Markov Chain Modeling of HIV, Tuberculosis, and Hepatitis B Transmission in Ghana

Twumasi, Clement; Asiedu, Louis; Nortey, Ezekiel N. N.

doi:10.1155/2019/9362492

Cited by 14 publications

(9 citation statements)

References 6 publications

(7 reference statements)

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“…In this study Markov chain model showed that both rate of infection and severity were relatively low in all the three classifications. The findings relate with Twumasi et al (2019) where similar outcome, was obtained but with different disease scope namely, HIV, Hepatitis B (HBV) and tuberculosis TB). These diseases are classified as infectious diseases.…”

Section: Discussionsupporting

confidence: 75%

A Stochastic H-U Model for Malaria Transmission via Markov Theory

Arku¹,

Kallah-Dagadu²

2020

Preprint

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The purpose of this study is to estimate the mean transitioning probabilities from a Healthy state to malaria positive uncomplicated state or to malaria positive severe state. It also classifies the various transitioning probabilities of moving through the various states based on some baseline characteristics. Malaria test results for 2019 over a 12-month period were collected from the University of Ghana school clinic. An H-U model for the study was developed and the transition rates from the cross-sectional data are indicated. With two states Healthy (H) and Uncomplicated (U) forming a state space, there were four possible transitions. The results show that the probability of transitioning from a Healthy state to a malaria positive state is 0.03% while the probability that an individual will remain at Healthy state (H) after the test is 99.73%. It was found that if an individual is already positive and has taken medication the probability that its second test came out negative is 6.45% while the chances that it will remain positive but uncomplicated is 93.55%. The study also showed that in the long run, about 95.98% of persons who visited the student clinic with malaria symptoms recorded negative tests for malaria parasite while about 4% recorded positive for malaria. In terms of disaggregation by gender, it was realized that the number of reported negative test results were higher for females (97.08%) than for males (96.13%). However, the infection rate is higher for males (3.87%) than females (2.92%). It is recommended that in as much as the University of Ghana has two health centers (a clinic and hospital), there should be a centralized system to track students’ health so research done would not be biased.

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Section: Discussionsupporting

confidence: 75%

A Stochastic H-U Model for Malaria Transmission via Markov Theory

Arku¹,

Kallah-Dagadu²

2020

Preprint

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“…Nevertheless, estimates of the epidemic thresholds (R 0 � 0.53 < 1, ρ � − 0.073 < 0, and q c � − 0.87 < 0) from bootstrap, jackknife, and Latin Hypercube sampling schemes for the entire region suggested that there may not be tuberculosis outbreak in the Ashanti Region since the probability of TB extinction was unity within the region as a whole; hence, the disease-free equilibrium point will be stable for the entire Ashanti Region. A similar result was found by Twumasi et al where they discovered with a certain probability that TB-infected individuals can recover in the region via a discrete-time Markov model [37]. Nonetheless, approximately 12% and 14% of the study population in Obuasi Municipal and Amansie West district, respectively, need TB immunization to control the spread of the disease.…”

Section: Type Of Modelsupporting

confidence: 84%

Modelling the Transmission Dynamics of Tuberculosis in the Ashanti Region of Ghana

Mettle

Affi

Twumasi

2020

Interdisciplinary Perspectives on Infectious Diseases

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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.

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“…Markov chain models are able to estimate relevant disease metrics such as probability of first infection and recovery as well as the expected time to infection and recovery for both susceptible and infected individuals. These models can generalize the transition estimates of disease outcomes at discrete time steps for future predictions (Twumasi et al, 2019).…”

Section: Our Model Vs Markov Chain and Cellular Automata Modelsmentioning

confidence: 99%

An epidemic model to address the spread of plant pests. The case of Xylella fastidiosa in almond trees

Pont

Cortés‐Plana

Mora

et al. 2020

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Purpose The purpose of this paper is to present a discrete compartmental susceptible-asymptomatic-infected-dead (SAID) model to address the expansion of plant pests. The authors examined the case of Xylella fastidiosa in almond trees in the province of Alicante (Spain) to define the best eradication/contention protocol depending on the environmental parameters such as climatic factors, distance between trees, isolation of the plots, etc. Design/methodology/approach This approach considers the expansion of the disease among the almond trees orchards by means of a grid model. The cells of the grid represent a tree (or even a group of trees) that can be susceptible (healthy), asymptomatic (infected by the bacterium but without symptoms), infected or dead. When time passes, the status of the cells is determined by binary rules that update following both a neighborhood and a delay pattern. The model assumes that the environmental parameters have a crucial impact on the expansion of the disease, so a grid is assigned to each parameter to model the single effect caused by this parameter. The expansion is then the weighted sum of all the grids. Findings This proposal shows how the grid architecture, along with an update rule and a neighborhood pattern, is a valuable tool to model the pest expansion. This model has already been analyzed in previous works and has been compared with the corresponding continuous models solved by ordinary differential equations, coming to find the homologous parameters between both approaches. Thus, it has been possible to prove that the combination neighborhood-update rule is responsible for the rate of expansion and recovering/death of the illness. The delays (between susceptible and asymptomatic, asymptomatic and infected, infected and recovered/dead) may have a crucial impact on both the peak of infected and the recovery/death rate. This theoretical model has been successfully tested in the case of the dissemination of information through mobile social networks and is also currently under study in the case of expansion of COVID-19. Originality/value This work develops a new approach for the analysis of expansion of plant pests. This approach provides both behavioral variability at the cell level (by its capability to modify the neighborhood and/or the update rule and/or the delays) and modularity (by easy scaling the number of grids). This provides a wide range of possibilities to deal with realistic scenarios.

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Markov Chain Modeling of HIV, Tuberculosis, and Hepatitis B Transmission in Ghana

Cited by 14 publications

References 6 publications

A Stochastic H-U Model for Malaria Transmission via Markov Theory

A Stochastic H-U Model for Malaria Transmission via Markov Theory

Modelling the Transmission Dynamics of Tuberculosis in the Ashanti Region of Ghana

An epidemic model to address the spread of plant pests. The case of Xylella fastidiosa in almond trees

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