Abstracts are provided in the language submitted.

Introduction and Objective: It is not always possible to measure all state variables and estimate time-dependent parameters are given a mathematical model repressing a real world-phenomenon. One approach to address such problems is to consider state reconstruction problem (or inverse system design). The main objective of this work is to construct an observer to estimate time-dependent parameters and state variables of cholera dynamics with minimum infection dose applied to real data. Materials and Methods: A method based on the observer is proposed to estimate the state variables not accessible to measurement and the time-dependent parameters from real data. An auxiliary system is used, an observer whose solutions converge exponentially to those of an original system and solely utilizes known inputs and output of the model. Results: We showed that the system together with the observer designed is detectable but is not observable allowing us to design an observer. We derive the expressions for time-dependent parameters using real data and estimate their values for different periods, and estimate the state variables. Numerical simulations are then performed for the validation of estimation results. We have analytically shown and numerically confirmed the exponential convergence to zero of the estimation errors resulting from the observer. Conclusion and Significance/Implication: The time evolution of the states of the model system with their respective estimates obtained by the observer evolve together, which shows a good estimation yielded from the observer. The method used can be applied to other disease models and engineering problems.

Dr. Woldegebriel Assefa Woldegerima