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Environmental effect in logistically growing bacterial and human population. (English) Zbl 1156.92038

Summary: An SIS model in which the numbers of susceptibles obey logistic law has been analyzed in this paper. It is further assumed that the growth of the bacterial population is also logistic. The interaction between the bacterial and infective population has been taken into account. It has been observed that even after this modification some of the results are invariant. The stability criteria for the trivial and non-trivial equilibrium are studied. The analysis of the authors [Varāhmihir J. Math. Sci. 6, No. 2, 619–626 (2006 ; Zbl 1134.92348)] and M. Ghosh et al. [Nonlinear Anal., Real World Appl. 7, No. 3, 341–363 (2006; Zbl 1102.92045)] can be obtained by particularising the generalisation parameter.

MSC:

92D30 Epidemiology
92D40 Ecology
34D20 Stability of solutions to ordinary differential equations
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