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Cabrera, M.; Cordova-Lepe, F.; Gutierrez-Jara, J.P-; Vogt-Geisse, K. |
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An SIR-type epidemiological model that integrates social distancing as a dynamic law based on point prevalence and socio-behavioral factors |
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2021 |
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Scientific Reports |
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Sci. Rep. |
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11 |
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1 |
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10170 |
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EFFECTIVE REPRODUCTION NUMBER; INFECTIOUS-DISEASE; TRANSMISSION; COVID-19; BEHAVIOR; CHALLENGES; AWARENESS; IMPACT; RISK |
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Modeling human behavior within mathematical models of infectious diseases is a key component to understand and control disease spread. We present a mathematical compartmental model of Susceptible-Infectious-Removed to compare the infected curves given by four different functional forms describing the transmission rate. These depend on the distance that individuals keep on average to others in their daily lives. We assume that this distance varies according to the balance between two opposite thrives: the self-protecting reaction of individuals upon the presence of disease to increase social distancing and their necessity to return to a culturally dependent natural social distance that occurs in the absence of disease. We present simulations to compare results for different society types on point prevalence, the peak size of a first epidemic outbreak and the time of occurrence of that peak, for four different transmission rate functional forms and parameters of interest related to distancing behavior, such as: the reaction velocity of a society to change social distance during an epidemic. We observe the vulnerability to disease spread of close contact societies, and also show that certain social distancing behavior may provoke a small peak of a first epidemic outbreak, but at the expense of it occurring early after the epidemic onset, observing differences in this regard between society types. We also discuss the appearance of temporal oscillations of the four different transmission rates, their differences, and how this oscillatory behavior is impacted through social distancing; breaking the unimodality of the actives-curve produced by the classical SIR-model. |
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2045-2322 |
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WOS:000656941100009 |
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UAI @ alexi.delcanto @ |
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1417 |
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Cordova-Lepe, F.; Vogt-Geisse, K. |
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Adding a reaction-restoration type transmission rate dynamic-law to the basic SEIR COVID-19 model |
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2022 |
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Plos One |
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PLos One |
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17 |
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6 |
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e0269843 |
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The classical SEIR model, being an autonomous system of differential equations, has important limitations when representing a pandemic situation. Particularly, the geometric unimodal shape of the epidemic curve is not what is generally observed. This work introduces the beta SEIR model, which adds to the classical SEIR model a differential law to model the variation in the transmission rate. It considers two opposite thrives generally found in a population: first, reaction to disease presence that may be linked to mitigation strategies, which tends to decrease transmission, and second, the urge to return to normal conditions that pulls to restore the initial value of the transmission rate. Our results open a wide spectrum of dynamic variabilities in the curve of new infected, which are justified by reaction and restoration thrives that affect disease transmission over time. Some of these dynamics have been observed in the existing COVID-19 disease data. In particular and to further exemplify the potential of the model proposed in this article, we show its capability of capturing the evolution of the number of new confirmed cases of Chile and Italy for several months after epidemic onset, while incorporating a reaction to disease presence with decreasing adherence to mitigation strategies, as well as a seasonal effect on the restoration of the initial transmissibility conditions. |
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1932-6203 |
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WOS:000843613300089 |
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UAI @ alexi.delcanto @ |
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1629 |
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Gutierrez-Jara, J.P.; Vogt-Geisse, K.; Cabrera, M. |
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Title |
Collateral Effects of Insecticide-Treated Nets on Human and Environmental Safety in an Epidemiological Model for Malaria with Human Risk Perception |
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2022 |
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International Journal of Environmental Research and Public Health |
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Int. J. Environ. Res. Public Health |
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19 |
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23 |
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16327 |
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mathematical epidemiology; malaria; insecticide-treated nets; insecticide exposure; risk perception; ecosystem damage; mosquito net fishing; impulsive differential equations |
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Malaria remains a major health problem in many parts of the world, including Sub-Saharan Africa. Insecticide-treated nets, in combination with other control measures, have been effective in reducing malaria incidence over the past two decades. Nevertheless, there are concerns about improper handling and misuse of nets, producing possible health effects from intoxication and collateral environmental damage. The latter is caused, for instance, from artisanal fishing. We formulate a model of impulsive differential equations to describe the interplay between malaria dynamics, human intoxication, and ecosystem damage; affected by human awareness to these risks and levels of net usage. Our results show that an increase in mosquito net coverage reduces malaria prevalence and increases human intoxications. In addition, a high net coverage significantly reduces the risk perception to disease, naturally increases the awareness for intoxications from net handling, and scarcely increases the risk perception to collateral damage from net fishing. According to our model, campaigns aiming at reducing disease prevalence or intoxications are much more successful than those creating awareness to ecosystem damage. Furthermore, we can observe from our results that introducing closed fishing periods reduces environmental damage more significantly than strategies directed towards increasing the risk perception for net fishing. |
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1660-4601 |
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WOS:000897264200001 |
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UAI @ alexi.delcanto @ |
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1695 |
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Gutierrez-Jara, J.P.; Vogt-Geisse, K.; Cabrera, M.; Cordova-Lepe, F.; Munoz-Quezada, M.T. |
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Effects of human mobility and behavior on disease transmission in a COVID-19 mathematical model |
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2022 |
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Scientific Reports |
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Sci. Rep. |
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12 |
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1 |
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10840 |
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INFECTIOUS-DISEASE; EPIDEMIC MODEL; DYNAMICS; CHALLENGES; RESISTANCE; DISTANCES; AWARENESS |
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Human interactions and perceptions about health risk are essential to understand the evolution over the course of a pandemic. We present a Susceptible-Exposed-Asymptomatic-Infectious-Recovered-Susceptible mathematical model with quarantine and social-distance-dependent transmission rates, to study COVID-19 dynamics. Human activities are split across different location settings: home, work, school, and elsewhere. Individuals move from home to the other locations at rates dependent on their epidemiological conditions and maintain a social distancing behavior, which varies with their location. We perform simulations and analyze how distinct social behaviors and restrictive measures affect the dynamic of the disease within a population. The model proposed in this study revealed that the main focus on the transmission of COVID-19 is attributed to the “home” location setting, which is understood as family gatherings including relatives and close friends. Limiting encounters at work, school and other locations will only be effective if COVID-19 restrictions occur simultaneously at all those locations and/or contact tracing or social distancing measures are effectively and strictly implemented, especially at the home setting. |
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2045-2322 |
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WOS:000818980100021 |
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UAI @ alexi.delcanto @ |
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1594 |
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Gutiérrez-Jara, J.P.; Vogt-Geisse, K.; Correa, M.C.G.; Vilches-Ponce, K.; Pérez, L.M.; Chowell, G. |
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Alert Results Modeling the Impact of Agricultural Mitigation Measures on the Spread of Sharka Disease in Sweet Cherry Orchards 26 of 41 Modeling the Impact of Agricultural Mitigation Measures on the Spread of Sharka Disease in Sweet Cherry Orchards |
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2023 |
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Plants-Basel |
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Plants-Basel |
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12 |
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19 |
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3442 |
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plum pox virus; aphids; mathematical modeling; agricultural management |
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Sharka is a disease affecting stone fruit trees. It is caused by the Plum pox virus (PPV), with Myzus persicae being one of the most efficient aphid species in transmitting it within and among Prunus orchards. Other agricultural management strategies are also responsible for the spread of disease among trees, such as grafting and pruning. We present a mathematical model of impulsive differential equations to represent the dynamics of Sharka disease in the tree and vector population. We consider three transmission routes: grafting, pruning, and through aphid vectors. Grafting, pruning, and vector control occur as pulses at specific instants. Within the model, human risk perception towards disease influences these agricultural management strategies. Model results show that grafting with infected biological material has a significant impact on the spread of the disease. In addition, detecting infectious symptomatic and asymptomatic trees in the short term is critical to reduce disease spread. Furthermore, vector control to prevent aphid movement between trees is crucial for disease mitigation, as well as implementing awareness campaigns for Sharka disease in agricultural communities that provide a long-term impact on responsible pruning, grafting, and vector control. |
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2223-7747 |
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WOS:001083391000001 |
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UAI @ alexi.delcanto @ |
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1896 |
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Kapitanov, G.; Alvey, C.; Vogt-Geisse, K.; Feng, Z.L. |
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An Age-Structured Model For The Coupled Dynamics Of Hiv And Hsv-2 |
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2015 |
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Mathematical Biosciences And Engineering |
Abbreviated Journal |
Math. Biosci. Eng. |
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12 |
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4 |
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803-840 |
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HIV; HSV-2; mathematical epidemiology; co-infection; population dynamics; basic reproduction number; invasion reproduction number; partial differential equations; sensitivity analysis; age-structure; sexually transmitted diseases |
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Evidence suggests a strong correlation between the prevalence of HSV-2 (genital herpes) and the perseverance of the HIV epidemic. HSV-2 is an incurable viral infection, characterized by periodic reactivation. We construct a model of the co-infection dynamics between the two diseases by incorporating a time-since-infection variable to track the alternating periods of infectiousness of HSV-2. The model considers only heterosexual relationships and distinguishes three population groups: males, general population females, and female sex workers. We calculate the basic reproduction numbers for each disease that provide threshold conditions, which determine whether a disease dies out or becomes endemic in the absence of the other disease. We also derive the invasion reproduction numbers that determine whether or not a disease can invade into a population in which the other disease is endemic. The calculations of the invasion reproduction numbers suggest a new aspect in their interpretation – the class from which the initial disease carrier arises is important for understanding the invasion dynamics and biological interpretation of the expressions of the reproduction numbers. Sensitivity analysis is conducted to examine the role of model parameters in influencing the model outcomes. The results are discussed in the last section. |
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[Kapitanov, Georgi; Alvey, Christina; Vogt-Geisse, Katia; Feng, Zhilan] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA, Email: georgi.i.kapitanov@grnail.com; |
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Amer Inst Mathematical Sciences |
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1547-1063 |
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WOS:000354138400012 |
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UAI @ eduardo.moreno @ |
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488 |
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Soto, P.C.; Cartes, C.; Davies, T.P.; Olivari, J.; Rica, S.; Vogt-Geisse, K. |
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The anatomy of the 2019 Chilean social unrest |
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2020 |
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Chaos |
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Chaos |
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30 |
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7 |
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14 pp |
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We analyze the 2019 Chilean social unrest episode, consisting of a sequence of events, through the lens of an epidemic-like model that considers global contagious dynamics. We adjust the parameters to the Chilean social unrest aggregated public data available from the Undersecretary of Human Rights and observe that the number of violent events follows a well-defined pattern already observed in various public disorder episodes in other countries since the 1960s. Although the epidemic-like models display a single event that reaches a peak followed by an exponential decay, we add standard perturbation schemes that may produce a rich temporal behavior as observed in the 2019 Chilean social turmoil. Although we only have access to aggregated data, we are still able to fit it to our model quite well, providing interesting insights on social unrest dynamics. |
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[Soto, Pauline Caroca; Olivari, Jocelyn; Rica, Sergio; Vogt-Geisse, Katia] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Avda Diagonal Torres 2640, Santiago, Chile, Email: jocelyn.olivari@uai.cl |
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Amer Inst Physics |
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1054-1500 |
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WOS:000554870700001 |
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UAI @ eduardo.moreno @ |
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1214 |
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Tariq, A.; Undurraga, EA.; Laborde, CC.; Vogt-Geisse, K.; Luo, RY.; Rothenberg, R.; Chowell, G. |
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Transmission dynamics and control of COVID-19 in Chile, March-October, 2020 |
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2021 |
Publication |
Plos Neglected Tropical Diseases |
Abbreviated Journal |
PLOS Negl. Trop. Dis. |
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15 |
Issue |
1 |
Pages |
e0009070 |
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EPIDEMIC; CHARACTERIZE; GROWTH |
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ince the detection of the first case of COVID-19 in Chile on March 3(rd), 2020, a total of 513,188 cases, including similar to 14,302 deaths have been reported in Chile as of November 2(nd), 2020. Here, we estimate the reproduction number throughout the epidemic in Chile and study the effectiveness of control interventions especially the effectiveness of lockdowns by conducting short-term forecasts based on the early transmission dynamics of COVID-19. Chile's incidence curve displays early sub-exponential growth dynamics with the deceleration of growth parameter, p, estimated at 0.8 (95% CI: 0.7, 0.8) and the reproduction number, R, estimated at 1.8 (95% CI: 1.6, 1.9). Our findings indicate that the control measures at the start of the epidemic significantly slowed down the spread of the virus. However, the relaxation of restrictions and spread of the virus in low-income neighborhoods in May led to a new surge of infections, followed by the reimposition of lockdowns in Greater Santiago and other municipalities. These measures have decelerated the virus spread with R estimated at similar to 0.96 (95% CI: 0.95, 0.98) as of November 2(nd), 2020. The early sub-exponential growth trend (p similar to 0.8) of the COVID-19 epidemic transformed into a linear growth trend (p similar to 0.5) as of July 7(th), 2020, after the reimposition of lockdowns. While the broad scale social distancing interventions have slowed the virus spread, the number of new COVID-19 cases continue to accrue, underscoring the need for persistent social distancing and active case detection and isolation efforts to maintain the epidemic under control.
Author summary
In context of the ongoing COVID-19 pandemic, Chile has been one of the hardest-hit countries in Latin America, struggling to contain the spread of the virus. In this manuscript, we employ renewal equation to estimate the reproduction number (R) for the early ascending phase of the COVID-19 epidemic and by July 7(th), 2020 to guide the magnitude and intensity of interventions required to combat the COVID-19 epidemic. We also estimate the instantaneous reproduction number throughout the epidemic in Chile. Moreover, we generate short-term forecasts based on the epidemic trajectory using phenomenological models, and assess counterfactual scenarios to understand any additional resources required to contain the virus' spread. Our results indicate early sustained transmission of SARS-CoV-2. However, the initial control measures at the start of the epidemic significantly slowed down the spread of the virus. The easing of COVID-19 restrictions in April led to a new wave of infections, followed by the re-imposition of lockdowns in Greater Santiago and several municipalities. Most recent estimates of reproduction number indicate a decline in the virus transmission. While broad-scale social distancing interventions have slowed the virus spread, the number of new COVID-19 cases continue to accrue, underscoring the need for persistent social distancing efforts. |
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1935-2735 |
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WOS:000612932700004 |
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UAI @ alexi.delcanto @ |
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1345 |
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Vogt-Geisse, K.; Lorenzo, C.; Feng, Z.L. |
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Title |
Impact Of Age-Dependent Relapse And Immunity On Malaria Dynamics |
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2013 |
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Journal Of Biological Systems |
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J. Biol. Syst. |
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21 |
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4 |
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49 pp |
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Malaria; Endemic Model; Age-structure; Reproductive Number; Uncertainty and Sensitivity Analysis |
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An age-structured mathematical model for malaria is presented. The model explicitly includes the human and mosquito populations, structured by chronological age of humans. The infected human population is divided into symptomatic infectious, asymptomatic infectious and asymptomatic chronic infected individuals. The original partial differential equation (PDE) model is reduced to an ordinary differential equation (ODE) model with multiple age groups coupled by aging. The basic reproduction number R-0 is derived for the PDE model and the age group model in the case of general n age groups. We assume that infectiousness of chronic infected individuals gets triggered by bites of even susceptible mosquitoes. Our analysis points out that this assumption contributes greatly to the R0 expression and therefore needs to be further studied and understood. Numerical simulations for n = 2 age groups and a sensitivity/uncertainty analysis are presented. Results suggest that it is important not only to consider asymptomatic infectious individuals as a hidden cause for malaria transmission, but also asymptomatic chronic infections (>60%), which often get neglected due to undetectable parasite loads. These individuals represent an important reservoir for future human infectiousness. By considering age-dependent immunity types, the model helps generate insight into effective control measures, by targeting age groups in an optimal way. |
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[Vogt-Geisse, Katia; Lorenzo, Christina; Feng, Zhilan] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA, Email: kvogtgei@math.purdue.edu; |
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World Scientific Publ Co Pte Ltd |
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0218-3390 |
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WOS:000331243400002 |
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UAI @ eduardo.moreno @ |
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351 |
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Vogt-Geisse, K.; Ngonghala, C.N.; Feng, Z.L. |
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The Impact Of Vaccination On Malaria Prevalence: A Vaccine-Age-Structured Modeling Approach |
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2020 |
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Journal Of Biological Systems |
Abbreviated Journal |
J. Biol. Syst. |
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28 |
Issue |
2 |
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475-513 |
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Control Reproduction Number; Vaccine-age Structure; Vector-borne Disease; Backward Bifurcation; Partial Differential Equations; Vaccination Model |
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A deterministic model for the effects on disease prevalence of the most advanced preerythrocytic vaccine against malaria is proposed and studied. The model includes two vaccinated classes that correspond to initially vaccinated and booster dose vaccinated individuals. These two classes are structured by time-since-initial-vaccination (vaccine-age). This structure is a novelty for vector-host models; it allows us to explore the effects of parameters that describe timed and delayed delivery of a booster dose, and immunity waning on disease prevalence. Incorporating two vaccinated classes can predict more accurately threshold vaccination coverages for disease eradication under multi-dose vaccination programs. We derive a vaccine-age-structured control reproduction number R and establish conditions for the existence and stability of equilibria to the system. The model is bistable when R < 1. In particular, it exhibits a backward (sub-critical) bifurcation, indicating that R = 1 is no longer the threshold value for disease eradication. Thus, to achieve eradication we must identify and implement control measures that will reduce R to a value smaller than unity. Therefore, it is crucial to be cautious when using R to guide public health policy, although it remains a key quantity for decision making. Our results show that if the booster vaccine dose is administered with delay, individuals may not acquire its full protective effect, and that incorporating waning efficacy into the system improves the accuracy of the model outcomes. This study suggests that it is critical to follow vaccination schedules closely, and anticipate the consequences of delays in those schedules. |
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[Vogt-Geisse, Katia] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Diagonal Las Torres 2640, Santiago 791169, Chile, Email: katia.vogt@uai.cl; |
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World Scientific Publ Co Pte Ltd |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0218-3390 |
ISBN |
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Medium |
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Expedition |
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Conference |
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Notes |
WOS:000566337000010 |
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Call Number |
UAI @ alexi.delcanto @ |
Serial |
1252 |
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