Dynamical analysis of a two-strain treatment model for Anthrax in a population where it is deployed as bioterrorism weapon

پوختە

The major short coming associated with the use of antibiotics to combat anthrax in a population under the siege of its attack, is the emergence and transmission of anthrax that are resistant to these drugs. Consequently, our focus in this work is the formulation of a new deterministic treatment model which incorporates a wild (drug-sensitive) and drug resistant strain for gaining insight into the dynamical features of the two strains of anthrax, with a view to determining result-oriented, and effective ways to control the spread of the disease and its treatment in this circumstance. Discoveries from both the qualitative and numerical analysis of the model, is that the model has two equilibria: the disease free equilibrium (DFE) which is locally asymptotically stable when a certain epidemiological threshold  (the associated reproduction number) is not up to unity, that is,  and the disease will persist in the community when the threshold exceeds unity, that is, . In addition, for the case where   , it is shown that the model can have two co-existing endemic equilibria and there is occurrence of a phenomenon, competitive exclusion whenever the associated reproduction number of the drug-resistant strain () is greater than that of the wild strain (). On the other hand, unlike in the treatment model, it is shown that the model without treatment can have a family of infinitely many endemic equilibria when its associated epidemiological threshold () exceeds unity. Whenever    and , it is shown that widespread application of treatment regimen of combination of prophylaxis and antibiotics against the wild strain of the disease can lead to its elimination from the community if the associated reduction in infectiousness of infected individuals who were treated for the wild strain infection does not exceed a certain threshold value, which in this case, is the use of treatment expected to make  .