Compartmental epidemic models are intriguing in the sense that the generic model may explain different kinds of infectious diseases with minor modifications. However, there may exist some ailments that may not fit the generic capsule. Amoebiasis is one such example where transmission through the population demands a more detailed and sophisticated approach, both mathematical and numerical. The manuscript engages in a deep analytical study of the compartmental epidemic model; susceptible-exposed-infectious-carrier-recovered-susceptible (SEICRS
), formulated for Amoebiasis. We have shown that the model allows the single disease-free equilibrium (DFE) state if
, the basic reproduction number, is less than unity and the unique endemic equilibrium (EE) state if
is greater than unity. Furthermore, the basic reproduction number depends uniquely on the input parameters and constitutes a key threshold indicator to portray the general trends of the dynamics of Amoebiasis transmission. We have also shown that
is highly sensitive to the changes in values of the direct transmission rate in contrast to the change in values of the rate of transfer from latent infection to the infectious state. Using the Routh–Hurwitz criterion and Lyapunov direct method, we have proven the conditions for the disease-free equilibrium and the endemic equilibrium states to be locally and globally asymptotically stable. In other words, the conditions for Amoebiasis “die-out” and “infection propagation” are presented.
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