Mathematical modeling and simulating of Helicobacter pylori treatment and transmission implications on stomach cancer dynamics

Abstract

Deterministic mathematical model of the nonlinear first-order differential equation is proposed considering both direct and indirect contact transmission to capture some of the control measures such as treatment in limiting the infection. Six compartments are considered in the model that is; susceptible humans, exposed humans, infected humans with H. pylori, treated humans, infected humans with stomach cancer and the bacteria concentration from the environment. The qualitative behavior of the model was performed including, the existence of nonnegative invariant solution, boundness region, equilibria (both disease-free as well as endemic) and stabilities of two-equilibrium point. Moreover, control reproduction number and bifurcation analysis were also studied. Based on the analysis of sensitivity, the method of partial rank correlation coefficient (PRCC) and Latin hypercube sampling (LHS) was studied to find out which parameters are useful for the model. Furthermore, sensitivity analysis of some parameters was also studied based on the control reproduction number. The simulation results show that increasing the Helicobacter pylori infections treatment rate, has a vital role in the reduction of infections and stomach cancer in the community. Therefore, we concluded that effective treatment rate and low contact rate are most significant to eradicate stomach cancer from the community.