Stability and bifurcation analysis of a Taenia saginata model with control measures

Bovine cysticercosis and human taeniasis are neglected diseases caused by the beef tapeworm Taenia saginata. These diseases affect both human and animal health, rural livestock producers' livelihoods, and the economies of the nations. Bovine cysticercosis makes beef unfit for human consumption, thus decreasing the cattle market value. In this study, a mathematical model for the dynamics of human taeniasis and bovine cysticercosis is examined in the context of diseases' control efforts. The analysis of the basic model shows that both disease free and endemic equilibria exist. The basic reproduction number R0 is computed by the next generation method. The disease free equilibrium is globally asymptotically stable (GAS) when R-0 < 1 whereas the endemic equilibrium is GAS when R-0 > 1. To determine parameters that drive the diseases, the normalized forward sensitivity index method is adopted. The findings demonstrate that human and animal recruitment rates, the probability of humans to contract taeniasis, the rate at which humans with taeniasis defecate in the environment and T. saginata eggs' natural mortality rate influence the diseases' dynamics. The effects of several interventions including vaccination of cattle, treatment of infected humans and cattle, proper beef cooking, enhanced hygiene and sanitation, and the use of chemicals to kill T. saginata eggs in the environment are evaluated. When such interventions are administered, the model exhibits forward bifurcation, and secondary infections reduce significantly with time. Therefore, to control the diseases we recommend that more efforts be directed to treat humans with taeniasis and proper beef cooking and meat inspection be encouraged.