Tufail Malik

Does dormancy increase fitness of bacterial populations in time-varying environments?

A simple family of models of a bacterial population in a time varying environment in which cells can transit between dormant and active states is constructed. It consists of a linear system of ordinary differential equations for active and dormant cells with time-dependent coefficients reflecting an environment which may be periodic or random, with alternate periods of low and high resource levels. The focus is on computing/estimating the dominant Lyapunov exponent, the fitness, and determining its dependence on various parameters and the two strategies—responsive and stochastic—by which organisms switch between dormant and active states. A responsive switcher responds to good and bad times by making timely and appropriate transitions while a stochastic switcher switches continuously without regard to the environmental state. The fitness of a responsive switcher is examined and compared with fitness of a stochastic switcher, and with the fitness of a dormancy-incapable organism. Analytical methods show that both switching strategists have higher fitness than a dormancy-incapable organism when good times are rare and that responsive switcher has higher fitness than stochastic switcher when good times are either rare or common. Numerical calculations show that stochastic switcher can be most fit when good times are neither too rare or too common.

The impact of an imperfect vaccine and pap cytology screening on the transmission of human papillomavirus and occurrence of associated cervical dysplasia and cancer.

A mathematical model for the natural history of human papillomavirus (HPV) is designed and used to assess the impact of a hypothetical anti-HPV vaccine and Pap cytology screening on the transmission dynamics of HPV in a population. Rigorous qualitative analysis of the model reveals that it undergoes the phenomenon of backward bifurcation. It is shown that the backward bifurcation is caused by the imperfect nature of the HPV vaccine or the HPV-induced and cancer-induced mortality in females. For the case when the disease-induced and cancer-induced mortality is negligible, it is shown that the disease-free equilibrium (i.e., equilibrium in the absence of HPV and associated dysplasia) is globally-asymptotically stable if the associated reproduction number is less than unity. The model has a unique endemic equilibrium when the reproduction threshold exceeds unity. The unique endemic equilibrium is globally-asymptotically stable for a special case, where the associated HPV-induced and cancer-induced mortality is negligible. Numerical simulations of the model, using a reasonable set of parameter values, support the recent recommendations by some medical agencies and organizations in the USA to offer Pap screening on a 3-year basis (rather than annually). (rather than annually).

A polynomial goal programming model with application to energy consumption and emissions in United Arab Emirates

Sustainable growth and development of nations requires strategic vision and plan to accommodate growing energy needs while preserving and protecting the natural environment. Studies that couple energy and environment often present conflicting objectives which requires the explicit use of quantitative models to develop appropriate solutions for policy planning and analysis. Goal programming offers an analytical framework to solve multi-objective problems that simultaneously satisfy decision makers preferences. In this paper we develop a polynomial goal programming model to study the effects of electricity consumption and greenhouse gas emissions applied to the economy of United Arab Emirates. The results provide valuable insights for improvement opportunities and quantitative justification for the required investments and efforts in implementing sustainable development plans.

Optimal control with multiple human papillomavirus vaccines

A two-sex, deterministic ordinary differential equations model for human papillomavirus (HPV) is constructed and analyzed for optimal control strategies in a vaccination program administering three types of vaccines in the female population: a bivalent vaccine that targets two HPV types and provides longer duration of protection and cross-protection against some non-target types, a quadrivalent vaccine which targets an additional two HPV types, and a nonavalent vaccine which targets nine HPV types (including those covered by the quadrivalent vaccine), but with lesser type-specific efficacy. Considering constant vaccination controls, the disease-free equilibrium and the effective reproduction number Rv for the autonomous model are computed in terms of the model parameters. Local-asymptotic stability of the disease-free equilibrium is established in terms of Rv. Uncertainty and Sensitivity analyses are carried out to study the influence of various important model parameters on the HPV infection prevalence. Assuming the HPV infection prevalence in the population under the constant control, optimal control theory is used to devise optimal vaccination strategies for the associated non-autonomous model when the vaccination rates are functions of time. The impact of these strategies on the number of infected individuals and the accumulated cost is assessed and compared with the constant control case. Switch times from one vaccine combination to a different combination including the nonavalent vaccine are assessed during an optimally designed HPV immunization program.

Mathematical analysis of swine influenza epidemic model with optimal control

A deterministic model is designed and used to analyze the transmission dynamics and the impact of antiviral drugs in controlling the spread of the 2009 swine influenza pandemic. In particular, the model considers the administration of the antiviral both as a preventive as well as a therapeutic agent. Rigorous analysis of the model reveals that its disease-free equilibrium is globally asymptotically stable under a condition involving the threshold quantity-reproduction number

Mathematical analysis of the role of hospitalization/isolation in controlling the spread of Zika fever

{\mathcal {R}}_c

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

Rc. The disease persists uniformly if