Mathematical Model Of Malaria Transmission Research Articles

Global Stability Analysis of the Mathematical Model for Malaria Transmission between Vector and Host Population

Global Stability Analysis of the Mathematical Model for Malaria Transmission between Vector and Host Population

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.

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.

Optimal Control and Cost-Effectiveness Strategies of Malaria Transmission with Impact of Climate Variability

We proposed in this study a deterministic mathematical model of malaria transmission with climate variation factor. In the first place, fundamental properties of the model, such as positivity of solution and boundedness of the biological feasibility of the model, were proved whenever all initial data of the states were nonnegative. The next-generation matrix method is used to compute a basic reproduction number with respect to the disease-free equilibrium point. The Jacobian matrix and the Lyapunov function are used to check the local and global stability of disease-free equilibriums. If the basic reproduction number is less than one, the model’s disease-free equilibrium points are both locally and globally asymptotically stable; otherwise, an endemic equilibrium occurs. The results of the sensitivity analysis of the basic reproduction numbers were obtained, and its biological interpretation was provided. The existence of bifurcation was discussed, and the model exhibits forward and backward bifurcations with respect to the first and second basic reproduction numbers, respectively. Secondly, using the maximum principle of Pontryagin, the optimal malaria reduction strategies are described with three control measures, namely, treated bed nets, infected human treatment, and indoor residual spraying. Finally, based on numerical simulations of the optimality system, the combination of treatment and indoor spraying is the most efficient and least expensive strategy for malaria eradication.

Estimating the potential impact of Attractive Targeted Sugar Baits (ATSBs) as a new vector control tool for Plasmodium falciparum malaria

BackgroundAttractive targeted sugar baits (ATSBs) are a promising new tool for malaria control as they can target outdoor-feeding mosquito populations, in contrast to current vector control tools which predominantly target indoor-feeding mosquitoes.MethodsIt was sought to estimate the potential impact of these new tools on Plasmodium falciparum malaria prevalence in African settings by combining data from a recent entomological field trial of ATSBs undertaken in Mali with mathematical models of malaria transmission. The key parameter determining impact on the mosquito population is the excess mortality due to ATSBs, which is estimated from the observed reduction in mosquito catch numbers. A mathematical model capturing the life cycle of P. falciparum malaria in mosquitoes and humans and incorporating the excess mortality was used to estimate the potential epidemiological effect of ATSBs.ResultsThe entomological study showed a significant reduction of ~ 57% (95% CI 33–72%) in mosquito catch numbers, and a larger reduction of ~ 89% (95% CI 75–100%) in the entomological inoculation rate due to the fact that, in the presence of ATSBs, most mosquitoes do not live long enough to transmit malaria. The excess mortality due to ATSBs was estimated to be lower (mean 0.09 per mosquito per day, seasonal range 0.07–0.11 per day) than the bait feeding rate obtained from one-day staining tests (mean 0.34 per mosquito per day, seasonal range 0.28–0.38 per day).ConclusionsFrom epidemiological modelling, it was predicted that ATSBs could result in large reductions (> 30% annually) in prevalence and clinical incidence of malaria, even in regions with an existing high malaria burden. These results suggest that this new tool could provide a promising addition to existing vector control tools and result in significant reductions in malaria burden across a range of malaria-endemic settings.

A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics

Abstract In this paper, we formulate a temperature-dependent model for malaria transmission dynamics which includes immature stages of mosquitoes. The model is constructed by using ordinary differential equations with some parameters which are periodic functions. Two thresholds dynamics associated to the model have been derived: the vector reproduction ratio ℛ v and the basic reproduction ratio ℛ0. Through a rigorous analysis via theories and methods of dynamical systems, we prove that the global behavior of the model depends strongly on these two parameters. More precisely, we show that if ℛ v is greater than one and ℛ0 is less than one then, the disease-free periodic equilibrium is globally attractive. If ℛ v is greater than one and ℛ0 is greater than one, the disease remains persistent and the system admits at least one positive periodic solution. Finally, using the reported monthly mean temperature for Burkina Faso, numerical simulations are carried out to illustrate our mathematical results.

An optimal control problem of malaria model with seasonality effect using real data

In this study, we present a mathematical model of malaria transmission with a seasonality effect to describe the dynamics of the infection. In the absent seasonality effect, we prove the local stability of the malaria-free equilibrium point. The parameters of the model are fitted to the cumulative number of malaria cases of Papua province, Indonesia for the year 2018 and parameterized using the least-squares technique. The sensitivity analysis of the model to changes in the parameters is explored. Further, the malaria model with the seasonality effect via a periodic mosquito birth rate is investigated numerically. Finally, we formulate an optimal control problem with a control function and obtain the optimal control characterization. The optimal control problem is solved numerically, and the results comprised of a controls system for different strategies.

Assessing the impact of low-technology emanators alongside long-lasting insecticidal nets to control malaria.

Malaria control in sub-Saharan Africa relies on the widespread use of long-lasting insecticidal nets (LLINs) or the indoor residual spraying of insecticide. Disease transmission may be maintained even when these indoor interventions are universally used as some mosquitoes will bite in the early morning and evening when people are outside. As countries seek to eliminate malaria, they can target outdoor biting using new vector control tools such as spatial repellent emanators, which emit airborne insecticide to form a protective area around the user. Field data are used to incorporate a low-technology emanator into a mathematical model of malaria transmission to predict its public health impact across a range of scenarios. Targeting outdoor biting by repeatedly distributing emanators alongside LLINs increases the chance of elimination, but the additional benefit depends on the level of anthropophagy in the local mosquito population, emanator effectiveness and the pre-intervention proportion of mosquitoes biting outdoors. High proportions of pyrethroid-resistant mosquitoes diminish LLIN impact because of reduced mosquito mortality. When mosquitoes are highly anthropophagic, this reduced mortality leads to more outdoor biting and a reduced additional benefit of emanators, even if emanators are assumed to retain their effectiveness in the presence of pyrethroid resistance. Different target product profiles are examined, which show the extra epidemiological benefits of spatial repellents that induce mosquito mortality.This article is part of the theme issue ‘Novel control strategies for mosquito-borne diseases’.

Quantifying the impact of insecticide resistance in the transmission dynamics of malaria

Abstract The fitness cost imposed by insecticide resistance on malaria vectors has appeared as an asset for vector control despite the evolution and spread of insecticide resistance. However, certain levels of insecticide resistance intensity may reduce the efficacy of insecticide-treated nets for certain coverage levels. In this study, we consider a non-autonomous mathematical model for malaria transmission that investigates the impact of the interaction between the intensity of resistance, the coverage of insecticide-treated nets and the fitness cost of resistance on resistant vectors (fitness disadvantage or decreased performance) on the transmission dynamics of malaria. It is shown that the disease-free periodic solution of the model is globally attractive if the time-dependent reproduction number ( R T ( t ) 1 ). The model also admits a unique positive periodic solution when R T ( t ) > 1 . We numerically studied the interaction between the fitness cost imposed by resistance on resistant vectors, the intensity of resistance and bed-net coverage. We observed that the intensity level present in the population may significantly affect the impact of the fitness cost that resistance imposes on resistant mosquitoes as well as reduce the effectiveness of control measures.

Modeling pyrethroids repellency and its role on the bifurcation analysis for a bed net malaria model

• Bed net lethal and repellent effects are incorporated in a dynamical malaria model and the disease contact rates are explicitly modeled by highly nonlinear functions of their rates. • The complete asymptotic behavior of the model is established, using Lyapunov-LaSalle techniques and geometric approach. • An in-depth bifurcation analysis is performed, with all the equilibrium points topologically classified and the existence of trans-critical forward and backward bifurcations established. • Bed net repellency and disease-induced mortality are solely or jointly the causes of backward bifurcation, which impedes the classical requirement that, bringing the basic reproduction number below unity is sufficient to control malaria. • Bed nets with high lethal effect is better that bed nets with high repellency effect.Both bed net repellency and lethal effects decrease disease contact rates, and lethal effect rate does it faster than repellency effect. • Bed net repellency effect regulates the disease burden and its negligence underestimates that burden. We develop and analyze a simple mathematical model for malaria transmission where pyrethroids treated nets (PTNs) are used for control purposes, and in which knock-down/lethal, excito-repellent/deterrent effects are incorporated. We explicitly describe the contact rates between mosquitoes and humans by nonlinear functions of bed net usage and repellency rates. Using center manifold theory, we show that our model exhibits, saddle-node, transcritical forward and backward bifurcation when the reproduction number R 0 crosses one. Our model reveals that repellency effect plays an important role for the existence of both the endemic equilibrium points and the occurrence of backward bifurcation and a threshold repellency rate is calculated. The epidemiological implication of the backward bifurcation is that, reducing R 0 below one alone is not enough to eliminate malaria. We establish that, increasing either the rate of bed nets usage (i.e community protection) or their repellent effect (i.e personal protection) or the combination of both, decreases the contact rates between humans and mosquitoes. As a result, the disease burden metric R 0 is reduced. The global asymptotic stability of equilibrium points are proven using the geometric approach and Lyapunov-LaSalle techniques. Furthermore, we show that neglecting repellency underestimates the basic reproduction number and hinders the control of malaria. The disease free equilibrium is shown to be a saddle-node of co-dimension 1 when R 0 = 1 . We also observe that R 0 is mostly influenced by the bed net coverage rate, repellent effect of pyrethroids and the probability that mosquitoes target human hosts. Our results confirm that PTNs usage is an efficient control strategy to mitigate the malaria ability to spread, and suggest that the utilization of PTNs with high lethal rate, but low repellency rate is better than the use of those with high repellency and low lethal rates.

The duration of chemoprophylaxis against malaria after treatment with artesunate-amodiaquine and artemether-lumefantrine and the effects of pfmdr1 86Y and pfcrt 76T: a meta-analysis of individual patient data

BackgroundThe majority of Plasmodium falciparum malaria cases in Africa are treated with the artemisinin combination therapies artemether-lumefantrine (AL) and artesunate-amodiaquine (AS-AQ), with amodiaquine being also widely used as part of seasonal malaria chemoprevention programs combined with sulfadoxine-pyrimethamine. While artemisinin derivatives have a short half-life, lumefantrine and amodiaquine may give rise to differing durations of post-treatment prophylaxis, an important additional benefit to patients in higher transmission areas.MethodsWe analyzed individual patient data from 8 clinical trials of AL versus AS-AQ in 12 sites in Africa (n = 4214 individuals). The time to PCR-confirmed reinfection after treatment was used to estimate the duration of post-treatment protection, accounting for variation in transmission intensity between settings using hidden semi-Markov models. Accelerated failure-time models were used to identify potential effects of covariates on the time to reinfection. The estimated duration of chemoprophylaxis was then used in a mathematical model of malaria transmission to determine the potential public health impact of each drug when used for first-line treatment.ResultsWe estimated a mean duration of post-treatment protection of 13.0 days (95% CI 10.7–15.7) for AL and 15.2 days (95% CI 12.8–18.4) for AS-AQ overall. However, the duration varied significantly between trial sites, from 8.7–18.6 days for AL and 10.2–18.7 days for AS-AQ. Significant predictors of time to reinfection in multivariable models were transmission intensity, age, drug, and parasite genotype. Where wild type pfmdr1 and pfcrt parasite genotypes predominated (<=20% 86Y and 76T mutants, respectively), AS-AQ provided ~ 2-fold longer protection than AL. Conversely, at a higher prevalence of 86Y and 76T mutant parasites (> 80%), AL provided up to 1.5-fold longer protection than AS-AQ. Our simulations found that these differences in the duration of protection could alter population-level clinical incidence of malaria by up to 14% in under-5-year-old children when the drugs were used as first-line treatments in areas with high, seasonal transmission.ConclusionChoosing a first-line treatment which provides optimal post-treatment prophylaxis given the local prevalence of resistance-associated markers could make a significant contribution to reducing malaria morbidity.

Advocating an attack against severe malaria: a cost-effectiveness analysis

BackgroundA recent study found that the gut microbiota, Lactobacillus and Bifidobacterium, have the ability to modulate the severity of malaria. The modulation of the severity of malaria is not however, the typical focal point of most widespread interventions. Thus, an essential element of information required before serious consideration of any intervention that targets reducing severe malaria incidence is a prediction of the health benefits and costs required to be cost-effective.MethodsHere, we developed a mathematical model of malaria transmission to evaluate an intervention that targets reducing severe malaria incidence. We consider intervention scenarios of a 2-, 7-, and 14-fold reduction in severe malaria incidence, based on the potential reduction in severe malaria incidence caused by gut microbiota, under entomological inoculation rates occurring in 41 countries in sub-Saharan Africa. For each intervention scenario, disability-adjusted life years averted and incremental cost-effectiveness ratios were estimated using country specific data, including the reported proportions of severe malaria incidence in healthcare settings.ResultsOur results show that an intervention that targets reducing severe malaria incidence with annual costs between $23.65 to $30.26 USD per person and causes a 14-fold reduction in severe malaria incidence would be cost-effective in 15–19 countries and very cost-effective in 9–14 countries respectively. Furthermore, if model predictions are based on the distribution of gut microbiota through a freeze-dried yogurt that cost $0.20 per serving, a 2- to 14-fold reduction in severe malaria incidence would be cost-effective in 29 countries and very cost-effective in 25 countries.ConclusionOur findings indicate interventions that target severe malaria can be cost-effective, in conjunction with standard interventions, for reducing the health burden and costs attributed to malaria. While our results illustrate a stronger cost-effectiveness for greater reductions, they consistently show that even a limited reduction in severe malaria provides substantial health benefits, and could be economically viable. Therefore, we suggest that interventions that target severe malaria are worthy of consideration, and merit further empirical and clinical investigation.

A global mathematical model of malaria transmission dynamics with structured mosquito population and temperature variations

In this paper, a mathematical model of malaria transmission which takes into account the four distinct mosquito metamorphic stages is presented. The model is formulated thanks to the coupling of two sub-models, namely the model of mosquito population and the model of malaria parasite transmission due to the interaction between mosquitoes and humans. Moreover, considering that climate factors have a great impact on the mosquito life cycle and parasite survival in mosquitoes, we incorporate seasonality in the model by considering some parameters which are periodic functions. Through a rigorous analysis via theories and methods of dynamical systems, we prove that the global behavior of the model depends strongly on two biological insightful quantities : the vector reproduction ratio Rv and the basic reproduction ratio R0. Indeed, if Rv<1, mosquitoes and malaria die out; if Rv>1 and R0<1, the disease-free periodic equilibrium is globally attractive; and if Rv>1 and R0>1 the disease remains persistent. Finally, using the reported monthly mean temperature of Burkina Faso, we perform some numerical simulations to illustrate our theoretical results.

Reducing malaria burden and accelerating elimination with long-lasting systemic insecticides: a modelling study of three potential use cases

BackgroundWhile bed nets and insecticide spraying have had significant impact on malaria burden in many endemic regions, outdoor vector feeding and insecticide resistance may ultimately limit their contribution to elimination and control campaigns. Complementary vector control methods such as endectocides or systemic insecticides, where humans or animals are treated with drugs that kill mosquitoes upon ingestion via blood meal, are therefore generating much interest. This work explores the conditions under which long-lasting systemic insecticides would have a substantial impact on transmission and burden.MethodsHypothetical long-lasting systemic insecticides with effective durations ranging from 14 to 90 days are simulated using an individual-based mathematical model of malaria transmission. The impact of systemic insecticides when used to complement existing vector control and drug campaigns is evaluated in three settings—a highly seasonal high-transmission setting, a near-elimination setting with seasonal travel to a high-risk area, and a near-elimination setting in southern Africa.ResultsAt 60% coverage, a single round of long-lasting systemic insecticide with effective duration of at least 60 days, distributed at the start of the season alongside a seasonal malaria chemoprevention campaign in a high-transmission setting, results in further burden reduction of 30–90% depending on the sub-populations targeted. In a near-elimination setting where transmission is sustained by seasonal travel to a high-risk area, targeting high-risk travellers with systemic insecticide with effective duration of at least 30 days can result in likely elimination even if intervention coverage is as low as 50%. In near-elimination settings with robust vector control, the addition of a 14-day systemic insecticide alongside an anti-malarial in mass drug administration (MDA) campaigns can decrease the necessary MDA coverage from about 85% to the more easily achievable 65%.ConclusionsWhile further research into the safety profile of systemic insecticides is necessary before deployment, models predict that long-lasting systemic insecticides can play a critical role in reducing burden or eliminating malaria in a range of contexts with different target populations, existing malaria control methods, and transmission intensities. Continued investment in lengthening the duration of systemic insecticides and improving their safety profile is needed for this intervention to achieve its fullest potential.

Prioritizing the scale-up of interventions for malaria control and elimination

BackgroundA core set of intervention and treatment options are recommended by the World Health Organization for use against falciparum malaria. These are treatment, long-lasting insecticide-treated bed nets, indoor residual spraying, and chemoprevention options. Both domestic and foreign aid funding for these tools is limited. When faced with budget restrictions, the introduction and scale-up of intervention and treatment options must be prioritized.MethodsEstimates of the cost and impact of different interventions were combined with a mathematical model of malaria transmission to estimate the most cost-effective prioritization of interventions. The incremental cost effectiveness ratio was used to select between scaling coverage of current interventions or the introduction of an additional intervention tool.ResultsPrevention, in the form of vector control, is highly cost effective and scale-up is prioritized in all scenarios. Prevention reduces malaria burden and therefore allows treatment to be implemented in a more cost-effective manner by reducing the strain on the health system. The chemoprevention measures (seasonal malaria chemoprevention and intermittent preventive treatment in infants) are additional tools that, provided sufficient funding, are implemented alongside treatment scale-up. Future tools, such as RTS,S vaccine, have impact in areas of higher transmission but were introduced later than core interventions.ConclusionsIn a programme that is budget restricted, it is essential that investment in available tools be effectively prioritized to maximize impact for a given investment. The cornerstones of malaria control: vector control and treatment, remain vital, but questions of when to scale and when to introduce other interventions must be rigorously assessed. This quantitative analysis considers the scale-up or core interventions to inform decision making in this area.

Mathematical Model for Malaria Transmission and Chemical Control with Human-Related Activities

In this paper effect of insecticides has been studied for the control of vector-borne diseases, like malaria. A nonlinear SIS mathematical model has been proposed and analyzed for transmission of malaria caused by infected mosquito population on susceptible human population using chemicals to control the disease. It is further assumed that susceptible human population becomes infected by direct contact with vector mosquitoes. The mosquito population density is assumed to be governed by general logistic model. It is found that model exhibits three nonnegative equilibria, namely mosquito and disease-free equilibrium \(E_{0} ,\) mosquito persistence and disease-free equilibrium \(E_{1}\) and endemic equilibrium \(E^{*}\). The model is analyzed by using local and global stability theory of differential equations and numerical simulation.

A Mathematical Model for the Population Dynamics of Malaria with a Temperature Dependent Control

In this work, we develop a mathematical model for malaria transmission that investigates the impact of temperature on the efficacy of ITNs. The disease free state of the autonomous version of the formulated model is seen to be globally asymptotically stable in the absence of disease induced mortality when the associated reproduction number is less than unity. Also, when the associated reproduction number of the non-autonomous model is greater than unity, the disease persist in the population. Sensitivity and uncertainty analysis of the autonomous model, using the associated reproduction number, number of infected humans and vectors as response functions, show that the probability of transmission from human to vectors ( $$\beta _{hv}$$ ), maximum biting rate of vectors ( $$b_{max}$$ ), vector carrying capacity ( $$k_v$$ ) as well as ITN efficacy and coverage ( $$\varepsilon _b$$ and $$b_o$$ ) have the most impact on all three response functions. In the non-autonomous model, for temperature values in the range $$[18\pm 4-32\pm 4]\,^\circ $$ C and using the number of infected humans and vectors as response functions, it can be seen that the bed-net coverage lost its significance for temperature values in the range $$[22\pm 4-30\pm 4]\,^\circ $$ C and $$[22\pm 4-26\pm 4] \,^\circ $$ C respectively. Numerical simulations of the time-averaged reproduction number for the case where the efficacy of the bed-net is temperature-dependent showed that temperature values in the range [22–27] $$\,^\circ $$ C effects the efficacy of the bed-nets most. Numerical simulations of the non-autonomous model for the case where ITN efficacy is temperature-dependent, we determine temperature ranges that make for increase in the effectiveness of the bed-nets in the fight against malaria.

Sensitivity Analysis of Mathematical Model for Malaria Transmission with Saturated Incidence Rate

Sensitivity Analysis of Mathematical Model for Malaria Transmission with Saturated Incidence Rate

Discrete-time model for malaria transmission with constant releases of sterile mosquitoes

ABSTRACTIn this study, we first formulate a baseline discrete-time mathematical model for malaria transmission where the survival function of mosquitoes is of Beverton–Holt type. We then introduce sterile mosquitoes to the baseline model to explore the transmission dynamics with sterile mosquitoes. We derive formulas for the reproductive number of infection and determine the existence and uniqueness of endemic fixed points as well, for the models with or without sterile mosquitoes. We then study the impact of the releases of sterile mosquitoes on the disease transmissions by investigating the effects of varying the release rates of the sterile mosquitoes. We use a numerical example to illustrate our results for all cases and finally give brief discussions of our findings.

Mathematical Model for Malaria Transmission with Optimal Control Strategies and Their Effects

Mathematical Model for Malaria Transmission with Optimal Control Strategies and Their Effects