dynamics have been published and used in malaria transmission models.

Methods

Mechanistic within-host models of parasite dynamics were identified through a review of published literature. For a subset of these, model code was reproduced and descriptive statistics compared between the models using fitted data. Through simulation and model analysis, key features of the models were compared, including assumptions on growth, immune response components, variant switching mechanisms, and inter-individual variability.

Results

The assessed within-host malaria models generally replicate infection dynamics in malaria-naïve individuals. However, there are substantial differences between the model dynamics after disease onset, and models do not always reproduce late infection parasitaemia data used for calibration of the within host infections. Models have attempted to capture the considerable variability in parasite dynamics between individuals by including stochastic parasite multiplication rates; variant switching dynamics leading to immune escape; variable effects of the host immune responses; or via probabilistic events. For models that capture realistic length of infections, model representations of innate immunity explain early peaks in infection density that cause clinical symptoms, and model representations of antibody immune responses control the length of infection. Models differed in their assumptions concerning variant switching dynamics, reflecting uncertainty in the underlying mechanisms of variant switching revealed by recent clinical data during early infection. Overall, given the scarce availability of the biological evidence there is limited support for complex models.

Conclusions

This study suggests that much of the inter-individual variability observed in clinical malaria infections has traditionally been attributed in models to random variability, rather than mechanistic disease dynamics. Thus, it is proposed that newly developed models should assume simple immune dynamics that minimally capture mechanistic understandings and avoid over-parameterization and large stochasticity which inaccurately represent unknown disease mechanisms.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12936-021-03813-z.

Malaria Temporal Variation and Modelling Using Time-Series in Sussundenga District, Mozambique

Malaria is one of the leading causes of morbidity and mortality in Mozambique, which has the fifth highest prevalence in the world. Sussundenga District in Manica Province has documented high P. falciparum incidence at the local rural health center (RHC). This study's objective was to analyze the P. falciparum temporal variation and model its pattern in Sussundenga District, Mozambique. Data from weekly epidemiological bulletins (BES) was collected from 2015 to 2019 and a time-series analysis was applied. For temporal modeling, a Box-Jenkins method was used with an autoregressive integrated moving average (ARIMA). Over the study period, 372,498 cases of P. falciparum were recorded in Sussundenga. There were weekly and yearly variations in incidence overall (p < 0.001). Children under five years had decreased malaria tendency, while patients over five years had an increased tendency. The ARIMA (2,2,1) (1,1,1) 52 model presented the least Root Mean Square being the most appropriate for forecasting. The goodness of fit was 68.15% for malaria patients less than five years old and 73.2% for malaria patients over five years old. The findings indicate that cases are decreasing among individuals less than five years and are increasing slightly in those older than five years. The P. falciparum case occurrence has a weekly temporal pattern peaking during the wet season. Based on the spatial and temporal distribution using ARIMA modelling, more efficient strategies that target this seasonality can be implemented to reduce the overall malaria burden in both Sussundenga District and regionally.

Accessing the syndemic of COVID-19 and malaria intervention in Africa

BACKGROUND

The pandemic of the coronavirus disease 2019 (COVID-19) has caused substantial disruptions to health services in the low and middle-income countries with a high burden of other diseases, such as malaria in sub-Saharan Africa. The aim of this study is to assess the impact of COVID-19 pandemic on malaria transmission potential in malaria-endemic countries in Africa.

METHODS

We present a data-driven method to quantify the extent to which the COVID-19 pandemic, as well as various non-pharmaceutical interventions (NPIs), could lead to the change of malaria transmission potential in 2020. First, we adopt a particle Markov Chain Monte Carlo method to estimate epidemiological parameters in each country by fitting the time series of the cumulative number of reported COVID-19 cases. Then, we simulate the epidemic dynamics of COVID-19 under two groups of NPIs: (1) contact restriction and social distancing, and (2) early identification and isolation of cases. Based on the simulated epidemic curves, we quantify the impact of COVID-19 epidemic and NPIs on the distribution of insecticide-treated nets (ITNs). Finally, by treating the total number of ITNs available in each country in 2020, we evaluate the negative effects of COVID-19 pandemic on malaria transmission potential based on the notion of vectorial capacity.

RESULTS

We conduct case studies in four malaria-endemic countries, Ethiopia, Nigeria, Tanzania, and Zambia, in Africa. The epidemiological parameters (i.e., the basic reproduction number [Formula: see text] and the duration of infection [Formula: see text]) of COVID-19 in each country are estimated as follows: Ethiopia ([Formula: see text], [Formula: see text]), Nigeria ([Formula: see text], [Formula: see text]), Tanzania ([Formula: see text], [Formula: see text]), and Zambia ([Formula: see text], [Formula: see text]). Based on the estimated epidemiological parameters, the epidemic curves simulated under various NPIs indicated that the earlier the interventions are implemented, the better the epidemic is controlled. Moreover, the effect of combined NPIs is better than contact restriction and social distancing only. By treating the total number of ITNs available in each country in 2020 as a baseline, our results show that even with stringent NPIs, malaria transmission potential will remain higher than expected in the second half of 2020.

CONCLUSIONS

By quantifying the impact of various NPI response to the COVID-19 pandemic on malaria transmission potential, this study provides a way to jointly address the syndemic between COVID-19 and malaria in malaria-endemic countries in Africa. The results suggest that the early intervention of COVID-19 can effectively reduce the scale of the epidemic and mitigate its impact on malaria transmission potential.

The effectiveness of malaria camps as part of the Durgama Anchalare Malaria Nirakaran (DAMaN) program in Odisha, India: study protocol for a cluster-assigned quasi-experimental study

The Indian state of Odisha has a longstanding battle with forest malaria. Many remote and rural villages have poor access to health care, a problem that is exacerbated during the rainy season when malaria transmission is at its peak. Approximately 62% of the rural population consists of tribal groups who are among the communities most negatively impacted by malaria. To address the persistently high rates of malaria in these remote regions, the Odisha State Malaria Control Program introduced 'malaria camps' in 2017 where teams of health workers visit villages to educate the population, enhance vector control methods, and perform village-wide screening and treatment. Malaria rates declined statewide, particularly in forested areas, following the introduction of the malaria camps, but the impact of the intervention is yet to be externally evaluated. This study protocol describes a cluster-assigned quasi-experimental stepped-wedge study with a pretest-posttest control group design that evaluates if malaria camps reduce the prevalence of malaria, compared to control villages which receive the usual malaria control interventions (e.g. IRS, ITNs), as detected by PCR.

Migration rate estimation in an epidemic network

Most of the recent epidemic outbreaks in the world have as a trigger, a strong migratory component as has been evident in the recent Covid-19 pandemic. In this work we address the problem of migration of human populations and its effect on pathogen reinfections in the case of Dengue, using a Markov-chain susceptible-infected-susceptible (SIS) metapopulation model over a network. Our model postulates a general contact rate that represents a local measure of several factors: the population size of infected hosts that arrive at a given location as a function of total population size, the current incidence at neighboring locations, and the connectivity of the network where the disease spreads. This parameter can be interpreted as an indicator of outbreak risk at a given location. This parameter is tied to the fraction of individuals that move across boundaries (migration). To illustrate our model capabilities, we estimate from epidemic Dengue data in Mexico the dynamics of migration at a regional scale incorporating climate variability represented by an index based on precipitation data.

Towards Building a Sustainable Future: Positioning Ecological Modelling for Impact in Ecosystems Management

As many ecosystems worldwide are in peril, efforts to manage them sustainably require scientific advice. While numerous researchers around the world use a great variety of models to understand ecological dynamics and their responses to disturbances, only a small fraction of these models are ever used to inform ecosystem management. There seems to be a perception that ecological models are not useful for management, even though mathematical models are indispensable in many other fields. We were curious about this mismatch, its roots, and potential ways to overcome it. We searched the literature on recommendations and best practices for how to make ecological models useful to the management of ecosystems and we searched for 'success stories' from the past. We selected and examined several cases where models were instrumental in ecosystem management. We documented their success and asked whether and to what extent they followed recommended best practices. We found that there is not a unique way to conduct a research project that is useful in management decisions. While research is more likely to have impact when conducted with many stakeholders involved and specific to a situation for which data are available, there are great examples of small groups or individuals conducting highly influential research even in the absence of detailed data. We put the question of modelling for ecosystem management into a socio-economic and national context and give our perspectives on how the discipline could move forward.

Targeting Malaria Hotspots to Reduce Transmission Incidence in Senegal

In central Senegal, malaria incidence declined in response to scaling-up of control measures from 2000 to 2010 and has since remained stable, making elimination unlikely in the short term. Additional control measures are needed to reduce transmission. We simulated chemoprophylaxis interventions targeting malaria hotspots using a metapopulation mathematical model, based on a differential-equation framework and incorporating human mobility. The model was fitted to weekly malaria incidence from 45 villages. Three approaches for selecting intervention targets were compared: (a) villages with malaria cases during the low transmission season of the previous year; (b) villages with highest incidence during the high transmission season of the previous year; (c) villages with highest connectivity with adjacent populations. Our results showed that intervention strategies targeting hotspots would be effective in reducing malaria incidence in both targeted and untargeted areas. Regardless of the intervention strategy used, pre-elimination (1-5 cases per 1000 per year) would not be reached without simultaneously increasing vector control by more than 10%. A cornerstone of malaria control and elimination is the effective targeting of strategic locations. Mathematical tools help to identify those locations and estimate the impact in silico.

Asymptotic analysis of a vector-borne disease model with the age of infection

Vector-borne infectious diseases may involve both horizontal transmission between hosts and transmission from infected vectors to susceptible hosts. In this paper, we incorporate these two transmission modes into a vector-borne disease model that includes general nonlinear incidence rates and the age of infection for both hosts and vectors. We show the existence, uniqueness, nonnegativity, and boundedness of solutions for the model. We study the existence and local stability of steady states, which is shown to be determined by the basic reproduction number. By showing the existence of a global compact attractor and uniform persistence of the system, we establish the threshold dynamics using the Fluctuation Lemma and the approach of Lyapunov functionals. When the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable and otherwise the disease will be established when there is initial infection force for the hosts. We also study a model with the standard incidence rate and discuss the effect of different incidence rates on the disease dynamics.

Accounting for regional transmission variability and the impact of malaria control interventions in Ghana: a population level mathematical modelling approach

BACKGROUND

This paper investigates the impact of malaria preventive interventions in Ghana and the prospects of achieving programme goals using mathematical models based on regionally diverse climatic zones of the country.

METHODS

Using data from the District Health Information Management System of the Ghana Health Service from 2008 to 2017, and historical intervention coverage levels, ordinary non-linear differential equations models were developed. These models incorporated transitions amongst various disease compartments for the three main ecological zones in Ghana. The Approximate Bayesian Computational sampling approach, with a distance based rejection criteria, was adopted for calibration. A leave-one-out approach was used to validate model parameters and the most sensitive parameters were evaluated using a multivariate regression analysis. The impact of insecticide-treated bed nets and their usage, and indoor residual spraying, as well as their protective efficacy on the incidence of malaria, was simulated at various levels of coverage and protective effectiveness in each ecological zone to investigate the prospects of achieving goals of the Ghana malaria control strategy for 2014-2020.

RESULTS

Increasing the coverage levels of both long-lasting insecticide-treated bed nets and indoor residual spraying activities, without a corresponding increase in their recommended utilization, does not impact highly on averting predicted incidence of malaria. Improving proper usage of long-lasting insecticide-treated bed nets could lead to substantial reductions in the predicted incidence of malaria. Similar results were obtained with indoor residual spraying across all ecological zones of Ghana.

CONCLUSIONS

Projected goals set in the national strategic plan for malaria control 2014-2020, as well as World Health Organization targets for malaria pre-elimination by 2030, are only likely to be achieved if a substantial improvement in treated bed net usage is achieved, coupled with targeted deployment of indoor residual spraying with high community acceptability and efficacy.

The impact of within-vector parasite development on the extrinsic incubation period

Mosquito-borne diseases, in particular malaria, have a significant burden worldwide leading to nearly half a million deaths each year. The malaria parasite requires a vertebrate host, such as a human, and a vector host, the Anopheles mosquito, to complete its full life cycle. Here, we focus on the parasite dynamics within the vector to examine the first appearance of sporozoites in the salivary glands, which indicates a first time of infectiousness of mosquitoes. The timing of this period of pathogen development in the mosquito until transmissibility, known as the extrinsic incubation period, remains poorly understood. We develop compartmental models of within-mosquito parasite dynamics fitted with experimental data on oocyst and sporozoite counts. We find that only a fraction of oocysts burst to release sporozoites and bursting must be delayed either via a time-dependent function or a gamma-distributed set of compartments. We use Bayesian inference to estimate distributions of parameters and determine that bursting rate is a key epidemiological parameter. A better understanding of the factors impacting the extrinsic incubation period will aid in the development of interventions to slow or stop the spread of malaria.

Adaptive immunity selects against malaria infection blocking mutations

The mutation responsible for Duffy negativity, which impedes Plasmodium vivax infection, has reached high frequencies in certain human populations. Conversely, mutations capable of blocking the more lethal P. falciparum have not succeeded in malarious zones. Here we present an evolutionary-epidemiological model of malaria which demonstrates that if adaptive immunity against the most virulent effects of malaria is gained rapidly by the host, mutations which prevent infection per se are unlikely to succeed. Our results (i) explain the rarity of strain-transcending P. falciparum infection blocking adaptations in humans; (ii) make the surprising prediction that mutations which block P. falciparum infection are most likely to be found in populations experiencing low or infrequent malaria transmission, and (iii) predict that immunity against some of the virulent effects of P. vivax malaria may be built up over the course of many infections.

Modelling the influence of progressive social awareness, lockdown and anthropogenic migration on the dynamics of an epidemic

The basic Susceptible-Infected-Recovered (SIR) model is extended to include effects of progressive social awareness, lockdowns and anthropogenic migration. It is found that social awareness can effectively contain the spread by lowering the basic reproduction rate R 0 . Interestingly, the awareness is found to be more effective in a society which can adopt the awareness faster compared to the one having a slower response. The paper also separates the mortality fraction from the clinically recovered fraction and attempts to model the outcome of lockdowns, in absence and presence of social awareness. It is seen that staggered exits from lockdowns are not only economically beneficial but also helps to curb the infection spread. Moreover, a staggered exit strategy with progressive social awareness is found to be the most efficient intervention. The paper also explores the effects of anthropogenic migration on the dynamics of the epidemic in a two-zone scenario. The calculations yield dissimilar evolution of different fractions in different zones. Such models can be convenient to strategize the division of a large zone into smaller sub-zones for a disproportionate imposition of lockdown, or, an exit from one. Calculations are done with parameters consistent with the SARS-COV-2 pathogen in the Indian context.

Solutions of a disease model with fractional white noise

We consider an epidemic disease system by an additive fractional white noise to show that epidemic diseases may be more competently modeled in the fractional-stochastic settings than the ones modeled by deterministic differential equations. We generate a new SIRS model and perturb it to the fractional-stochastic systems. We study chaotic behavior at disease-free and endemic steady-state points on these systems. We also numerically solve the fractional-stochastic systems by an trapezoidal rule and an Euler type numerical method. We also associate the SIRS model with fractional Brownian motion by Wick product and determine numerical and explicit solutions of the resulting system. There is no SIRS-type model which considers fractional epidemic disease models with fractional white noise or Wick product settings which makes the paper totally a new contribution to the related science.

Inference and prediction of malaria transmission dynamics using time series data

BACKGROUND

Disease surveillance systems are essential for effective disease intervention and control by monitoring disease prevalence as time series. To evaluate the severity of an epidemic, statistical methods are widely used to forecast the trend, seasonality, and the possible number of infections of a disease. However, most statistical methods are limited in revealing the underlying dynamics of disease transmission, which may be affected by various impact factors, such as environmental, meteorological, and physiological factors. In this study, we focus on investigating malaria transmission dynamics based on time series data.

METHODS

A data-driven nonlinear stochastic model is proposed to infer and predict the dynamics of malaria transmission based on the time series of prevalence data. Specifically, the dynamics of malaria transmission is modeled based on the notion of vectorial capacity (VCAP) and entomological inoculation rate (EIR). A particle Markov chain Monte Carlo (PMCMC) method is employed to estimate the model parameters. Accordingly, a one-step-ahead prediction method is proposed to project the number of future malaria infections. Finally, two case studies are carried out on the inference and prediction of Plasmodium vivax transmission in Tengchong and Longling, Yunnan province, China.

RESULTS

The results show that the trained data-driven stochastic model can well fit the historical time series of P. vivax prevalence data in both counties from 2007 to 2010. Moreover, with well-trained model parameters, the proposed one-step-ahead prediction method can achieve better performances than that of the seasonal autoregressive integrated moving average model with respect to predicting the number of future malaria infections.

CONCLUSIONS

By involving dynamically changing impact factors, the proposed data-driven model together with the PMCMC method can successfully (i) depict the dynamics of malaria transmission, and (ii) achieve accurate one-step-ahead prediction about malaria infections. Such a data-driven method has the potential to investigate malaria transmission dynamics in other malaria-endemic countries/regions.