1
|
An Optimal Control Model to Understand the Potential Impact of the New Vaccine and Transmission-Blocking Drugs for Malaria: A Case Study in Papua and West Papua, Indonesia. Vaccines (Basel) 2022; 10:vaccines10081174. [PMID: 35893823 PMCID: PMC9331692 DOI: 10.3390/vaccines10081174] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Revised: 07/19/2022] [Accepted: 07/19/2022] [Indexed: 11/16/2022] Open
Abstract
Malaria is one of the major causes of a high death rate due to infectious diseases every year. Despite attempts to eradicate the disease, results have not been very successful. New vaccines and other treatments are being constantly developed to seek optimal ways to prevent malaria outbreaks. In this article, we formulate and analyze an optimal control model of malaria incorporating the new pre-erythrocytic vaccine and transmission-blocking treatment. Sufficient conditions to guarantee local stability of the malaria-free equilibrium were derived based on the controlled reproduction number condition. Using the non-linear least square fitting method, we fitted the incidence data from the province of Papua and West Papua in Indonesia to estimate the model parameter values. The optimal control characterization and optimality conditions were derived by applying the Pontryagin Maximum Principle, and numerical simulations were also presented. Simulation results show that both the pre-erythrocytic vaccine and transmission-blocking treatment significantly reduce the spread of malaria. Accordingly, a high doses of pre-erythrocytic vaccine is needed if the number of infected individuals is relatively small, while transmission blocking is required if the number of infected individuals is relatively large. These results suggest that a large-scale implementation of both strategies is vital as the world continues with the effort to eradicate malaria, especially in endemic regions across the globe.
Collapse
|
2
|
Mistry A, Odwar B, Olewe F, Kurtis J, Moormann AM, Ong’echa JM. Pediatric Participant Retention Rates in a Longitudinal Malaria Immunology Study. Am J Trop Med Hyg 2022; 106:tpmd211052. [PMID: 35436763 PMCID: PMC9209909 DOI: 10.4269/ajtmh.21-1052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Accepted: 12/20/2021] [Indexed: 11/16/2022] Open
Abstract
The resurgence of drug-resistant Plasmodium falciparum parasites continues to motivate the development of a safe and efficacious malaria vaccine. Immuno-epidemiologic studies of naturally acquired immunity (NAI) have been a useful strategy to identify new malaria vaccine targets. However, retention of pediatric participants throughout longitudinal studies is essential for gathering comprehensive exposure and outcome data. Within the context of a 3-year cohort (N = 400) study involving monthly finger prick and bi-annual venous blood sample collections, we conducted qualitative surveys to assess factors impacting participant retention. Phase 1 was conducted 3 months after enrollment in July 2018 and phase 2, 12 months later. In phase 1, 236 parents/guardians participated in focus groups and three withdrawn participants and 10 community health volunteers (CHVs) in key informant interviews. Qualitative analysis indicated overall satisfaction with the study, with 61.8% (136/220 respondents) reporting no concerns. Focus group discussants associated attendance with benefits such as improved access to comprehensive healthcare services. Community health volunteers reported concerns over village rumors of inappropriate use of blood samples and dangers associated with venous blood draws. Phase 2 involved 205 parents/guardians and revealed continued satisfaction, with 46.3% (95/205) identifying no concerns, but expressed increasing worries regarding the amount of venous blood sample. This concern was reflected in an uptick of missed visits when venous blood samples were scheduled. Future studies will address parental concerns to determine whether community engagement and education measures increase study retention until completion.
Collapse
Affiliation(s)
- Anushay Mistry
- University of Massachusetts Chan Medical School, Worcester, Massachusetts
| | - Boaz Odwar
- Kenya Medical Research Institute, Kisumu, Kenya
| | | | | | - Ann M. Moormann
- University of Massachusetts Chan Medical School, Worcester, Massachusetts
| | | |
Collapse
|
3
|
Buonomo B, Della Marca R, d'Onofrio A. Optimal public health intervention in a behavioural vaccination model: the interplay between seasonality, behaviour and latency period. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2020; 36:297-324. [PMID: 30060156 DOI: 10.1093/imammb/dqy011] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2017] [Revised: 07/02/2018] [Accepted: 07/03/2018] [Indexed: 01/17/2023]
Abstract
Hesitancy and refusal of vaccines preventing childhood diseases are spreading due to 'pseudo-rational' behaviours: parents overweigh real and imaginary side effects of vaccines. Nonetheless, the 'Public Health System' (PHS) may enact public campaigns to favour vaccine uptake. To determine the optimal time profiles for such campaigns, we apply the optimal control theory to an extension of the susceptible-infectious-removed (SIR)-based behavioural vaccination model by d'Onofrio et al. (2012, PLoS ONE, 7, e45653). The new model is of susceptible-exposed-infectious-removed (SEIR) type under seasonal fluctuations of the transmission rate. Our objective is to minimize the total costs of the disease: the disease burden, the vaccination costs and a less usual cost: the economic burden to enact the PHS campaigns. We apply the Pontryagin minimum principle and numerically explore the impact of seasonality, human behaviour and latency rate on the control and spread of the target disease. We focus on two noteworthy case studies: the low (resp. intermediate) relative perceived risk of vaccine side effects and relatively low (resp. very low) speed of imitation. One general result is that seasonality may produce a remarkable impact on PHS campaigns aimed at controlling, via an increase of the vaccination uptake, the spread of a target infectious disease. In particular, a higher amplitude of the seasonal variation produces a higher effort and this, in turn, beneficially impacts the induced vaccine uptake since the larger is the strength of seasonality, the longer the vaccine propensity remains large. However, such increased effort is not able to fully compensate the action of seasonality on the prevalence.
Collapse
Affiliation(s)
- Bruno Buonomo
- Department of Mathematics and Applications, University of Naples Federico II, via Cintia, Naples, Italy
| | - Rossella Della Marca
- Department of Mathematical, Physical and Computer Sciences, University of Parma, Parco Area delle Scienze, Parma, Italy
| | - Alberto d'Onofrio
- International Prevention Research Institute, Cours Lafayette, Lyon, France
| |
Collapse
|
4
|
Danbaba UA, Garba SM. Stability Analysis and Optimal Control for Yellow Fever Model with Vertical Transmission. INTERNATIONAL JOURNAL OF APPLIED AND COMPUTATIONAL MATHEMATICS 2020; 6:105. [PMID: 32835032 PMCID: PMC7336115 DOI: 10.1007/s40819-020-00860-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
In this study, a deterministic model for the transmission dynamics of yellow fever (YF) in a human-mosquito setting in the presence of control measures is constructed and rigorously analyzed. In addition to horizontal transmissions, vertical transmission within mosquito population is incorporated. Analysis of the mosquito-only component of the model shows that the reduced model has a mosquito-extinction equilibrium, which is globally-asymptotically stable whenever the basic offspring number ( N 0 ) is less than unity. The vaccinated and type reproduction numbers of the full-model are computed. Condition for global-asymptotic stability of the disease-free equilibrium of the model whenN 0 > 1 is presented. It is shown that, fractional dosing of YF vaccine does not meet YF vaccination requirements. Optimal control theory is applied to the model to characterize the controls parameters. Using Pontryagin's maximum principle and modified forward-backward sweep technique, the necessary conditions for existence of solutions to the optimal control problem is determined. Numerical simulations of the models to assess the effect of fractional vaccine dosing on the disease dynamics and global sensitivity analysis are presented.
Collapse
Affiliation(s)
- UA Danbaba
- Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002 South Africa
| | - SM Garba
- Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002 South Africa
| |
Collapse
|
5
|
Abstract
A current challenge for disease modeling and public health is understanding pathogen dynamics across scales since their ecology and evolution ultimately operate on several coupled scales. This is particularly true for vector-borne diseases, where within-vector, within-host, and between vector–host populations all play crucial roles in diversity and distribution of the pathogen. Despite recent modeling efforts to determine the effect of within-host virus-immune response dynamics on between-host transmission, the role of within-vector viral dynamics on disease spread is overlooked. Here, we formulate an age-since-infection-structured epidemic model coupled to nonlinear ordinary differential equations describing within-host immune-virus dynamics and within-vector viral kinetics, with feedbacks across these scales. We first define the within-host viral-immune response and within-vector viral kinetics-dependent basic reproduction number [Formula: see text] Then we prove that whenever [Formula: see text] the disease-free equilibrium is locally asymptotically stable, and under certain biologically interpretable conditions, globally asymptotically stable. Otherwise, if [Formula: see text] it is unstable and the system has a unique positive endemic equilibrium. In the special case of constant vector to host inoculum size, we show the positive equilibrium is locally asymptotically stable and the disease is weakly uniformly persistent. Furthermore, numerical results suggest that within-vector-viral kinetics and dynamic inoculum size may play a substantial role in epidemics. Finally, we address how the model can be utilized to better predict the success of control strategies such as vaccination and drug treatment.
Collapse
Affiliation(s)
- HAYRIYE GULBUDAK
- Department of Mathematics, University of Louisiana at Lafayette, 104 E. University Circle, Lafayette, LA 70503, USA
| |
Collapse
|
6
|
Optimal Impulse Vaccination Approach for an SIR Control Model with Short-Term Immunity. MATHEMATICS 2019. [DOI: 10.3390/math7050420] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Vaccines are not administered on a continuous basis, but injections are practically introduced at discrete times often separated by an important number of time units, and this differs depending on the nature of the epidemic and its associated vaccine. In addition, especially when it comes to vaccination, most optimization approaches in the literature and those that have been subject to epidemic models have focused on treating problems that led to continuous vaccination schedules but their applicability remains debatable. In search of a more realistic methodology to resolve this issue, a control modeling design, where the control can be characterized analytically and then optimized, can definitely help to find an optimal regimen of pulsed vaccinations. Therefore, we propose a susceptible-infected-removed (SIR) hybrid epidemic model with impulse vaccination control and a compartment that represents the number of vaccinated individuals supposed to not acquire sufficient immunity to become permanently recovered due to the short-term effect of vaccines. A basic reproduction number, when the control is defined as a constant parameter, is calculated. Since we also need to find the optimal values of this impulse control when it is defined as a function of time, we start by stating a general form of an impulse version of Pontryagin’s maximum principle that can be adapted to our case, and then we apply it to our model. Finally, we provide our numerical simulations that are obtained via an impulse progressive-regressive iterative scheme with fixed intervals between impulse times (theoretical example of an impulse at each week), and we conclude with a discussion of our results.
Collapse
|
7
|
Mohammed-Awel J, Agusto F, Mickens RE, Gumel AB. Mathematical assessment of the role of vector insecticide resistance and feeding/resting behavior on malaria transmission dynamics: Optimal control analysis. Infect Dis Model 2019; 3:301-321. [PMID: 30839928 PMCID: PMC6326232 DOI: 10.1016/j.idm.2018.10.003] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2018] [Revised: 10/06/2018] [Accepted: 10/24/2018] [Indexed: 12/22/2022] Open
Abstract
The large-scale use of insecticide-treated bednets (ITNs) and indoor residual spraying (IRS), over the last two decades, has resulted in a dramatic reduction of malaria incidence globally. However, the effectiveness of these interventions is now being threatened by numerous factors, such as resistance to insecticide in the mosquito vector and their preference to feed and rest outdoors or early in the evening (when humans are not protected by the bednets). This study presents a new deterministic model for assessing the population-level impact of mosquito insecticide resistance on malaria transmission dynamics. A notable feature of the model is that it stratifies the mosquito population in terms of type (wild or resistant to insecticides) and feeding preference (indoor or outdoor). The model is rigorously analysed to gain insight into the existence and asymptotic stability properties of the various disease-free equilibria of the model namely the trivial disease-free equilibrium, the non-trivial resistant-only boundary disease-free equilibrium and a non-trivial disease-free equlibrium where both the wild and resistant mosquito geneotypes co-exist). Simulations of the model, using data relevant to malaria transmission dynamics in Ethiopia (a malaria-endemic nation), show that the use of optimal ITNs alone, or in combination with optimal IRS, is more effective than the singular implementation of an optimal IRS-only strategy. Further, when the effect of the fitness cost of insecticide resistance with respect to fecundity (i.e., assuming a decrease in the baseline birth rate of new resistant-type adult female mosquitoes) is accounted for, numerical simulations of the model show that the combined optimal ITNs-IRS strategy could lead to the effective control of the disease, and insecticide resistance effectively managed during the first 8 years of the 15-year implementation period of the insecticides-based anti-malaria control measures in the community.
Collapse
Affiliation(s)
- Jemal Mohammed-Awel
- Department of Mathematics, Valdosta State University, Valdosta, GA 31698, USA
- Corresponding author.
| | - Folashade Agusto
- Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS USA
| | - Ronald E. Mickens
- Department of Physics, Clark Atlanta University, Atlanta, GA 30314, USA
| | - Abba B. Gumel
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA
| |
Collapse
|
8
|
Mohammed-Awel J, Gumel AB. Mathematics of an epidemiology-genetics model for assessing the role of insecticides resistance on malaria transmission dynamics. Math Biosci 2019; 312:33-49. [PMID: 30825481 DOI: 10.1016/j.mbs.2019.02.008] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2017] [Revised: 02/05/2019] [Accepted: 02/24/2019] [Indexed: 12/11/2022]
Abstract
Although the widespread use of indoors residual spraying (IRS) and insecticides treated bednets (ITNs; later replaced by long-lasting insecticidal nets (LLINs)) has led to a dramatic reduction of malaria burden in endemic areas, such usage has also resulted in the major challenge of the evolution of insecticide resistance in the mosquito population in those areas. Thus, efforts to combat malaria also include the urgent problem of effectively managing insecticide resistance. This study is based on the design and analysis of a new mathematical model for assessing the impact of insecticides resistance in the mosquito population (due to widespread use of IRS and ITNs) on the transmission dynamics and control of malaria in a community. The model, which couples disease epidemiology with vector population genetics, incorporates several fitness costs associated with insecticide resistance. Detailed rigorous analysis of the model is presented. Using data and parameter values relevant to malaria dynamics in moderate and high malaria transmission settings in some parts of Ethiopia, simulations of the model show that, while the ITNs-IRS strategy can lead to the effective control of the disease in both the moderate and high malaria transmission setting if the ITNs coverage level in the community is high enough (regardless of the level of IRS coverage), it fails to manage insecticide resistance (as measured in terms of the frequency of resistant allele at equilibrium in the community). It is further shown that the effective size of the coverage level of the ITNs and IRS required to effectively control the disease, while effectively managing insecticide resistance in the mosquito population, depends on the magnitude of the level of resistant allele dominance (in mosquitoes with heterozygous genotype) and several fitness costs associated with the insecticide resistance in the vector population. For instance, in a moderate transmission setting, malaria burden can be reduced to low levels of endemicity (even with low coverage of ITNs and IRS), and insecticide resistance effectively managed, if the fitness costs of resistance are at their assumed baseline values. Such reduction is not achievable if the fitness costs of resistance are lower than the baseline values.
Collapse
Affiliation(s)
- Jemal Mohammed-Awel
- Department of Mathematics, Valdosta State University, Valdosta, Ga 31698, USA.
| | - Abba B Gumel
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA; Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa
| |
Collapse
|
9
|
Cai L, Li X, Tuncer N, Martcheva M, Lashari AA. Optimal control of a malaria model with asymptomatic class and superinfection. Math Biosci 2017; 288:94-108. [PMID: 28284964 DOI: 10.1016/j.mbs.2017.03.003] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2016] [Revised: 02/22/2017] [Accepted: 03/01/2017] [Indexed: 10/20/2022]
Abstract
In this paper, we introduce a malaria model with an asymptomatic class in human population and exposed classes in both human and vector populations. The model assumes that asymptomatic individuals can get re-infected and move to the symptomatic class. In the case of an incomplete treatment, symptomatic individuals move to the asymptomatic class. If successfully treated, the symptomatic individuals recover and move to the susceptible class. The basic reproduction number, R0, is computed using the next generation approach. The system has a disease-free equilibrium (DFE) which is locally asymptomatically stable when R0<1, and may have up to four endemic equilibria. The model exhibits backward bifurcation generated by two mechanisms; standard incidence and superinfection. If the model does not allow for superinfection or deaths due to the disease, then DFE is globally stable which suggests that backward bifurcation is no longer possible. Simulations suggest that total prevalence of malaria is the highest if all individuals show symptoms upon infection, but then undergoes an incomplete treatment and the lowest when all the individuals first move to the symptomatic class then treated successfully. Total prevalence is average if more individuals upon infection move to the asymptomatic class. We study optimal control strategies applied to bed-net use and treatment as main tools for reducing the total number of symptomatic and asymptomatic individuals. Simulations suggest that the optimal control strategies are very dynamic. Although they always lead to decrease in the symptomatic infectious individuals, they may lead to increase in the number of asymptomatic infectious individuals. This last scenario occurs if a large portion of newly infected individuals move to the symptomatic class but many of them do not complete treatment or if they all complete treatment but the superinfection rate of asymptomatic individuals is average.
Collapse
Affiliation(s)
- Liming Cai
- College of Mathematics and Statistic Science, Xinyang Normal University, Xinyang, 46400, CHINA.
| | - Xuezhi Li
- College of Mathematics and information Science, Xinyang Normal University, Xinyang, 46400, CHINA
| | - Necibe Tuncer
- Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA.
| | - Maia Martcheva
- Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611-8105, United States.
| | - Abid Ali Lashari
- Department of Mathematics, Stockholms University, SE-106 91 Stockholm, Sweden
| |
Collapse
|
10
|
Ngonghala CN, Mohammed-Awel J, Zhao R, Prosper O. Interplay between insecticide-treated bed-nets and mosquito demography: implications for malaria control. J Theor Biol 2016; 397:179-92. [PMID: 26976050 DOI: 10.1016/j.jtbi.2016.03.003] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2015] [Revised: 02/14/2016] [Accepted: 03/02/2016] [Indexed: 11/24/2022]
Abstract
Although malaria prevalence has witnessed a significant reduction within the past decade, malaria still constitutes a major health and economic problem, especially to low-income countries. Insecticide-treated nets (ITNs) remain one of the primary measures for preventing the malignant disease. Unfortunately, the success of ITN campaigns is hampered by improper use and natural decay in ITN-efficacy over time. Many models aimed at studying malaria transmission and control fail to account for this decay, as well as mosquito demography and feeding preferences exhibited by mosquitoes towards humans. Omitting these factors can misrepresent disease risk, while understanding their effects on malaria dynamics can inform control policy. We present a model for malaria dynamics that incorporates these factors, and a systematic analysis, including stability and sensitivity analyses of the model under different conditions. The model with constant ITN-efficacy exhibits a backward bifurcation emphasizing the need for sustained control measures until the basic reproduction number, R0, drops below a critical value at which control is feasible. The infectious and partially immune human populations and R0 are highly sensitive to the probability that a mosquito feeds successfully on a human, ITN coverage and the maximum biting rate of mosquitoes, irrespective of whether ITN-efficacy is constant or declines over time. This implies that ITNs play an important role in disease control. When ITN-efficacy wanes over time, we identify disease risks and corresponding ITN coverage, as well as feeding preference levels for which the disease can be controlled or eradicated. Our study leads to important insights that could assist in the design and implementation of better malaria control strategies. We conclude that ITNs that can retain their effectiveness for longer periods will be more appropriate in the fight against malaria and that making more ITNs available to highly endemic regions is necessary for malaria containment.
Collapse
Affiliation(s)
- Calistus N Ngonghala
- Department of Global Health and Social Medicine, Harvard Medical School, Boston, MA 02115, USA.
| | - Jemal Mohammed-Awel
- Department of Mathematics and Computer Science, Valdosta State University, Valdosta, GA 31698 USA
| | - Ruijun Zhao
- Department of Mathematics and Statistics, Minnesota State University, Mankato, MN 56001, USA
| | - Olivia Prosper
- Department of Mathematics, University of Kentucky, Lexington, KY 40506,USA
| |
Collapse
|
11
|
Zakary O, Rachik M, Elmouki I. On the analysis of a multi-regions discrete SIR epidemic model: an optimal control approach. INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL 2016; 5:917-930. [PMID: 32288981 PMCID: PMC7133609 DOI: 10.1007/s40435-016-0233-2] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/23/2015] [Revised: 02/12/2016] [Accepted: 02/16/2016] [Indexed: 11/26/2022]
Abstract
In this paper, we devise a discrete time SIR model depicting the spread of infectious diseases in various geographical regions that are connected by any kind of anthropological movement, which suggests disease-affected people can propagate the disease from one region to another via travel. In fact, health policy-makers could manage the problem of the regional spread of an epidemic, by organizing many vaccination campaigns, or by suggesting other defensive strategies such as blocking movement of people coming from borders of regions at high-risk of infection and entering very controlled regions or with insignificant infection rate. Further, we introduce in the discrete SIR systems, two control variables which represent the effectiveness rates of vaccination and travel-blocking operation. We focus in our study to control the outbreaks of an epidemic that affects a hypothetical population belonging to a specific region. Firstly, we analyze the epidemic model when the control strategy is based on the vaccination control only, and secondly, when the travel-blocking control is added. The multi-points boundary value problems, associated to the optimal control problems studied here, are obtained based on a discrete version of Pontryagin's maximum principle, and resolved numerically using a progressive-regressive discrete scheme that converges following an appropriate test related to the Forward-Backward Sweep Method on optimal control.
Collapse
Affiliation(s)
- Omar Zakary
- Laboratory of Analysis, Modeling and Simulation (LAMS), Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Avenue Commandant Driss ELHARTI, Ben M’Sik, B.P. 7955, 20800 Casablanca, Morocco
| | - Mostafa Rachik
- Laboratory of Analysis, Modeling and Simulation (LAMS), Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Avenue Commandant Driss ELHARTI, Ben M’Sik, B.P. 7955, 20800 Casablanca, Morocco
| | - Ilias Elmouki
- Laboratory of Analysis, Modeling and Simulation (LAMS), Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Avenue Commandant Driss ELHARTI, Ben M’Sik, B.P. 7955, 20800 Casablanca, Morocco
| |
Collapse
|
12
|
Dudley HJ, Goenka A, Orellana CJ, Martonosi SE. Multi-year optimization of malaria intervention: a mathematical model. Malar J 2016; 15:133. [PMID: 26931111 PMCID: PMC4774123 DOI: 10.1186/s12936-016-1182-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Accepted: 02/18/2016] [Indexed: 11/18/2022] Open
Abstract
Background Malaria is a mosquito-borne, lethal disease that affects millions and kills hundreds of thousands of people each year, mostly children. There is an increasing need for models of malaria control. In this paper, a model is developed for allocating malaria interventions across geographic regions and time, subject to budget constraints, with the aim of minimizing the number of person-days of malaria infection. Methods The model considers a range of several conditions: climatic characteristics, treatment efficacy, distribution costs, and treatment coverage. An expanded susceptible-infected-recovered compartment model for the disease dynamics is coupled with an integer linear programming model for selecting the disease interventions. The model produces an intervention plan for all regions, identifying which combination of interventions, with which level of coverage, to use in each region and year in a 5-year planning horizon. Results Simulations using the model yield high-level, qualitative insights on optimal intervention policies: The optimal intervention policy is different when considering a 5-year time horizon than when considering only a single year, due to the effects that interventions have on the disease transmission dynamics. The vaccine intervention is rarely selected, except if its assumed cost is significantly lower than that predicted in the literature. Increasing the available budget causes the number of person-days of malaria infection to decrease linearly up to a point, after which the benefit of increased budget starts to taper. The optimal policy is highly dependent on assumptions about mosquito density, selecting different interventions for wet climates with high density than for dry climates with low density, and the interventions are found to be less effective at controlling malaria in the wet climates when attainable intervention coverage is 60 % or lower. However, when intervention coverage of 80 % is attainable, then malaria prevalence drops quickly in all geographic regions, even when factoring in the greater expense of the higher coverage against a constant budget. Conclusions The model provides a qualitative decision-making tool to weigh alternatives and guide malaria eradication efforts. A one-size-fits-all campaign is found not to be cost-effective; it is better to consider geographic variations and changes in malaria transmission over time when determining intervention strategies.
Collapse
Affiliation(s)
- Harry J Dudley
- University of Colorado Boulder, 526 UCB, University of Colorado, Boulder, CO, 80309-0526, USA.
| | - Abhishek Goenka
- Harvey Mudd College, 301 Platt Blvd, Claremont, CA, 91711, USA.
| | | | | |
Collapse
|
13
|
Modeling ITNs Usage: Optimal Promotion Programs Versus Pure Voluntary Adoptions. MATHEMATICS 2015. [DOI: 10.3390/math3041241] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|