SIAM Journal on Applied Mathematics, Volume 81, Issue 3, Page 1226-1247, January 2021.
Following the implantation of indwelling medical devices, bacteria inoculated during the surgery or coming from a preexistent focus of infection race for the medical surface where they attach. Adaptation to survive is a common feature of life, and microorganisms are not an exception. Bacteria form, in short periods of time, a habitat---the biofilm---where they develop multiresistance and tolerance to antibiotics and to the host immune system. To avoid its formation, researchers in the biomedical sciences showed evidence that coating medical devices with antibacterial agents---antibiotics---is a promising strategy. We present a mathematical model to simulate the action of an antibiotic, released from a medical surface, to fight bacterial infection. The model is composed by a system of partial differential equations that describe the distribution of drug and the evolution of a bacterial population. The preexistence of infection focus, the inoculation of bacteria during the surgery, the race for the medical surface, the resistance and tolerance of the population are taken into account. Analytical estimates of the bacterial density show the crucial importance of aseptic surgical procedures and of timely detection of preexisting infection focus. Numerical simulations illustrate several scenario.

中文翻译：

---

从挽救生命到威胁生命：模拟外科手术中细菌感染的数学模型

SIAM Journal on Applied Mathematics，第 81 卷，第 3 期，第 1226-1247 页，2021 年 1 月。
植入留置医疗设备后，细菌会在手术过程中接种或来自先前存在的感染焦点，以争夺它们附着的医疗表面。适应生存是生命的共同特征，微生物也不例外。细菌在短时间内形成栖息地——生物膜——在那里它们对抗生素和宿主免疫系统产生多重耐药性和耐受性。为了避免它的形成，生物医学科学的研究人员证明了用抗菌剂——抗生素——涂覆医疗设备是一种很有前途的策略。我们提出了一个数学模型来模拟从医疗表面释放的抗生素对抗细菌感染的作用。该模型由描述药物分布和细菌种群进化的偏微分方程系统组成。感染病灶的先存性，手术过程中细菌的接种，医疗表面的竞争，人群的抵抗力和耐受性都被考虑在内。细菌密度的分析估计表明无菌外科手术和及时检测先前存在的感染病灶至关重要。数值模拟说明了几种情况。细菌密度的分析估计表明无菌外科手术和及时检测先前存在的感染病灶至关重要。数值模拟说明了几种情况。细菌密度的分析估计表明无菌外科手术和及时检测先前存在的感染病灶至关重要。数值模拟说明了几种情况。