Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Nonquasimonotone delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.

Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith

A mathematical model of malaria dynamics with naturally acquired transient immunity in the presence of protected travellers is presented. The qualitative analysis carried out on the autonomous mode...

https://www.tandfonline.com/doi/pdf/10.1080/17513758.2020.1722265

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis.

Analysis of a co-infection model for HPV-TB

Abstract A deterministic mathematical model of the Middle East respiratory syndrome (MERS) disease is introduced. Medical masks, supportive care treatment and a government campaign about the importance of medical masks will be involved in the model as time dependent variables. The problem is formulated as an optimal control one to minimize the number of infected people and keep the intervention costs as low as possible. Assuming that all control variables are constant, we find a disease free equilibrium point and an endemic equilibrium point explicitly. The existence and local stability criteria of these equilibria depend on the basic reproduction number. A sensitivity analysis of the basic reproduction number with respect to control parameters tells us that the intervention on medical mask use and the campaign about the importance of medical masks are much more effective for reducing the basic reproduction number than supportive care intervention. Numerical experiments for optimal control problems are presented for three different scenarios, i.e., a scenario of different initial conditions for the human population, a scenario of different initial basic reproduction numbers and a scenario of different budget limitations. Under budget limitations, it is much better to implement the medical mask intervention in the field, rather than give supportive care to control the spread of the MERS disease in the endemic prevention scenario. On the other hand, the medical mask intervention should be implemented partially together with supportive care to obtain the lowest number of infected people, with the lowest cost in the endemic reduction scenario.

/pdf/analyzing-the-mers-disease-control-strategy-through-an-332kn0697k.pdf

Analyzing the MERS disease control strategy through an optimal control problem

A two-sex deterministic model for Human Papillomavirus (HPV) that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigorously analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection, when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional, and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e. condom use and vaccination of both males and females). Numerical simulations of the model showed that, based on the parameter values used therein, a vaccine (with 75% efficacy) for male population with about 40% condom compliance by females will result in a significant reduction in the disease burden in the population. Also, the numerical simulations of the model rev...

Mathematical analysis of a two-sex Human Papillomavirus (HPV) model

Analysis of Risk-Structured Vaccination Model for the Dynamics of Oncogenic and Warts-Causing HPV Types

A new deterministic model for the transmission dynamics of human papillomavirus (HPV) and related cancers, in the presence of the Gardasil vaccine (which targets four HPV types), is presented. In the absence of routine vaccination in the community, the model is shown to undergo the phenomenon of backward bifurcation. This phenomenon, which has important consequences on the feasibility of effective disease control in the community, arises due to the re-infection of recovered individuals. For the special case when backward bifurcation does not occur, the disease-free equilibrium (DFE) of the model is shown to be globally-asymptotically stable (GAS) if the associated reproduction number is less than unity. The model with vaccination is also rigorously analyzed. Numerical simulations of the model with vaccination show that, with the assumed 90% efficacy of the Gardasil vaccine, the effective community-wide control of the four Gardasil-preventable HPV types is feasible if the Gardasil coverage rate is high enough (in the range 78–88%).

Dynamics analysis of a vaccination model for hpv transmission

1 A two-group model for Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is de2 signed and used to assess the impact of quarantine of susceptible individuals and a hypothetical 3 anti-MERS-CoV vaccine on the transmission dynamics of MERS-CoV within the two groups. 4 The model undergoes a backward bifurcation, which is shown to arise due to the assumption 5 that the hypothetical vaccine offers incomplete protection against infection. The model can 6 have one or more endemic equilibria when the associated reproduction number exceeds unity. 7 Uncertainty and sensitivity analyses are carried out to determine the effect of uncertainties in 8 the parameter estimates of the model, as well as to determine the main parameters that drive 9 the disease transmission process. The model is re-formulated as an optimal control problem, 10 and the resulting model is used to evaluate the impact of various control strategies. Numerical 11 simulations of the optimal control model suggest that if the cost of implementing quarantine and 12 vaccination strategies are high, the two strategies can be administered optimally by using their 13 maximum feasible (coverage) levels for a relatively shorter period of time (i.e., “hit-hard and 14 hit-early”), and the coverage level then continuously decreased the next few days afterwards. 15 Furthermore, a universal strategy, based on the combined use of quarantine and vaccination 16 strategies, is shown to be more effective than the singular implementation of either the vaccina17 tion or quarantine strategy. 18

Aliya A. Alsaleh

Papers

Analysis of Risk-Structured Vaccination Model for the Dynamics of Oncogenic and Warts-Causing HPV Types

Dynamics analysis of a vaccination model for hpv transmission

Optimal strategies for controlling the MERS coronavirus during a mass gathering