Threshold Dynamics and Stability Analysis of a Host-Parasite Model for Paragonimiasis with Numerical Simulations

Resumen

Paragonimiasis, commonly referred to as Lung fluke disease, is a neglected tropical disease that poses a serious risk to public health in endemic areas. Eating uncooked or undercooked freshwater crustaceans that contain Paragonimus larvae is the primary way that the disease is spread. This paper develops a system of nonlinear ordinary differential equations that model the interaction between definitive and intermediate host populations, including vaccination and treatment, in order to better understand its transmission. Basic reproduction numbers ($R_0$) were calculated for the subpopulations in order to assess transmission potential and create essential threshold conditions for disease persistence or extinction. The Routh-Hurwitz criterion was used to demonstrate the local asymptotic stability of the Disease-Free Equilibrium (DFE) for $R_0<1$, whereas instability arises for $R_0>1$. Similarly, under certain conditions, the Castillo-Chavez, Feng, and Huang framework was used to establish the global asymptotic stability of the DFE. A sensitivity analysis on $R_0$ was carried out to determine the key variables influencing transmission. The analytical results were supported by numerical simulations, which showed that vaccination and treatment together significantly lower the number of infected classes and can eventually eradicate the disease. Thus, this framework offers important epidemiological insights, showing that increasing vaccination, enhancing treatment and hygiene can successfully lower environmental contamination and manage the spread of \textit{Paragonimiasis} in human population.