JISE


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Journal of Information Science and Engineering, Vol. 36 No. 6, pp. 1261-1277


Modeling and Analysis of Scabies Transmission Disease


N. H. ALSHAMRANI1,2, A. M. ELAIW1,3, H. BATARFI1
AND A. D. HOBINY1
1Department of Mathematics
King Abdulaziz University
Jeddah, 21589 Saudi Arabia
E-mail: {nalshmrane; aelaiwksu.edu.sa; hbatarfi; ahobany}@kau.edu.sa

2Department of Mathematics
University of Jeddah
Jeddah, 21589 Saudi Arabia
E-mail: nhalshamrani@uj.edu.sa

3Department of Mathematics
Al-Azhar University
Assiut, 71524 Egypt


In this work we present two mathematical models for the infection dynamics of scabies. The dynamics is described by four-dimensional system of ordinary differential equations that expresses the transmissions between susceptible and infectious/infective individuals. In the second model, we include the importance of adult scabiei mite in the real interaction with hosts. Nonnegativity and boundedness of solutions of the models are conducted. A threshold parameter is calculated for each model which ensures the existence of all corresponding equilibria. Using candidate Lyapunov functions, it is shown that whenever the threshold parameter is less than or equal unity, the models have an associated disease-free equilibrium that is globally asymptotically stable. In addition, when the threshold exceeds unity the models have a globally asymptotically stable endemic equilibrium. Finally, using some parameter values related to the scabies infection dynamics, numerical simulation results are demonstrated to clarify the main theoretical results.


Keywords: scabies transmissions, infectious diseases, local stability, global stability, infection rate, Lyapunov function

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