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Author |
Kapitanov, G.; Alvey, C.; Vogt-Geisse, K.; Feng, Z.L. |
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Title |
An Age-Structured Model For The Coupled Dynamics Of Hiv And Hsv-2 |
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Year |
2015 |
Publication |
Mathematical Biosciences And Engineering |
Abbreviated Journal |
Math. Biosci. Eng. |
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Volume |
12 |
Issue |
4 |
Pages |
803-840 |
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Keywords |
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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Abstract |
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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Address |
[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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English |
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1547-1063 |
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WOS:000354138400012 |
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UAI @ eduardo.moreno @ |
Serial |
488 |
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Author |
Towers, S.; Vogt Geisse, K.; Chia-Chun, T.; Han, Q.; Feng, Z.L. |
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Title |
The Impact Of School Closures On Pandemic Influenza: Assessing Potential Repercussions Using A Seasonal Sir Model |
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Year |
2012 |
Publication |
Mathematical Biosciences And Engineering |
Abbreviated Journal |
Math. Biosci. Eng. |
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Volume |
9 |
Issue |
2 |
Pages |
413-430 |
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Keywords |
Pandemic influenza; epidemic model; dynamic systems |
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Abstract |
When a new pandemic influenza strain has been identified, mass-production of vaccines can take several months, and antiviral drugs are expensive and usually in short supply. Social distancing measures, such as school closures, thus seem an attractive means to mitigate disease spread. However, the transmission of influenza is seasonal in nature, and as has been noted in previous studies, a decrease in the average transmission rate in a seasonal disease model may result in a larger final size. In the studies presented here, we analyze a hypothetical pandemic using a SIR epidemic model with time- and age-dependent transmission rates; using this model we assess and quantify, for the first time, the the effect of the timing and length of widespread school closures on influenza pandemic final size and average peak time. We find that the effect on pandemic progression strongly depends on the timing of the start of the school closure. For instance, we determine that school closures during a late spring wave of an epidemic can cause a pandemic to become up to 20% larger, but have the advantage that the average time of the peak is shifted by up to two months, possibly allowing enough time for development of vaccines to mitigate the larger size of the epidemic. Our studies thus suggest that when heterogeneity in transmission is a significant factor, decisions of public health policy will be particularly important as to how control measures such as school closures should be implemented. |
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Address |
[Towers, Sherry; Geisse, Katia Vogt; Chia-Chun, Tsai; Han, Qing; Feng, Zhilan] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA, Email: stowers@purdue.edu |
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Publisher |
Amer Inst Mathematical Sciences |
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English |
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1547-1063 |
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Notes |
WOS:000301177600010 |
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Call Number |
UAI @ eduardo.moreno @ |
Serial |
198 |
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