Abstract
In this paper, we study the dynamic behavior of a stochastic tungiasis model for public health education. First, the existence and uniqueness of global positive solution of stochastic models are proved. Secondly, by constructing Lyapunov function and using It formula, sufficient conditions for disease extinction and persistence in the stochastic model are proved. Thirdly, under the condition of disease persistence, the existence and uniqueness of an ergodic stationary distribution of the model is obtained. Finally, the importance of public health education in preventing the spread of tungiasis is illustrated through the combination of theoretical results and numerical simulation.
Highlights
Tungiasis is a parasitic skin disease caused by female sand fleas invading the human epidermis
About 2.6 million (6.5%) Kenyans are known to have been affected by the disease, and 10 million are at risk of tungiasis [7]
We investigate the dynamics of a stochastic tungiasis model in public health education
Summary
Tungiasis is a parasitic skin disease caused by female sand fleas invading the human epidermis. A large number of reported infections indicate that the disease spreads in many countries in economically disadvantaged areas, such as Latin America, the Caribbean, and subSaharan Africa [4]. In these areas, many patients cannot walk properly due to the effects of the disease, leading to further poverty. Nyang’ inja et al [13] discussed a mathematical model of the impact of public health education on tungiasis. Since the impact of public health education is not permanent and the control measures are taken gradually disappear, the educated population will be infected at a lower rate αβEI, where 0 < α < 1.
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