AUTHOR=Kailan Suhuyini Abdulai , Seidu Baba 

TITLE=A mathematical model on the transmission dynamics of typhoid fever with treatment and booster vaccination

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 9 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2023.1151270

DOI=10.3389/fams.2023.1151270

ISSN=2297-4687

ABSTRACT=<p>Typhoid fever is a potentially fatal illness that is caused by the bacteria <italic>Salmonella typhi</italic>. In this study, a deterministic mathematical model was formulated to look into transmission dynamics of typhoid fever with treatment and booster vaccination. The reproduction number <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="-tex-caligraphic">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is calculated using the next-generation matrix approach. Then, a stability analysis on the equilibrium points was performed using Routh–Hurwitz criteria. It was revealed that the disease-free equilibrium point is locally asymptotically stable whenever <inline-formula><mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="-tex-caligraphic">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is less than 1 together with other conditions. We also showed that <inline-formula><mml:math id="M3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="-tex-caligraphic">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> does not guarantee global stability of the typhoid-free equilibrium point and corroborated the result by showing the possible existence of backward bifurcation at <inline-formula><mml:math id="M4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="-tex-caligraphic">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>. The model parameters in <inline-formula><mml:math id="M5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="-tex-caligraphic">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> were also subjected to sensitivity analysis, which revealed that the transmission rate, infection through an exposed person, and bacteria are the most influential parameters of the reproduction number <inline-formula><mml:math id="M6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="-tex-caligraphic">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>. Numerical simulations were run to determine the impact of various parameters on the dynamics of typhoid.</p>