Mathematical Modelling of Infectious Disease: Mathematical Biology. Stability Analysis of Dynamical Leptospirosis Disease with Harmonic Mean Incidence Rate

      Аннотация: In this book, we studied Dynamical Leptospirosis Disease, which is caused by Leptospira Genus Bacteria spread by Rate, Raccoon, Pigs, Dogs, etc. by the contract of their Urine in Mud, Soil, water, and Hilly Rocks, etc. Leptospira Genus Bacteria transfers into the human body through nose, eyes, and mouth. After feelings, the symptoms of the disease, Penicillin, or Doxycycline antibiotics may be prescribed by doctors. The symptoms of this disease occur after infection during five (5) and fourteen days. If the infected person does not make an appointment with a doctor after the infection, then this disease may be fatal. Therefore, we study the Basics Reproduction Number R0, Local Stability, Global Stability, how they spread in a local area and globally, Finally, we have done some Numerical Simulation using software used for Numerical Computation and Simulation is MATLAB-SIMULINK. We have obtained our numerical results in Chapter “Numerical Simulation”. For the confirmation of the solution we use three different methods such methods are Runge-Kutta Method of order fourth (RK4), Non-Standard Finite Difference Method (NSFD), and Homotopy Perturbation Method (HPM).

Ключевые слова: Mathematical Modelling of infectious diseases, mathematical analysis, stability analysis, leptospirosis disease, SIR model, system of ordinary differential equations, Mathematical Biology, epidemiology, bio mathematics, numerical simulations, Homotopy Perturbation Method, Runge kutta scheme