Recurrent malaria dynamics: insight from mathematical modelling

Abimbade, Sulaimon F.; Olaniyi, Samson; Ajala, Olusegun Adebayo

doi:10.1140/epjp/s13360-022-02510-3

Cited by 16 publications

(13 citation statements)

References 26 publications

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“…There are many mathematical models discussing malaria transmission, such as [ 4 , 14 , 15 , 17 , 21 , 23 ] and many more, but none of the mentioned references discuss the impact of relapse, recrudescence, and reinfection all together in one model. Recently, the authors of [ 29 ] introduced a complex nine-dimensional system of ordinary differential equations model to describe malaria transmission under the impact of relapse, recrudescence, and reinfection. They found that backward bifurcation phenomena can be avoided in the absence of reinfection.…”

Section: Discussionmentioning

confidence: 99%

“…They found that backward bifurcation phenomena can be avoided in the absence of reinfection. Different than [ 29 ], here we introduced a mathematical model for malaria transmission considering the impact of relapse, reinfection, recrudescence, and limited hospital bed capacity which affect the recovery rate. Malaria incidence data from the Wee Luri district in Central Sumba, Kupang, Indonesia, were used to estimate the model parameters.…”

Section: Discussionmentioning

confidence: 99%

“…To date, not many mathematical models include three types of infection in malaria: recrudescence, relapse, and reinfection in a single model. Recently, [ 29 ] introduced their malaria model involving the three types of infection mentioned before. A mathematical analysis regarding the equilibrium points, the basic reproduction number, the backward bifurcation phenomena, and the global stability of the endemic equilibrium was discussed in detail.…”

Section: Introductionmentioning

confidence: 99%

“…A mathematical analysis regarding the equilibrium points, the basic reproduction number, the backward bifurcation phenomena, and the global stability of the endemic equilibrium was discussed in detail. However, the authors in [ 29 ] did not yet include limited hospital capacity in their model. This factor is essential since health services will be able to be provided more optimally if the hospital capacity is also adequate in number.…”

Section: Introductionmentioning

confidence: 99%

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Assessing the Impact of Relapse, Reinfection and Recrudescence on Malaria Eradication Policy: A Bifurcation and Optimal Control Analysis

et al. 2022

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In the present study, we propose and analyze an epidemic mathematical model for malaria dynamics, considering multiple recurrent phenomena: relapse, reinfection, and recrudescence. A limitation in hospital bed capacity, which can affect the treatment rate, is modeled using a saturated treatment function. The qualitative behavior of the model, covering the existence and stability criteria of the endemic equilibrium, is investigated rigorously. The concept of the basic reproduction number of the proposed model is obtained using the concept of the next-generation matrix. We find that the malaria-free equilibrium point is locally asymptotically stable if the basic reproduction number is less than one and unstable if it is larger than one. Our observation on the malaria-endemic equilibrium of the proposed model shows possible multiple endemic equilibria when the basic reproduction number is larger or smaller than one. Hence, we conclude that a condition of a basic reproduction number less than one is not sufficient to guarantee the extinction of malaria from the population. To test our model in a real-life situation, we fit our model parameters using the monthly incidence data from districts in Central Sumba, Indonesia called Wee Luri, which were collected from the Wee Luri Health Center. Using the first twenty months’ data from Wee Luri district, we show that our model can fit the data with a confidence interval of 95%. Both analytical and numerical experiments show that a limitation in hospital bed capacity and reinfection can trigger a more substantial possibility of the appearance of backward bifurcation. On the other hand, we find that an increase in relapse can reduce the chance of the appearance of backward bifurcation. A non-trivial result appears in that a higher probability of recrudescence (treatment failure) does not always result in the appearance of backward bifurcation. From the global sensitivity analysis using a combination of Latin hypercube sampling and partial rank correlation coefficient, we found that the initial infection rate in humans and the mosquito infection rate are the most influential parameters in determining the increase in total new human infections. We expand our model as an optimal control problem by including three types of malaria interventions, namely the use of bed net, hospitalization, and fumigation as a time-dependent variable. Using the Pontryagin maximum principle, we characterize our optimal control problem. Results from our cost-effectiveness analysis suggest that hospitalization only is the most cost-effective strategy required to control malaria disease.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Assessing the Impact of Relapse, Reinfection and Recrudescence on Malaria Eradication Policy: A Bifurcation and Optimal Control Analysis

et al. 2022

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“…Infectious disease models had been to the core of scientific studies in the last century, and researchers have used them for various diseases, such as tuberculosis (TB) [1,2], human immunodeficiency virus (HIV) [3,4], influenza [5,6], malaria [7][8][9], and the recent one COVID-19 [10,11]. Infectious diseases outbreaks have always heavily impacted the social and economic well-being of the affected countries and have proved to be havoc, especially for third world countries.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a SIRI model incorporating the impact of information and saturated treatment with optimal control

2022

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In this article, we propose and analyze an infectious disease model with reinfection and investigate disease dynamics by incorporating saturated treatment and information effect. In the model, we consider the case where an individual's immunity deteriorates and they become infected again after recovering. According to our findings, multiple steady states and backward bifurcation may occur as a result of treatment saturation. Further, if treatment is available for all, the disease will be eradicated provided R 0 < 1; however, because limited medical resources caused saturation in treatment, the disease may persist even if R 0 < 1. The global stability of the unique endemic steady state is established using a geometric approach. We also establish certain conditions on the transmission rate for the occurrence of periodic oscillations in the model system. Among nonlinear dynamics, we show supercritical Hopf bifurcation, bi-stability, backward Hopf bifurcation, and double Hopf bifurcation. To illustrate and validate our theoretical results, we present numerical examples. We found that when disease information coverage is high, infection cases fall considerably, and the disease persists when the reinfection rate is high. We then extend our model by incorporating two time-dependent controls, namely inhibitory interventions and treatment. Using Pontryagin's maximum principle, we prove the existence of optimal control paths and find the optimal pair of controls. According to our numerical simulations, the second control is less effective than the first. Furthermore, while implementing a single intervention at a time may be effective, combining both interventions is most effective in reducing disease burden and cost.

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Efficiency and economic analysis of intervention strategies for recurrent malaria transmission

et al. 2023

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Recurrent malaria dynamics: insight from mathematical modelling

Cited by 16 publications

References 26 publications

Assessing the Impact of Relapse, Reinfection and Recrudescence on Malaria Eradication Policy: A Bifurcation and Optimal Control Analysis

Assessing the Impact of Relapse, Reinfection and Recrudescence on Malaria Eradication Policy: A Bifurcation and Optimal Control Analysis

Nonlinear dynamics of a SIRI model incorporating the impact of information and saturated treatment with optimal control

Efficiency and economic analysis of intervention strategies for recurrent malaria transmission

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