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

Abstract

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.

Mathematical models of Plasmodium vivax transmission: A scoping review

“…Acquiring some partial immunity (i.e. some degree of protection against malaria) following infection that wanes over time, is most common among published models [ 56 , 58 – 62 , 64 , 69 , 70 , 79 , 84 ]. Some assumptions regarding immunity include that, if treated, individuals acquire some level of immunity that reduces the probability of reinfection (i.e.…”

“…In most of the models included in this review, it was assumed that treatment would be targeted towards infected individuals [ 21 , 30 , 32 , 64 – 66 , 70 , 79 , 80 , 83 , 85 , 145 ], but a range of other interventions can contribute to malaria control. The impact of a pre-erythrocytic vaccine on reducing P. vivax transmission has been studied and hypothesised that even with low efficacy, it can substantially reduce transmission [ 67 ].…”

“…Across the different approaches of mathematical modelling of P. vivax , there were varying assumptions regarding parasite dynamics and acquisition of immunity. Some models were motivated to capture realistic biological aspects of the parasite [ 32 , 35 , 38 ], or epidemiological and public health aspects [ 4 , 20 , 21 , 28 – 30 , 33 , 34 , 39 , 54 – 56 , 64 , 65 , 67 , 72 , 74 , 79 , 83 – 87 ], whereas some models were motivated to construct a novel or extended mathematical model of P. vivax dynamics, i.e., focusing on the mathematical aspects of P. vivax dynamics [ 24 , 58 – 63 , 66 , 68 – 71 , 73 , 75 , 77 , 78 , 80 ]. As the dynamics of these type of models are well established, we argue that more importance should be placed on using these models to address the current hurdles and setbacks in achieving P. vivax elimination.…”

Enhancing Malaria Control Strategy: Optimal Control and Cost‐Effectiveness Analysis on the Impact of Vector Bias on the Efficacy of Mosquito Repellent and Hospitalization

“…We solve the model in (20) with and without control numerically by applying the backward and forward sweep as described in [45]. Readers who are interested to see further examples on the implementation of this algorithm may refer to [33,[46][47][48]. In the beginning, we give an initial guess for u 1 t and u 2 t constant for all time t. With this initial guess, we solve system (20) forward in time.…”

Host metabolomic responses in recurrent P. vivax malaria

“…Recrudescence is the reappearance of parasite forms in the bloodstream after they have been treated to undetectable levels for a period of time, with the presence of plasma concentrations of chloroquine (CQ) and desethylchloroquine (DCQ) higher than 100 ng/mL 11 – 13 . Relapse occurs due to the reactivation of the dormant "hypnozoite" located in the liver 14 . Previous research indicated that relapses account for approximately 90% of P. vivax malaria cases in several countries where the disease is prevalent 15 .…”