Oluwaseun Sharomi

Curtailing smoking dynamics: a mathematical modeling approach

This paper provides a rigorous mathematical study for assessing the dynamics of smoking and its public health impact in a community. A basic mathematical model, which is a slight refinement of the model presented in [F. Brauer, C. Castillo-Chavez. Mathematical Models in Population Biology and Epidemiology. Text in Applied Mathematics. Springer, 2000; G.C. Castillo, S.G. Jordan, A.H. Rodriguez. Mathematical models for the dynamics of tobacco use, recovery and relapse. Technical Report Series, BU-1505-M. Department of Biometrics, Cornell University. 2000], is designed first of all. It is based on subdividing the total population in the community into non-smokers, smokers and those smokers who quit smoking either temporarily or permanently. The theoretical analysis of the basic model reveals that the associated smoking-free equilibrium is globally-asymptotically stable whenever a certain threshold, known as the smokers-generation number, is less than unity, and unstable if this threshold is greater than unity. The public health implication of this result is that the number of smokers in the community will be effectively controlled (or eliminated) at steady-state if the threshold is made to be less than unity. Such a control is not feasible if the threshold exceeds unity (a global stability result for the smoking-present equilibrium is provided for a special case). The basic model is extended to account for variability in smoking frequency, by introducing two classes of mild and chain smokers as well as the development and the public health impact of smoking-related illnesses. The analysis and simulations of the extended model, using an arbitrary but reasonable set of parameter values, reveal that the number of smokers in the community will be significantly reduced (or eliminated) if chain smokers do not remain as chain smokers for longer than 1.5 years before reverting to the mild smoking class, regardless of the time spent by mild smokers in their (mild smoking) class. Similarly, if mild smokers practice their mild smoking habit for less than 1.5 years, the number of smokers in the community will be effectively controlled irrespective of the dynamics in the chain smoking class.

Modelling the transmission dynamics and control of the novel 2009 swine influenza (H1N1) pandemic.

The paper presents a deterministic compartmental model for the transmission dynamics of swine influenza (H1N1) pandemic in a population in the presence of an imperfect vaccine and use of drug therapy for confirmed cases. Rigorous analysis of the model, which stratifies the infected population in terms of their risk of developing severe illness, reveals that it exhibits a vaccine-induced backward bifurcation when the associated reproduction number is less than unity. The epidemiological consequence of this result is that the effective control of H1N1, when the reproduction number is less than unity, in the population would then be dependent on the initial sizes of the subpopulations of the model. For the case where the vaccine is perfect, it is shown that having the reproduction number less than unity is necessary and sufficient for effective control of H1N1 in the population (in such a case, the associated disease-free equilibrium is globally asymptotically stable). The model has a unique endemic equilibrium when the reproduction number exceeds unity. Numerical simulations of the model, using data relevant to the province of Manitoba, Canada, show that it reasonably mimics the observed H1N1 pandemic data for Manitoba during the first (Spring) wave of the pandemic. Further, it is shown that the timely implementation of a mass vaccination program together with the size of the Manitoban population that have preexisting infection-acquired immunity (from the first wave) are crucial to the magnitude of the expected burden of disease associated with the second wave of the H1N1 pandemic. With an estimated vaccine efficacy of approximately 80%, it is projected that at least 60% of Manitobans need to be vaccinated in order for the effective control or elimination of the H1N1 pandemic in the province to be feasible. Finally, it is shown that the burden of the second wave of H1N1 is expected to be at least three times that of the first wave, and that the second wave would last until the end of January or early February, 2010.

Mathematical Analysis of a Model for Assessing the Impact of Antiretroviral Therapy, Voluntary Testing and Condom Use in Curtailing the Spread of HIV

This paper presents a deterministic model for evaluating the impact of anti-retroviral drugs (ARVs), voluntary testing (using standard antibody-based and a DNA-based testing methods) and condom use on the transmission dynamics of HIV in a community. Rigorous qualitative analysis of the model show that it has a globally-stable disease-free equilibrium whenever a certain epidemiological threshold, known as the effective reproduction number

Convergence order vs. parallelism in the numerical simulation of the bidomain equations

{(\mathcal{R}_{\rm eff})}

A multiple criteria economic growth model with environmental quality and logistic population behaviour with variable carrying capacity

, is less than unity. The model has an endemic equilibrium whenever

MATHEMATICAL ANALYSIS OF THE TRANSMISSION DYNAMICS OF HIV/TB COINFECTION IN THE PRESENCE OF TREATMENT

{\mathcal{R}_{\rm eff} > 1}