Abstract
Malaria remains by far the world's most important tropical disease, killing more people than any other communicable disease. A number of preventive and control measures have been put in place and most importantly drug treatment. The emergence of drug resistance against the most common and affordable antimalarials is widespread and poses a key obstacle to malaria control. A mathematical model that incorporates evolution of drug resistance and treatment as a preventive strategy is formulated and analyzed. The qualitative analysis of the model is given in terms of the effective reproduction number, Re. The existence and stability of the disease-free and endemic equilibria of the model are studied. We establish the threshold parameters below which the burden due to malaria can be brought under control. Numerical simulations are done to determine the role played by key parameters in the model. The public health implications of the results are twofold; firstly every effort should be taken to minimize the evolution of drug resistance due to treatment failure and secondly high levels of treatment and development of immunity are essential in reducing the malaria burden.
Highlights
Malaria is one of the most devastating infectious diseases in the world, infecting approximately 300–500 million people annually worldwide, resulting in over a million deaths [1, 2]
In the present paper we extend Tumwiine et al [30] model that is based on the susceptible-infective-immune (SIRS) in the human population and susceptible-infective (SI) in the mosquito population
The model incorporates that a fraction φ of the human population are infected with the sensitive strains and the remaining (1 − φ) are infected with the resistant strains
Summary
Malaria is one of the most devastating infectious diseases in the world, infecting approximately 300–500 million people annually worldwide, resulting in over a million deaths [1, 2]. Their use in the study of the evolution of drug resistance of the malaria parasites has been considered in [12, 22, 24, 29] Most of these models have been formulated as a simple mass action and assume constant human host and mosquito vector populations in which births and deaths are equal. They ignore disease induced mortality which seems to be unrealistic especially in the sub-Saharan Africa where most deaths are due to malaria related cases.
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