Mathematical investigation of a two-strain disease model with double dose vaccination control policies

Abstract

Antimicrobial resistance (AMR) is the microorganism's resistance to an antimicrobial drug developed and designed to handle an infection. A recent study showed that there were 1.27 million global deaths in 2019 attributable to AMR. In current decades, vaccination is the most effective treatment that can reduce the growing AMR by preventing the incidence of infectious diseases (directly or indirectly). Vaccination has become a popular treatment as this can reduce the number of circulating AMR strains and reduce the need for antimicrobial use. With a double-dose vaccination campaign, we analyzed drug-susceptible and drug-resistant pathogens for this survey. We considered the circumstances of positive invariances and boundedness with appropriate primary conditions. We have determined two basic reproduction numbers: one associated with drug-susceptible strain (R01) and the other with drug-resistant strain (R02). We also revealed that at any stage, one of the strain could spread in a population if max[R01, R02] > 1 and the disease fade-out if both are <1 (i.e., max[R01, R02] < 1). In this study, We evaluated that our model contains four equilibrium points: the disease-free equilibrium, mono-existent endemic equilibrium 1, mono-existent endemic equilibrium 2, and a disease-endemic equilibrium. In particular, we applied the Routh-Hurwitz criteria to generalize the stability of the equilibria. We also found that the drug-resistant strain prevalence increases when the drug-susceptible strain is vaccinated on time due to the poor quality of the vaccine. We carried out the sensitivity analysis through the partial rank correlation coefficient (PRCC) technique to identify most important parameters. We found that the transmission rate of both strains had the biggest stimulus on disease outbreak. We also demonstrate how vaccination rates affected the equilibrium level of prevalence and found that a proper vaccination program is more effective for reducing two-strain disease burden. Numerical simulations carried out using MATLAB routines to support the analytical conclusions.