Abstract
Malaria is a deadly infectious disease, which is transmitted to humans via the bites of infected female mosquitoes. Antimalarial drug resistance has been identified as one of the characteristics of malaria that complicates control efforts. Typically, the use of insecticide-treated bed-nets (ITNs) and drug treatment are some of the recommended control strategies against malaria. Here, the use of ITNs, drug treatment, and their efficacies and evolution of antimalarial drug resistance are considered to be the major driving forces in the dynamics of malaria transmissions. We formulate a mathematical model of two-strain malaria to assess the impacts of ITNs, drug treatment, and their efficacies on the transmission dynamics of the disease in a human population. We propose a simple mosquito biting rate function that depends on both the proportion of ITN usage and its efficacy. We show that both disease-free and co-existence equilibrium points are globally-asymptotically stable where they exist. The global uncertainty and sensitivity analysis conducted show that if about 95% of malaria cases can be treated with fewer than 5% treatment failure in a population with 95% ITN usage that remains 95% effective, malaria can be controlled. We find that the order in which numerous intervention measures are taken is important.
Highlights
Malaria is one of the most devastating infectious diseases in the world is caused by the protozoan Plasmodium and transmitted to humans through the bite of female Anopheles mosquitoes
The basic reproduction number is guaranteed to be bigger than the reproduction numbers in the presence of one or two intervention parameters whenever the ratio of the rates at which humans with sensitive malaria strain acquire immunity to that at which humans with the resistant strain acquire immunity is less than unity
We modeled the dynamics of a two-strain malaria transmission model by incorporating individuals infected with drug-sensitive and drug-resistant parasites in the human population
Summary
Malaria is one of the most devastating infectious diseases in the world is caused by the protozoan Plasmodium and transmitted to humans through the bite of female Anopheles mosquitoes. Mathematical models for the transmission dynamics of drug-sensitive and -resistant strains can be useful in providing valuable information that will help in understanding the factors that influence the spread of drug resistance This is important in designing rational intervention strategies for control of drug resistance and malaria transmissions in general. In the model of Tumwiine et al [19], the authors considered the infected human population to consist of individuals with drug-sensitive and -resistant malaria strains. Conducting a global sensitivity analysis to determine the influence of ITN usage, drug treatment, and their efficacies and other model parameters on the dynamics of malaria transmission
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