Abstract
Mathematical models can aid in elucidating the spread of infectious disease dynamics within a given population over time. In an attempt to model tuberculosis (TB) dynamics among high-burden districts in the Ashanti Region of Ghana, the SEIR epidemic model with demography was employed within both deterministic and stochastic settings for comparison purposes. The deterministic model showed success in modelling TB infection in the region to the transmission dynamics of the stochastic SEIR model over time. It predicted tuberculosis dying out in ten of twelve high-burden districts in the Ashanti Region, but an outbreak in Obuasi municipal and Amansie West district. The effect of introducing treatment at the incubation stage of TB transmission was also investigated, and it was discovered that treatment introduced at the exposed stage decreased the spread of TB. Branching process approximation was used to derive explicit forms of relevant epidemiological quantities of the deterministic SEIR model for stability analysis of equilibrium points. Numerical simulations were performed to validate the overall infection rate, basic reproductive number, herd immunity threshold, and Malthusian parameter based on bootstrapping, jackknife, and Latin Hypercube sampling schemes. It was recommended that the Ghana Health Service should find a good mechanism to detect TB in the early stages of infection in the region. Public health attention must also be given to districts with a potentially higher risk of experiencing endemic TB even though the estimates of the overall epidemic thresholds from our SEIR model suggested that the Ashanti Region as a whole had herd immunity against TB infection.
Highlights
Mathematical models can aid in elucidating the spread of infectious disease dynamics within a given population over time
Public health attention must be given to districts with a potentially higher risk of experiencing endemic TB even though the estimates of the overall epidemic thresholds from our SEIR model suggested that the Ashanti Region as a whole had herd immunity against TB infection
Estimates of relevant epidemic thresholds and the probability of TB extinction within the entire region suggest that TB infection cannot be epidemic, and it is certain to become extinct completely from the region. is implies further that with early diagnosis and treatment of TB, the prevalence of the disease can effectively be reduced over time within the region
Summary
Modelling the Transmission Dynamics of Tuberculosis in the Ashanti Region of Ghana. Received 7 November 2019; Revised 16 February 2020; Accepted 28 February 2020; Published 31 March 2020. In an attempt to model tuberculosis (TB) dynamics among high-burden districts in the Ashanti Region of Ghana, the SEIR epidemic model with demography was employed within both deterministic and stochastic settings for comparison purposes. We developed an SEIR model by incorporating other demographic information such as birth and death to explore the dynamics of TB in the Ashanti Region of Ghana, while examining the effects of (unknown) exposed individuals on the overall infection dynamics within deterministic and stochastic settings for comparison purposes. J s∗, e∗, i∗EEP − Iλ ⎡⎢⎢⎢⎢⎢⎢⎢⎣ αi∗ − (μ + ε) αs∗ ⎤⎥⎥⎥⎥⎥⎥⎥⎦ − ⎡⎢⎢⎢⎢⎢⎢⎢⎣ 0 λ 0 ⎤⎥⎥⎥⎥⎥⎥⎥⎦, ε − (μ + β) 0 0 λ
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