Mathematical Modeling of the Transmission Dynamics of Secondary Syphilis Co-Infected with Measles

Disease generally are disorder in plants or animals. The study examined the transmission dynamics of secondary syphilis that is co-infected with measles. The work basically is divided into four important compartments which are immigration factor in the susceptible, syphilis infected, syphilis latent and measles infected compartment. It was observed that no infection free equilibrium exists analytically due to immigration factor, thus, the endemic equilibrium points as the only equilibrium point was obtained. The analytical investigation of the behaviour of the sub-models for secondary syphilis and measles was done with the help of deterministic techniques. It is observed that the asymptotically stable system since all coefficients of equation are positive. Finally, the numerical investigation with the help of MATLAB established the sensitivity of the parameters such that while an increase in all parameters considered increased, the co-infected class did not show any effect on co-infected class. Due to the introduction of immigration factor, the disease-free equilibrium did not exist. Through analytical studies, it is determined that the endemic equilibrium point through which the establishment of the stability of the secondary syphilis and measles sub-models and the coinfection model were achieved. The study went further to numerically simulate the results of the proposed model and obtained the time series plots for each sub-model and the coinfection model. It is observed that the numerical results agreed with analytical findings. It also established the sensitivity of the parameters and observed while an increase in all parameters considered increased in the co-infected class though did not show any effect on co-infected class.