Modeling the Impact of Bed-Net Use and Treatment on Malaria Transmission Dynamics

Abstract

We modeled the impact of bed-net use and insecticide treated nets (ITNs), temperature, and treatment on malaria transmission dynamics using ordinary differential equations. To achieve this we formulated a simple model of mosquito biting rate that depends on temperature and usage of insecticides treated bed nets. We conducted global uncertainty and sensitivity analysis using Latin Hypercube Sampling (LHC) and Partial Rank Correlation Coefficient (PRCC) in order to find the most effective parameters that affect malaria transmission dynamics. We established the existence of the region where the model is epidemiologically feasible. We conducted the stability analysis of the disease-free equilibrium by the threshold parameter. We found the condition for the existence of the endemic equilibrium and provided necessary condition for its stability. Our results show that the peak of mosquitoes biting rate occurs at a range of temperature values not on a single value as previously reported in literature. The results also show that the combination of treatment and ITNs usage is the most effective intervention strategy towards control and eradication of malaria transmissions. Sensitivity analysis results indicate that the biting rate and the mosquitoes death rates are the most important parameters in the dynamics of malaria transmission.

Global Sensitivity Analysis to Study the Impacts of Bed-Nets, Drug Treatment, and Their Efficacies on a Two-Strain Malaria Model

“…This is because at least two different studies that utilized similar scaling as we have done in this work finished with different outcomes in terms of backward bifurcation. For example, in the work of Ngwa and Shu [27], the model did not exhibit backward bifurcation; however, backward bifurcation was reported in the work of Gimba and Bala [38]. Despite these discrepancies, it is reasonable to state that since there is a possibility of backward bifurcation in Model (3), which no longer exists in Model (15), one can say that scaling removes backward bifurcation in this work.…”

“…However, finding suitable data for model simulation and sensitivity analysis is still a big challenge without an appropriate answer. Following [9,18,19,26,27,35,38,50], we used parameter values from published work in the literature to simulate and to perform sensitivity analysis of our model where such information is found. In some cases, we assumed the values of some of the parameters as shown in Table 3.…”

“…This phenomenon has been observed in many epidemic models. See, for instance, [9,[35][36][37][38][39]. In this scenario, the requirement for the basic reproduction number to be less than one for the disease to be eradicated no longer holds.…”

“…According to the reports in [25,50,56,57], ITN possession does not translate into use, and the efficacy of ITNs could wane over time due to frequent washing and exposure to direct sunlight, among other reasons. Despite these drawbacks, ITNs usage was rated among the most important strategies against malaria transmissions [38,58,59]. One key constraint in sustainable use of ITNs is the need for regular re-treatment, otherwise they lose their efficiencies.…”

Mathematical Modeling of the Coinfection Dynamics of Malaria-Toxoplasmosis in the Tropics

“…Mathematical models have been formulated by many researchers, and the earliest malaria model was formulated by Ross (1911). Recent publications by Traore and Sangare (2018), Berretta and Capasso (1986), Beretta et al (2018) and Gimba and Bala (2017) have proved valuable in this study. Also, mathematical models have been developed and analyzed to describe toxoplasmosis in humans and the zoonotic host.…”