Model Of Malaria Transmission Research Articles

A two-strain malaria transmission model with seasonality and incubation period

A two-strain malaria transmission model with seasonality and incubation period

Threshold dynamics and regional optimal control of a malaria model with spatial heterogeneity and ivermectin therapy

The recent experimental results illustrate that adding ivermectin to artemisinin-based combination therapy can target malaria parasite and its vector, which may be a new treatment option. In this paper, we present a new malaria transmission model, which incorporates spatial heterogeneity, general incidence rate and treatment plan with ivermectin. The basic reproduction number R0 is introduced as a threshold parameter to determine whether malaria will eventually die out or not. Further, we propose and analyze the regional optimal control problem to minimize mosquito population, exposed and infectious humans as well as cost. Numerically, we investigate the transmission and control of malaria in The Gambia. Results show that the treatment plans with ivermectin and without ivermectin have the same contribution to R0, but have different effects on the epidemic level of malaria. This conclusion also holds for different incidence rates with some assumptions. Moreover, by comparing the cost and benefit of different strategies, the most cost-effective strategy is found.

A Sensitivity Analysis of a Mathematical Model for the Transmission of Endemic Malaria under Periodic Climatic Conditions

We perform sensitivity analysis on a periodic mathematical model of endemic malaria transmission to determine the relative importance and impact of model parameters to disease transmission and prevalence. In this analysis, two sets of baseline parameter values are compiled: one for areas that exhibit high transmission rate and another one for areas with low transmission rates. Sensitivity indices for the basic reproductive number and the endemic equilibrium points are computed. The study established that in areas of low transmission, the reproductive number is most sensitive to the mosquito biting rate, but the equilibrium proportion of the infectious humans is most sensitive to the human recovery rate. Sensitivity analysis on all state variables was conducted. The results indicated that the most influential factors in the transmission and persistence of malaria in the society are those related to vectorial competence. These findings suggests that strategies that target the vector characteristics such as the mosquito biting rate and those that target the human recovery rate can be very successful in controlling malaria. These strategies include the use of insecticide-treated mosquito nets, indoor residual spraying, prompt diagnosis and treatment of infectious individuals. However, a combination of intervention strategies is more effective than application of a single intervention.

Optimal control analysis of a malaria transmission model with applications to Democratic Republic of Congo

In this paper, a dynamical model of malaria transmission with vector-bias and timedependent controls is investigated. The controls include the RTS,S malaria vaccine, using insecticide-treated mosquito net, treatment of infectious human, and indoor spraying. For constant controls, the existence and stability of equilibrium, as well as the existence of backward bifurcation, are obtained. The sensitivity analysis quantifies the impact of parameters and controls on the basic reproduction number. For time-dependent controls, by using the Pontryagin’s maximum principle the existence and expression of optimal controls are established. As an application of the model and control strategies, the malaria transmission and controls in Democratic Republic of Congo are discussed. To be specific, we simulate the reported cases of Democratic Republic of Congo by World Health Organization and predict the trends. Cost-effectiveness analysis and numerical simulations show that combining all controls can minimize the number of infected humans to the full extent, using insecticide-treated mosquito net is the most cost-effectiveness strategy, combining RTS,S malaria vaccine with using insecticide-treated mosquito net and treatment of infectious human is also cost-effective among all the strategies with good effect.

Spatial dynamics of malaria transmission.

The Ross-Macdonald model has exerted enormous influence over the study of malaria transmission dynamics and control, but it lacked features to describe parasite dispersal, travel, and other important aspects of heterogeneous transmission. Here, we present a patch-based differential equation modeling framework that extends the Ross-Macdonald model with sufficient skill and complexity to support planning, monitoring and evaluation for Plasmodium falciparum malaria control. We designed a generic interface for building structured, spatial models of malaria transmission based on a new algorithm for mosquito blood feeding. We developed new algorithms to simulate adult mosquito demography, dispersal, and egg laying in response to resource availability. The core dynamical components describing mosquito ecology and malaria transmission were decomposed, redesigned and reassembled into a modular framework. Structural elements in the framework-human population strata, patches, and aquatic habitats-interact through a flexible design that facilitates construction of ensembles of models with scalable complexity to support robust analytics for malaria policy and adaptive malaria control. We propose updated definitions for the human biting rate and entomological inoculation rates. We present new formulas to describe parasite dispersal and spatial dynamics under steady state conditions, including the human biting rates, parasite dispersal, the "vectorial capacity matrix," a human transmitting capacity distribution matrix, and threshold conditions. An [Formula: see text] package that implements the framework, solves the differential equations, and computes spatial metrics for models developed in this framework has been developed. Development of the model and metrics have focused on malaria, but since the framework is modular, the same ideas and software can be applied to other mosquito-borne pathogen systems.

Mathematical Model of Malaria Transmission with Anti-Malarial Herbal Therapy as Control

Conventional anti–malarial drugs (chloroquine, Artesunate, Quinine, Amodiaquine etc) are used by most malaria-endemic countries as first-line treatment for uncomplicated malaria. However, resistance by plasmodium parasite against these conventional anti–malarial drugs has necessitated the need for herbal medicine as alternative. So in this study, we formulate a mathematical model of malaria transmission in two interacting population of human (host) and mosquito (vector) incorporating anti-malarial herbal therapy as first line treatment for uncomplicated malaria infection. The region where the model is epidemiological feasible and mathematically well–posed is established and the basic reproduction number R_0 is derived using next generation matrix approach. The numerical experiment carried out to access the impact of the control measure on malaria transmission revealed a reduction in the number of complicated infectious human population. Hence this research work suggests a massive campaign on use of anti-malarial herbal therapy as first- line treatment for malaria infection cases.

Modelling the impact of interventions on imported, introduced and indigenous malaria infections in Zanzibar, Tanzania

Malaria cases can be classified as imported, introduced or indigenous cases. The World Health Organization’s definition of malaria elimination requires an area to demonstrate that no new indigenous cases have occurred in the last three years. Here, we present a stochastic metapopulation model of malaria transmission that distinguishes between imported, introduced and indigenous cases, and can be used to test the impact of new interventions in a setting with low transmission and ongoing case importation. We use human movement and malaria prevalence data from Zanzibar, Tanzania, to parameterise the model. We test increasing the coverage of interventions such as reactive case detection; implementing new interventions including reactive drug administration and treatment of infected travellers; and consider the potential impact of a reduction in transmission on Zanzibar and mainland Tanzania. We find that the majority of new cases on both major islands of Zanzibar are indigenous cases, despite high case importation rates. Combinations of interventions that increase the number of infections treated through reactive case detection or reactive drug administration can lead to substantial decreases in malaria incidence, but for elimination within the next 40 years, transmission reduction in both Zanzibar and mainland Tanzania is necessary.

Application of mathematical modelling to inform national malaria intervention planning in Nigeria

BackgroundFor their 2021–2025 National Malaria Strategic Plan (NMSP), Nigeria’s National Malaria Elimination Programme (NMEP), in partnership with the World Health Organization (WHO), developed a targeted approach to intervention deployment at the local government area (LGA) level as part of the High Burden to High Impact response. Mathematical models of malaria transmission were used to predict the impact of proposed intervention strategies on malaria burden.MethodsAn agent-based model of Plasmodium falciparum transmission was used to simulate malaria morbidity and mortality in Nigeria’s 774 LGAs under four possible intervention strategies from 2020 to 2030. The scenarios represented the previously implemented plan (business-as-usual), the NMSP at an 80% or higher coverage level and two prioritized plans according to the resources available to Nigeria. LGAs were clustered into 22 epidemiological archetypes using monthly rainfall, temperature suitability index, vector abundance, pre-2010 parasite prevalence, and pre-2010 vector control coverage. Routine incidence data were used to parameterize seasonality in each archetype. Each LGA’s baseline malaria transmission intensity was calibrated to parasite prevalence in children under the age of five years measured in the 2010 Malaria Indicator Survey (MIS). Intervention coverage in the 2010–2019 period was obtained from the Demographic and Health Survey, MIS, the NMEP, and post-campaign surveys.ResultsPursuing a business-as-usual strategy was projected to result in a 5% and 9% increase in malaria incidence in 2025 and 2030 compared with 2020, while deaths were projected to remain unchanged by 2030. The greatest intervention impact was associated with the NMSP scenario with 80% or greater coverage of standard interventions coupled with intermittent preventive treatment in infants and extension of seasonal malaria chemoprevention (SMC) to 404 LGAs, compared to 80 LGAs in 2019. The budget-prioritized scenario with SMC expansion to 310 LGAs, high bed net coverage with new formulations, and increase in effective case management rate at the same pace as historical levels was adopted as an adequate alternative for the resources available.ConclusionsDynamical models can be applied for relative assessment of the impact of intervention scenarios but improved subnational data collection systems are required to allow increased confidence in predictions at sub-national level.

Seasonal dynamics of Anopheles stephensi and its implications for mosquito detection and emergent malaria control in the Horn of Africa

Invasion of the malaria vector Anopheles stephensi across the Horn of Africa threatens control efforts across the continent, particularly in urban settings where the vector is able to proliferate. Malaria transmission is primarily determined by the abundance of dominant vectors, which often varies seasonally with rainfall. However, it remains unclear how An. stephensi abundance changes throughout the year, despite this being a crucial input to surveillance and control activities. We collate longitudinal catch data from across its endemic range to better understand the vector's seasonal dynamics and explore the implications of this seasonality for malaria surveillance and control across the Horn of Africa. Our analyses reveal pronounced variation in seasonal dynamics, the timing and nature of which are poorly predicted by rainfall patterns. Instead, they are associated with temperature and patterns of land use; frequently differing between rural and urban settings. Our results show that timing entomological surveys to coincide with rainy periods is unlikely to improve the likelihood of detecting An. stephensi. Integrating these results into a malaria transmission model, we show that timing indoor residual spraying campaigns to coincide with peak rainfall offers little improvement in reducing disease burden compared to starting in a random month. Our results suggest that unlike other malaria vectors in Africa, rainfall may be a poor guide to predicting the timing of peaks in An. stephensi-driven malaria transmission. This highlights the urgent need for longitudinal entomological monitoring of the vector in its new environments given recent invasion and potential spread across the continent.

Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment

The application of fuzzy theory is vital in all scientific disciplines. The construction of mathematical models with fuzziness is little studied in the literature. With this in mind and for a better understanding of the disease, an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classical model of malaria transmission. The parameters and , being function of the malaria virus load, are considered fuzzy numbers. Three steady states and the reproduction number of the model are analyzed in fuzzy senses. A numerical technique is developed in a fuzzy environment to solve the studied model, which retains essential properties such as positivity and dynamic consistency. Moreover, numerical simulations are carried out to illustrate the analytical results of the developed technique. Unlike most of the classical methods in the literature, the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.

Global dynamics of a time-delayed malaria model with asymptomatic infections and standard incidence rate

<abstract><p>A time-delayed model of malaria transmission with asymptomatic infections and standard incidence rate is presented and its basic reproduction number $ {R}_{0} $ is calculated. We focus on the global dynamics of the model with respect to $ {R}_{0} $. If and only if $ {R}_{0} > 1 $, the model exists a unique malaria-infected equilibrium $ E^{\ast} $, whereas it always possesses the malaria-free equilibrium $ E_{0} $. We first prove the local stability of the equilibria $ E_0 $ and $ E^{\ast} $ by using proof by contradiction and the properties of complex modulus. Secondly, by utilizing the Lyapunov functional method and the limiting system of the model with some novel details, we show that the equilibrium $ {E}_{0} $ is globally asymptotically stable (GAS) when $ {R}_{0} < 1 $, globally attractive (GA) when $ {R}_{0} = 1 $ and unstable when $ {R}_{0} > 1 $; the equilibrium $ E^{\ast} $ is GAS if and only if $ {R}_{0} > 1 $. In particular, in order to obtain global attractivity of the equilibrium $ E^{\ast} $, we demonstrate the weak persistence of the system for $ {R}_{0} > 1 $. Our results imply that malaria will gradually disappear if $ {R}_{0}\leq1 $ and persistently exist if $ {R}_{0} > 1 $.</p></abstract>

Theoretical and numerical aspects of the Malaria transmission model with piecewise technique

<abstract><p>In this paper, we apply piecewise derivatives with both singular and non-singular kernels to investigate a malaria model. The singular kernel is the Caputo derivative, while the non-singular kernel is the Atangana-Baleanu operator in Caputo's sense (ABC). The existence, uniqueness, and numerical algorithm of the proposed model are presented using piecewise derivatives with both kernels. The stability is also presented for the proposed model using Ulam-Hyers stability. The numerical simulations are performed considering different fractional orders and compared the results with the real data to evaluate the efficiency of the proposed approach.</p></abstract>

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.

Optimal control of a two-group malaria transmission model with vaccination.

Malaria is a vector-borne disease that poses major health challenges globally, with the highest burden in children less than 5 years old. Prevention and treatment have been the main interventions measures until the recent groundbreaking highly recommended malaria vaccine by WHO for children below five. A two-group malaria model structured by age with vaccination of individuals aged below 5 years old is formulated and theoretically analyzed. The disease-free equilibrium is globally asymptotically stable when the disease-induced death rate in both human groups is zero. Descarte's rule of signs is used to discuss the possible existence of multiple endemic equilibria. By construction, mathematical models inherit the loss of information that could make prediction of model outcomes imprecise. Thus, a global sensitivity analysis of the basic reproduction number and the vaccination class as response functions using Latin-Hypercube Sampling in combination with partial rank correlation coefficient are graphically depicted. As expected, the most sensitive parameters are related to children under 5 years old. Through the application of optimal control theory, the best combination of interventions measures to mitigate the spread of malaria is investigated. Simulations results show that concurrently applying the three intervention measures, namely: personal protection, treatment, and vaccination ofchildreen under-five is the best strategy for fighting against malaria epidemic in a community, relative to using either single or any dual combination of intervention(s) at a time.

Dynamics of a multi-strain malaria model with diffusion in a periodic environment

This paper mainly explores the complex impacts of spatial heterogeneity, vector-bias effect, multiple strains, temperature-dependent extrinsic incubation period (EIP) and seasonality on malaria transmission. We propose a multi-strain malaria transmission model with diffusion and periodic delays and define the reproduction numbers and (i = 1, 2). Quantitative analysis indicates that the disease-free ω-periodic solution is globally attractive when , while if (), then strain i persists and strain j dies out. More interestingly, when and are greater than 1, the competitive exclusion of the two strains also occurs. Additionally, in a heterogeneous environment, the coexistence conditions of the two strains are and . Numerical simulations verify the analytical results and reveal that ignoring vector-bias effect or seasonality when studying malaria transmission will underestimate the risk of disease transmission.

Seasonal use case for the RTS,S/AS01 malaria vaccine: a mathematical modelling study

A 2021 clinical trial of seasonal RTS,S/AS01E (RTS,S) vaccination showed that vaccination was non-inferior to seasonal malaria chemoprevention (SMC) in preventing clinical malaria. The combination of these two interventions provided significant additional protection against clinical and severe malaria outcomes. Projections of the effect of this novel approach to RTS,S vaccination in seasonal transmission settings for extended timeframes and across a range of epidemiological settings are needed to inform policy recommendations. We used a mathematical, individual-based model of malaria transmission that was fitted to data on the relationship between entomological inoculation rate and parasite prevalence, clinical disease, severe disease, and deaths from multiple sites across Africa. The model was validated with results from a phase 3b trial assessing the effect of SV-RTS,S in Mali and Burkina Faso. We developed three intervention efficacy models with varying degrees and durations of protection for our population-level modelling analysis to assess the potential effect of an RTS,S vaccination schedule based on age (doses were delivered to children aged 6 months, 7·5 months, and 9 months for the first three doses, and at 27 months of age for the fourth dose) or season (children aged 5-17 months at the time of first vaccination received the first three doses in the 3 months preceding the transmission season, with any subsequent doses up to five doses delivered annually) in seasonal transmission settings both in the absence and presence of SMC with sulfadoxine-pyrimethamine plus amodiaquine. This is modelled as a full therapeutic course delivered every month for four or five months of the peak in transmission season. Estimates of cases and deaths averted in a population of 100 000 children aged 0-5 years were calculated over a 15-year time period for a range of levels of malaria transmission intensity (Plasmodium falciparum parasite prevalence in children aged 2-10 years between 10% and 65%) and over two west Africa seasonality archetypes. Seasonally targeting RTS,S resulted in greater absolute reductions in malaria cases and deaths compared with an age-based strategy, averting an additional 14 000-47 000 cases per 100 000 children aged 5 years and younger over 15 years, dependent on seasonality and transmission intensity. We predicted that adding seasonally targeted RTS,S to SMC would reduce clinical incidence by up to an additional 42 000-67 000 cases per 100 000 children aged 5 years and younger over 15 years compared with SMC alone. Transmission season duration was a key determinant of intervention effect, with the advantage of adding RTS,S to SMC predicted to be smaller with shorter transmission seasons. RTS,S vaccination in seasonal settings could be a valuable additional tool to existing interventions, with seasonal delivery maximising the effect relative to an age-based approach. Decisions surrounding deployment strategies of RTS,S in such settings will need to consider the local and regional variations in seasonality, current rates of other interventions, and potential achievable RTS,S coverage. UK Medical Research Council, UK Foreign Commonwealth & Development Office, The Wellcome Trust, and The Royal society.

Mathematical Modelling of the Transmission Mechanism of Plamodium Falciparum

In this paper, a deterministic model SEIR-SEI model of malaria transmission consisting of systems of ordinary differential equations, describing the transmission of malaria between humans and female anopheles mosquitoes, the definitive hosts of Plasmodium parasites, is examined. The reproduction number is estimated and the model equilibria and their stabilities are discussed. The diseasefree equilibrium for the model is found to be locally asymptotically stable if the reproduction number is less than one and unstable if the reproduction number is greater than one. Numerical simulations are carried out to demonstrate the analytical results, and suggest that malaria can be controlled by reducing the contact rate between human and mosquito, the use of active malaria drugs, insecticides and the use of mosquito treated nets.

Mathematical analysis of multi-compartmental malaria transmission model with reinfection

In this investigation, a mathematical compartmental model of the malaria disease transmission dynamical process with an associated learning mechanism between vector-to-host and vice-versa with memory, relapse, and reinfection conditions is proposed and analysed. Stability analysis of the disease-free equilibrium (DFE) concerning the fractional-order derivative α and the reproductive number R0 is evaluated. We find the α that depends on R0, for which we have two cases: i if R0<1, then DFE is always locally asymptotically stable (LAS), ii if R0>1, then DFE is always unstable. The model is solved numerically by using the Corrector-Predictor numerical method. The numerical simulation is performed to verify the analytic results.

Corrigendum: Frequency-dependent competition between strains imparts persistence to perturbations in a model of Plasmodium falciparum malaria transmission

Corrigendum: Frequency-dependent competition between strains imparts persistence to perturbations in a model of Plasmodium falciparum malaria transmission

Population replacement gene drive characteristics for malaria elimination in a range of seasonal transmission settings: a modelling study

BackgroundGene drives are a genetic engineering method where a suite of genes is inherited at higher than Mendelian rates and has been proposed as a promising new vector control strategy to reinvigorate the fight against malaria in sub-Saharan Africa.MethodsUsing an agent-based model of malaria transmission with vector genetics, the impacts of releasing population-replacement gene drive mosquitoes on malaria transmission are examined and the population replacement gene drive system parameters required to achieve local elimination within a spatially-resolved, seasonal Sahelian setting are quantified. The performance of two different gene drive systems—“classic” and “integral”—are evaluated. Various transmission regimes (low, moderate, and high—corresponding to annual entomological inoculation rates of 10, 30, and 80 infectious bites per person) and other simultaneous interventions, including deployment of insecticide-treated nets (ITNs) and passive healthcare-seeking, are also simulated.ResultsLocal elimination probabilities decreased with pre-existing population target site resistance frequency, increased with transmission-blocking effectiveness of the introduced antiparasitic gene and drive efficiency, and were context dependent with respect to fitness costs associated with the introduced gene. Of the four parameters, transmission-blocking effectiveness may be the most important to focus on for improvements to future gene drive strains because a single release of classic gene drive mosquitoes is likely to locally eliminate malaria in low to moderate transmission settings only when transmission-blocking effectiveness is very high (above ~ 80–90%). However, simultaneously deploying ITNs and releasing integral rather than classic gene drive mosquitoes significantly boosts elimination probabilities, such that elimination remains highly likely in low to moderate transmission regimes down to transmission-blocking effectiveness values as low as ~ 50% and in high transmission regimes with transmission-blocking effectiveness values above ~ 80–90%.ConclusionA single release of currently achievable population replacement gene drive mosquitoes, in combination with traditional forms of vector control, can likely locally eliminate malaria in low to moderate transmission regimes within the Sahel. In a high transmission regime, higher levels of transmission-blocking effectiveness than are currently available may be required.