Modeling Mayaro and Chikungunya Control Strategies in Rio de Janeiro Outbreaks

Mosquito-borne diseases have become a significant health issue in many regions around the world. For tropical countries, diseases such as Dengue, Zika, and Chikungunya, became epidemic in the last decades. Health surveillance reports during this period were crucial in providing scientific-based information to guide decision making and resources allocation to control outbreaks. In this work, we perform data analysis of last Chikungunya epidemics in the city of Rio de Janeiro by applying a compartmental mathematical model. We estimate the “basic reproduction number” for those outbreaks and predict the potential epidemic outbreak of Mayaro virus. We also simulated several scenarios with different public interventions to decrease the number of infected people. Such scenarios should provide insights about possible strategies to control future outbreaks.

Introduction the literature or obtained from the best fit from the data of Rio de Janeiro surveillance 22 report for the years of 2016, 2018 and 2019 [12]. Based on these parameters, we estimate 23 the basic reproduction number R o for Chikungunya outbreaks in those years. We also 24 simulate a scenario predicting if the Mayaro virus could be a potential epidemic disease 25 in Rio de Janeiro. Modifications in the standard model equations were implemented to 26 introduce different possible interventions in order to decrease the number of infected 27 people [13]. Those simulated interventions include actions such as killing adult 28 mosquitoes by fogging, decreasing mosquitoes birth rate by removing places where the 29 vector lays eggs, e.g., removing standing water and, decreasing the contact between an 30 infected human with mosquitoes by stimulating repellent usage. A scenario containing 31 September 5, 2019 3/19 all interventions was also performed for different intensities of those actions.
Materials and methods 33 In this work, we perform mathematical modeling of Chikungunya outbreaks in Rio de 34 Janeiro for the years 2016, 2017 and 2019 [12]. The Chikungunya virus infects humans 35 through mosquitoes as the disease vector. The model adopted here is a compartmental 36 model known as SEIR (Susceptible, Exposed, Infected, and Recovered) [8,10,14]. The 37 approaches using this class of models have been successful in modeling epidemic related 38 to human vector dynamics [11,15].   Table 1 and 2. The dashed lines represent the transmission of the disease between the two groups.
become infectious: either symptomatically I or asymptomatically I a ; the parameter φ 44 determines the ratio between the infectious states. Finally, the infected humans recover 45 reaching the state R at rate α.

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In the case of the vectors disease flow, shown by the red blocks in Fig 1, the susceptible mosquitoes X become exposed Y at a rate β m after acquiring the virus from 48 infectious humans. λ v defines the latent period for the exposed mosquito to transition 49 to the infectious state Z. In this modeling, we assume that human mortality and birth 50 rates are the same, keeping the human population constant. For the vectors, we set the 51 parameter µ and µ o as the mortality and birth rate, respectively. The model is 52 represented by the following set of differential equations: Table 1 shows the definition of each state in the model for both humans and 54 mosquitoes. Those states will dynamically vary during the model simulation in which 55 the parameter I related to the number of cases reported by the surveillance data will be 56 the variable used in the fitting of the model simulation.  [16,20] In this work we estimate the basic reproduction number R o by applying the next 61 generation matrix method [21,22]. R o indicates the number of secondary infections 62 derived from one single infectious subject and can be described by: Where ρ(K) is the spectral radius of the matrix K = ΠΓ −1 . Π is the transmission 64 matrix that contains the rates of humans to get infected by the vector and vice-versa: Γ is the transition matrix that takes into account the transitions from being exposed 66 to become infectious: The mathematical solution of (1) gives an expression [11]: The Eq 4 has parameters in which there is no information available such as β h and 69 β m . In order to estimate R o , these parameters will be obtained from the best fit of the 70 model simulations using data from the surveillance reports [12].

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The usage of the SEIR model to investigate diseases epidemics provides a tool to by an infected individual [3,23]. It estimates the potential of an outbreak to occur in 76 the case of R o > 1 [10,24]. The knowledge of R o also gives insights into the 77 understanding of the epidemiology of a particular disease and its spreading changes over 78 time and geography [25].

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The number of secondary infections in humans from an infected human, defined as 80 R T , the type reproduction number [26], can be obtained by R o squared [11]. The information of R T can be used to estimate the number of people 82 that need to be isolated or vaccinated (Q) to contain the epidemic using the relation  Table 3. Table 3 also shows in the last row, the estimation of R o using Eq 104 (4) for each investigated year. be at different neighborhoods [7,25,29,30]. The last column in Table 3  1, suggesting that Mayaro has the potential to be an epidemic disease as recent reports 120 are signaling for different locations [37][38][39].

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Interventions 122 In this section, we will discuss the outcome of different possible intervention strategies 123 to control the epidemic disease spreading [13,23]. The simulations were carried out using the Chikungunya epidemic outbreak data from Rio de Janeiro in 2018. The first 125 approach simulates the action of killing adult mosquitoes, which is related to the use of 126 insecticide as fogging. In the model, this strategy appears as an increase in the 127 mosquitoes mortality rate µ presented in Eq 5: where θ(...) is the unitary step function, µ c is the natural rate of birth/death of the 129 mosquito, C is the cumulative number of infected people and, ω is the parameter 130 related to the intensity of the fogging action reflected in the mosquito death rate µ. The 131 fogging action is triggered when the cumulative number of infected people C, described 132 in Eq 6, reaches the value C p which is 30% of the total number of cases from the real 133 data. For all the interventions discussed in this study, the trigger event will be the same 134 as the one present here in the fogging action.    The third and the last studied intervention acts as the reduction of the rate in which 167 infected humans transmit the disease to the mosquitoes. This effect can be associated 168 as a quarantine action, isolating infected people or, more realistic, the usage of