Modelling <i>Trypanosoma cruzi</i>-<i>Trypanosoma rangeli</i> co-infection and pathogenic effect on Chagas disease spread

Abstract

<p style='text-indent:20px;'>A mathematical model is developed to investigate the impact of <i>Trypanosoma cruzi</i> and <i>Trypanosoma rangeli</i> co-infection and <i>Trypanosoma rangeli</i>-induced pathogenicity of triatomine bugs on the spread of Chagas disease. Due to the presence of two parasites, basic reproduction numbers of one parasite in the absence of the other parasite (<inline-formula><tex-math id="M1">\begin{document}$ \mathcal{R}_{10} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_{20} $\end{document}</tex-math></inline-formula>) and invasion reproduction numbers of one parasite invading the other parasite (<inline-formula><tex-math id="M3">\begin{document}$ \mathcal{R}_{12} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_{21} $\end{document}</tex-math></inline-formula>) are derived to determine the dynamics of the co-infection system. With a simple case of two parasites' independent transmission, we have found that both parasites go extinct if both <inline-formula><tex-math id="M5">\begin{document}$ \mathcal{R}_{i0}&lt;1\,(i=1,2) $\end{document}</tex-math></inline-formula>, thus no Chagas disease spread. Nevertheless, the condition of <inline-formula><tex-math id="M6">\begin{document}$ \mathcal{R}_{i0}&gt;1\,(i=1,2) $\end{document}</tex-math></inline-formula> is not sufficient to cause Chagas disease persistence, the invasion reproduction number of <i>Trypanosoma cruzi</i> invading <i>Trypanosoma rangeli</i> transmission <inline-formula><tex-math id="M7">\begin{document}$ \mathcal{R}_{12} $\end{document}</tex-math></inline-formula> plays an important role. Specifically, Chagas disease could go extinct if <inline-formula><tex-math id="M8">\begin{document}$ \mathcal{R}_{12}&lt;1 $\end{document}</tex-math></inline-formula>, and uniformly persistent if <inline-formula><tex-math id="M9">\begin{document}$ \mathcal{R}_{12}&gt;1 $\end{document}</tex-math></inline-formula>. Moreover, due to pathogenicity, oscillation pattern of Chagas disease is observed, which is different from other mechanisms such as maturation delay, seasonality and regular spraying with insecticides for vector control. In conclusion, we have found that the presence of <i>Trypanosoma rangeli</i> infection leads to the risk reduction of Chagas disease infection. Our findings are beneficial to the prevention and control of Chagas disease.</p>