@article{Morales_Charles-Smith_Daniel_2017, title={Control and Cost-benefit Analysis of Fast Spreading Diseases: The case of Ebola}, volume={9}, url={https://ojphi.org/ojs/index.php/ojphi/article/view/7584}, DOI={10.5210/ojphi.v9i1.7584}, abstractNote={<div style="left: 90px; top: 320.758px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.11768);" data-canvas-width="82.63416666666666">Introduction</div><div style="left: 105px; top: 335.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0219);" data-canvas-width="379.3464999999998">Mitigating the spread of infectious disease is of great importance</div><div style="left: 90px; top: 352.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.980179);" data-canvas-width="392.8558333333332">for policy makers. Taking the recent outbreak of Ebola as an example,</div><div style="left: 90px; top: 369.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00392);" data-canvas-width="393.6024166666667">it was difficult for policy makers to identify the best course of action</div><div style="left: 90px; top: 385.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00165);" data-canvas-width="306.0708333333332">based on the cost-effectiveness of what was available.</div><div style="left: 105px; top: 402.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.964409);" data-canvas-width="377.8391666666664">In effort to address the needs of policy makers to mitigate the spread</div><div style="left: 90px; top: 419.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00785);" data-canvas-width="393.8517499999997">of infectious disease before an outbreak becomes uncontrollable, we</div><div style="left: 90px; top: 435.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.974329);" data-canvas-width="395.4313333333332">have devised a cost-benefit disease control model to simulate the</div><div style="left: 90px; top: 452.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03185);" data-canvas-width="394.47508333333326">effect of various control methods on disease incidence and the cost</div><div style="left: 90px; top: 469.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01903);" data-canvas-width="394.14499999999987">associated with each of the scenarios. Here, we present a case study</div><div style="left: 90px; top: 485.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04036);" data-canvas-width="394.4679999999999">of Ebola used to quantify the cost effectiveness of vaccination and</div><div style="left: 90px; top: 502.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.999494);" data-canvas-width="393.45083333333343">isolation methods to minimize the spread of the disease. We evaluate</div><div style="left: 90px; top: 519.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.994417);" data-canvas-width="393.3913333333333">the impact of changing strategy levels on the incidence of the disease</div><div style="left: 90px; top: 535.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00531);" data-canvas-width="393.66191666666674">and address the benefits of choosing one strategy over the other with</div><div style="left: 90px; top: 552.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00084);" data-canvas-width="224.6550000000001">regards to cost of vaccine and isolation.</div><div style="left: 90px; top: 584.091px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.07287);" data-canvas-width="58.23916666666666">Methods</div><div style="left: 105px; top: 599.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01809);" data-canvas-width="48.39333333333333">Disease.</div><div style="left: 153.393px; top: 599.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01783);" data-canvas-width="330.5735">We use a general SEIRJ model for disease transmission.</div><div style="left: 90px; top: 615.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.963764);" data-canvas-width="232.5883333333333">Here, S-Susceptible, E- Exposed (latent), I</div><div style="left: 322.698px; top: 625.434px; font-size: 8.5px; font-family: serif;">A</div><div style="left: 328.771px; top: 615.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.96082);" data-canvas-width="153.77916666666667">– Infected (asymptomatic),</div><div style="left: 90px; top: 632.376px; font-size: 14.1667px; font-family: serif;">I</div><div style="left: 94.8947px; top: 642.101px; font-size: 8.5px; font-family: serif;">M</div><div style="left: 102.559px; top: 632.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.993345);" data-canvas-width="189.53016666666673">– Infected (mild symptoms), I</div><div style="left: 292.052px; top: 642.101px; font-size: 8.5px; font-family: serif;">S</div><div style="left: 296.886px; top: 632.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.999548);" data-canvas-width="189.08108333333337">– Infected (severe symptoms),</div><div style="left: 90px; top: 649.043px; font-size: 14.1667px; font-family: serif;">J</div><div style="left: 95.773px; top: 658.767px; font-size: 8.5px; font-family: serif;">M</div><div style="left: 103.487px; top: 649.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03164);" data-canvas-width="253.6626666666667">– Isolated (mild symptoms at home), J</div><div style="left: 357.242px; top: 658.767px; font-size: 8.5px; font-family: serif;">S</div><div style="left: 362.125px; top: 649.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0309);" data-canvas-width="124.87633333333332">– Isolated (severe</div><div style="left: 90px; top: 665.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00875);" data-canvas-width="393.8673333333332">symptoms in hospital), and R- Recovered individuals. In this model,</div><div style="left: 90px; top: 682.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0049);" data-canvas-width="393.7030000000001">we consider the dynamics of the system and the effect of the relative</div><div style="left: 90px; top: 699.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.988776);" data-canvas-width="393.0385833333334">transmissibility of isolated individuals (L) compared to other infected</div><div style="left: 90px; top: 715.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00113);" data-canvas-width="62.970833333333324">individuals</div><div style="left: 152.962px; top: 716.084px; font-size: 8.5px; font-family: serif;">1</div><div style="left: 157.212px; top: 715.709px; font-size: 14.1667px; font-family: serif;">.</div><div style="left: 105px; top: 732.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02837);" data-canvas-width="30.302500000000002">Cost.</div><div style="left: 135.318px; top: 732.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.985542);" data-canvas-width="350.3274999999997">Ebola vaccination and treatment are very expensive and</div><div style="left: 90px; top: 749.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03136);" data-canvas-width="394.2356666666666">not widely available. Some preliminary data shows that it will take</div><div style="left: 90px; top: 765.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00857);" data-canvas-width="243.16658333333334">$73 million (M) to produce 27 M vaccines</div><div style="left: 333.132px; top: 766.084px; font-size: 8.5px; font-family: serif;">2</div><div style="left: 337.382px; top: 765.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01209);" data-canvas-width="146.46633333333332">plus the cost for vaccine</div><div style="left: 90px; top: 782.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.965239);" data-canvas-width="395.18483333333324">delivery and health care professionals (not included here). On the</div><div style="left: 90px; top: 799.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03621);" data-canvas-width="394.4">other hand, the treatment for Ebola in the U.S. would cost $25,000</div><div style="left: 90px; top: 815.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.993919);" data-canvas-width="134.42749999999998">dollars a day per person</div><div style="left: 224.415px; top: 816.084px; font-size: 8.5px; font-family: serif;">3</div><div style="left: 228.665px; top: 815.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.993645);" data-canvas-width="254.6713333333333">to ensure proper isolation and adequate care</div><div style="left: 90px; top: 832.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.975253);" data-canvas-width="392.96208333333334">(treatment, health care professionals, facilities and special equipment).</div><div style="left: 90px; top: 849.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01188);" data-canvas-width="393.95799999999997">Although not included in this research, the proper isolation of Ebola</div><div style="left: 90px; top: 865.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.949946);" data-canvas-width="394.92416666666696">patients would also lead to a loss in hospital revenue of $148,000</div><div style="left: 90px; top: 882.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03085);" data-canvas-width="228.57491666666658">per day due to reduced patient capacity</div><div style="left: 318.553px; top: 882.751px; font-size: 8.5px; font-family: serif;">3</div><div style="left: 322.825px; top: 882.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04078);" data-canvas-width="161.66858333333332">. Here, we use $27,000 per</div><div style="left: 90px; top: 899.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00082);" data-canvas-width="365.11749999999984">individual hospitalized per day and $2.70 per person vaccinated.</div><div style="left: 105px; top: 915.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.992063);" data-canvas-width="40.14549999999999">Model.</div><div style="left: 145.124px; top: 915.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04063);" data-canvas-width="339.4715833333333">To evaluate the cost-effectiveness of control methods on</div><div style="left: 90px; top: 932.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.974424);" data-canvas-width="395.3562499999999">disease transmission, we assessed the affect of different levels of</div><div style="left: 90px; top: 949.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.991982);" data-canvas-width="393.18874999999997">vaccination coverage on the resulting number of infected individuals.</div><div style="left: 90px; top: 965.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.966847);" data-canvas-width="395.03749999999997">Then, we calculated the overall estimated cost of vaccination and</div><div style="left: 90px; top: 982.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.997014);" data-canvas-width="390.01541666666657">resulting hospitalization for each scenario to identify the lowest cost-</div><div style="left: 90px; top: 999.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.012);" data-canvas-width="72.39166666666668">benefit ratio.</div><div style="left: 90px; top: 1030.76px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.08488);" data-canvas-width="51.17">Results</div><div style="left: 105px; top: 1045.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00414);" data-canvas-width="378.67925">Using a base population of 10 M individuals, we ran scenarios for</div><div style="left: 90px; top: 1062.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00198);" data-canvas-width="177.83558333333335">different levels of vaccination (</div><div style="left: 267.832px; top: 1065.07px; font-size: 14.1667px; font-family: sans-serif;">μ</div><div style="left: 275.995px; top: 1062.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0012);" data-canvas-width="207.58133333333333">= 0.01, 0.05, 0.1) while varying the</div><div style="left: 90px; top: 1079.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03663);" data-canvas-width="394.6436666666667">relative transmissibility of isolated individuals (L = 0.5, 0.6, 0.65).</div><div style="left: 90px; top: 1095.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0207);" data-canvas-width="394.4141666666666">For each combination, we calculated the incidence, vaccination and</div><div style="left: 90px; top: 1112.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04079);" data-canvas-width="394.5643333333332">hospitalization cost per individual per day (Fig 1). We note that an</div><div style="left: 90px; top: 1129.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.985159);" data-canvas-width="392.76658333333324">increase in the relative transmissibility of isolated individuals leads to</div><div style="left: 90px; top: 1145.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00211);" data-canvas-width="393.6123333333335">a higher number of infected people and, therefore, a reduced number</div><div style="left: 90px; top: 1162.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.979563);" data-canvas-width="393.1802500000001">of candidates for vaccination and an overall increase in cost. Since the</div><div style="left: 90px; top: 1179.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00986);" data-canvas-width="393.89425000000006">cost of vaccination is 1 ten-thousandth of the cost of hospitalization,</div><div style="left: 90px; top: 1195.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00968);" data-canvas-width="393.8418333333332">our results clearly show the cost-benefit of vaccinating over hospital</div><div style="left: 90px; top: 1212.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00583);" data-canvas-width="396.33091666666655">treatment. In every scenario studied, we observed a measurable</div><div style="left: 510px; top: 319.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01228);" data-canvas-width="393.9962500000001">reduction in disease incidence when vaccinating a higher fraction of</div><div style="left: 510px; top: 335.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00065);" data-canvas-width="358.88416666666643">the population compared to isolating individuals post infection.</div><div style="left: 510px; top: 367.425px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.10336);" data-canvas-width="85.01416666666667">Conclusions</div><div style="left: 525px; top: 382.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01131);" data-canvas-width="378.9555">Given these preliminary results, we plan to extend the framework</div><div style="left: 510px; top: 399.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.991326);" data-canvas-width="393.29216666666673">of our model to a dynamic control system where we consider the cost</div><div style="left: 510px; top: 415.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03213);" data-canvas-width="394.2385">of vaccination and isolation embedded in the system of differential</div><div style="left: 510px; top: 432.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04279);" data-canvas-width="397.35516666666626">equations. This approach will allow us see the best available</div><div style="left: 510px; top: 449.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02888);" data-canvas-width="394.4566666666665">control implementation while minimizing the cost of treatment and</div><div style="left: 510px; top: 465.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00097);" data-canvas-width="68.84999999999998">vaccination.</div><div style="left: 510px; top: 753.625px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.08992);" data-canvas-width="67.70249999999999">Keywords</div><div style="left: 510px; top: 768.576px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01626);" data-canvas-width="394.2073333333334">Control; Epidemiological Modeling; Transmission Dynamics; Cost;</div><div style="left: 510px; top: 785.243px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00108);" data-canvas-width="47.217499999999994">EBOLA</div><div style="left: 510px; top: 816.958px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.0556);" data-canvas-width="76.3725">References</div><div style="left: 510px; top: 840.985px; font-size: 13.3333px; font-family: serif; transform: scaleX(0.998064);" data-canvas-width="393.27066666666667">1. 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