Abstract
Sensitivity analysis has become increasingly useful in many fields of engineering and sciences. Researchers use sensitivity and uncertainty analysis in the mathematical modelling of biological phenomena because of its value in identifying essential parameters for model's output. Moreover, it can help in the process of experimental analysis, model order reduction, parameter estimation, decision making or development of recommendations for decision makers. Here, we demonstrate the use of local sensitivity analysis to understand the influence of different parameters on a threshold parameter, R_0^I, resulting from the analysis of a within human-host model for the dynamics of malaria parasites. %We highlight the different methods used in sensitivity analysis.Our results reveal that the obtained R_0^I is most sensitive to the infection rate of healthy red blood cells (RBCs) by merozoites, the average number of merozoites released per bursting parasitized RBCs, the proportion of parasitized RBCs that continue asexual reproduction and the per capita natural death rate of merozoites.
Highlights
Introduction and backgroundMalaria remains one of the most prevalent human diseases worldwide and still causes a significant problem in many tropical areas, especially in the tropical African region
Mathematical and statistical sensitivity analysis can be used to quantify the magnitude and relative importance of some of the malaria disease parameters towards the malaria control problem. Such a sensitivity analysis will be useful if appropriate models are developed that can simulate the malaria control problem and that can complement theoretical and experimental work
The interpretation of the elasticity indices in the third column of Table 4 are as follows: For the specified parameter values given in (24), R0I is most sensitive to β1, the contact rate between healthy/uninfected red blood cells (HRBCs) and free-floating merozoites, and r, the number of merozoites released per bursting IRBCs
Summary
Malaria remains one of the most prevalent human diseases worldwide and still causes a significant problem in many tropical areas, especially in the tropical African region. We use partial derivatives to determine local sensitivities by computing the changes in the model output (i.e. model solutions xi, i = 1, 2, · · · , n) with respect to the variations in the model inputs (parameters) at local points in the parameter space. And as an advantage, the difficulty in step size selection is not a main issue in the differential method but tends to cause problems in the finite-difference method [38] Another advantage of the differential method over the finite difference method is that the sensitivity of different outputs (state variables) with respect to certain parameters can be solved simultaneously. When several parameters are changed simultaneously, investigating their effects on model results via the sensitivity matrix S, using the direct differential method is time-consuming and computationallydemanding. Studying the monotonicity relations between the reproduction number and the parameters used in the model is important
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