Can treatment increase the epidemic size?
This paper studies an epidemic model with drug-sensitive and drug-resistant pathogen strains over a constant homogeneously mixed population. The model can be expressed in the form \[ \begin{aligned} S'&=-\beta(I_S+\delta_TI_T+\delta_RI_R)S, \\ I'_S&=\beta(I_S+\delta_TI_T)S-(\gamma_S+\eta)I_S,\\ I'_T&=\eta I_S+\int_0^t\eta I_S(\xi)e^{-\gamma_T(t-\xi)}\alpha'(t-\xi)d\xi-\gamma_TI_T,\\ I'_R&=\delta_R\beta I_RS-\int_0^t\eta I_S(\xi)e^{-\gamma_T(t-\xi)}\alpha'(t-\xi)d\xi-\gamma_RI_R,\end{aligned} \] where the status is classified as susceptible (\(S\)), infected with the sensitive strain (\(I_S\)), with the sensitive strain under treatment (\(I_T\)), and with the resistant strain (\(I_R\)). Here, \(\beta\) is the baseline transmission rate; \(\delta_R,\delta_T\), and \(\eta\) are the relative transmissibility of the resistant strain, treated infection with the sensitive strain, and the rate at which individuals infected with the sensitive strain are treated, respectively; \(\gamma_S,\gamma_T,\gamma_R\) are the corresponding recovery rates. \(\alpha(t)\) is a non-negative non-increasing function representing the probability of being in the treated class (\(I_T\)) at time \(t\) following the initiation of treatment without developing drug-resistance. Under some ad hoc assumptions on these parameters and functions, the authors obtain the final epidemic size relations with respect to the treatment rate for the model, giving an affirmative answer to the title. Numerical results are presented to illustrate the theoretical findings.
scientific article; zbMATH DE number 6538264