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F A Milner

Publications and source records attributed to F A Milner.

7 recordsLinked to original sources
PubMed1999

Periodic solutions: a robust numerical method for an S-I-R model of epidemics.

We describe and analyze a numerical method for an S-I-R type epidemic model. We prove that it is unconditionally convergent and that solutions it produces share many qualitative and quantitative properties of the solution of the differential problem being approximated. Finally, we establish explicit sufficient conditions for the unique endemic steady state of the system to be unstable and we use our numerical algorithm to approximate the solution in such cases and discover that it can be periodic, just as suggested by the instability of the endemic steady state.

Acquired Immunodeficiency Syndrome↗
PubMed1998

Existence and uniqueness of endemic states for the age-structured S-I-R epidemic model.

The existence and uniqueness of positive steady states for the age structured S-I-R epidemic model with intercohort transmission is considered. Threshold results for the existence of endemic states are established for most cases. Uniqueness is shown in each case. Threshold used are explicitly computable in terms of demographic and epidemiological parameters of the model.

Age Factors↗
PubMed1997

The HIV/AIDS epidemics among drug injectors: a study of contact structure through a mathematical model.

Numerical results of a model with variable infectivity for the dynamics of HIV/AIDS (human immunodeficiency virus/acquired immune deficiency syndrome) have been compared with the data of AIDS cases among intravenous drug users in Italy, especially in the Latium region. We examined several hypotheses about the dynamics of the epidemics; for each we obtained, mainly through a least-square approach but also minimizing a different quantity, a best-fit estimate of the parameters. In the simplest model, the population is assumed to be homogeneous, and we estimate contact rate and year of start of the epidemics, obtaining a good fit up to 1989, less so after. A substantial increase in fit is obtained in assuming either a decrease of the contact rate over time or a heterogeneous population with a smaller active group. We have also compared models with different infectivity curves during the incubation period: the assumption of constant infectivity is untenable, whereas the often suggested hypothesis of a peak in infectivity shortly after infection seems to be in agreement with data.

Acquired Immunodeficiency Syndrome↗
PubMed1992

Rapidly converging numerical algorithms for models of population dynamics.

We propose algorithms for the approximation of the age distributions of populations modeled by the McKendrick-von Foerster and the Gurtin-MacCamy systems both in one- and two-sex versions. For the one-sex model methods of second and fourth order are proposed. For the two-sex model a second order method is described. In each case the convergence is demonstrated. Several numerical examples are given.

Age Factors↗