Study of Transmission Dynamics of <i>Streptococcus suis</i> Infection Mathematical Model between Pig and Human under ABC Fractional Order Derivative

Abstract

In this paper, a mathematical model for Streptococcus suis infection is improved by using the fractional order derivative. The modified model also investigates the transmission between pigs and humans. The proposed model can classify the pig population density into four classes, which are pig susceptible class, pig infectious class, pig quarantine class, and pig recovery class. Moreover, the human population density has been separated into three classes, these are human susceptible class, human infectious class, and human recovery class. The spread of the infection is analyzed by considering the contact between humans and pigs. The basic reproduction number (R0), the infectious indicator, is carried out using the next generation matrix. The disease-free equilibrium is locally asymptotically stable if R01, and the endemic equilibrium is locally asymptotically stable if R0>1. The theoretical analyses of the fractional order derivative model, existence and uniqueness, have been proposed. The numerical examples were illustrated to support the proposed stability theorems. The results show that the fractional order derivative model provides the various possible solution trajectories with different fractional orders for the same parameters. In addition, transmission between pigs and humans resulted in the spread of Streptococcus suis infection.

Keywords

• <i>Streptococcus suis</i>
• endemic disease model
• stability analysis
• Atagana–Baleanu–Caputo fractional order derivative
• numerical simulation