Abstract
Abstract In this article, a mathematical model has been derived for studying the dynamics of malaria disease and the influence of awareness-based interventions, for control of the same, that depend on ‘level of awareness’. We have assumed the disease transmission rates from vector to human and from human to vector, as decreasing functions of ‘level of awareness’. The effect of insecticides for controlling the mosquito population is influenced by the level of awareness, modelled using a saturated term. Organizing any awareness campaign takes time. Therefore a time delay has been incorporated in the model. Some basic mathematical properties such as nonnegativity and boundedness of solutions, feasibility and stability of equilibria have been analysed. The basic reproduction number is derived which depends on media coverage. We found two equilibria of the model namely the disease-free and endemic equilibrium. Disease-free equilibrium is stable if basic reproduction number (ℛ0) is less than unity (ℛ0 < 1). Stability switches occur through Hopf bifurcation when time delay crosses a critical value. Numerical simulations confirm the main results. It has been established that awareness campaign in the form of using different control measures can lead to eradication of malaria.
Highlights
In most of the poor, rural and semirural areas of the world malaria is one of the major causes of mortality [1]
About 231 million cases of malaria were reported in the year 2017 alone by World Health Organization (WHO), occurring in 106 countries, of which, around 81% occurred in African Regions resulting in about 91% death of the infected persons [2]
(iii) The minimum awareness level such that we can rely on awareness for malaria eradication can be determined from Theorem 3, and it is given below:
Summary
In most of the poor, rural and semirural areas of the world malaria is one of the major causes of mortality [1]. Effective control of the infection include controlling the spread of disease through various methodologies at different levels or stages of life cycles of both parasite and vector. Time delay arises in controlling malaria with awareness, for example, there may be delay in reporting infected cases to the health organization. [8], a model for controlling vector-borne disease through media awareness campaign was proposed which assumed that arrangement of such programs should be in proportion to number of infected people. Delay model for malaria disease dynamics and possible control using public awareness has been proposed. A discussion concludes the paper with a future outline of the present work (Section 7)
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